Jean-Philippe Torre

Heinz Gornitzka

Romuald Coupan

Christophe Dicharry

Martín Peŕez-Rodríguez

Antonio Comesanã

Manuel M Pinẽiro

Insights into the Crystal Structure and Clathration Selectivity of Organic Clathrates Formed with Hydroquinone and (CO 2 + CH 4 ) Gas Mixtures

Organic clathrates, particularly those formed by hydroquinone (HQ) and gas mixtures, have been far less studied than other inclusion compounds, such as gas hydrates. In this study, experiments and molecular dynamics simulations were performed on mixed (CO 2 + CH 4 )-HQ clathrates. Single crystals were synthesized using gas mixtures with different compositions, ranging from pure CO 2 to pure CH 4 . The crystal structure, the guest occupancy in the clathrates, and the variation of the crystal lattice parameters according to clathrate composition were obtained by X-ray diffraction measurements. In addition, molecular dynamics simulations were performed on the same systems, with state-of-the-art molecular models and force fields. The experimental results obtained and the molecular dynamics simulation estimations were in good agreement. The clathration selectivity was also calculated on the basis of experimental results, and the composition of the solid phase was correlated with the composition of the gas phase at equilibrium. These new insights into these structures will be useful from both a fundamental and a practical point of view, particularly for further developing innovative gas separation techniques using HQ clathrates.

■ INTRODUCTION

The term "clathrate" refers to a solid-state supramolecular entity composed of a network of self-associating molecules (called hosts) forming cavities or channels in which other species (called guests) can be encaged. [START_REF] Steed | Core Concepts in Supramolecular Chemistry and Nanochemistry[END_REF] These host-guest complexes crystallize if the size of the cavities is compatible with the size and shape of the guests, but only under specific thermodynamic (i.e., temperature and pressure) conditions, and they are generally unstable if the cavities do not contain a certain fraction of guest molecules. Clathrate hydrates (usually known as gas hydrates or simply hydrates) represent the most studied category of clathrate compounds, 2 particularly natural gas hydrates that have been known for their propensity to plug the flowlines used in oil and gas transportation. [START_REF] Hammerschmidt | Formation of Gas Hydrates in Natural Gas Transmission Lines[END_REF] Clathrates whose framework is entirely made up of organic molecules are called organic clathrates. These compounds, particularly those formed with hydroquinone (HQ), have been far less studied than the well-known gas hydrates.

Hydroquinone (1,4 dihydroxybenzene, formerly referred to as quinol) is able to form organic clathrates by encaging gaseous guest molecules such as methane (CH 4 ), carbon dioxide (CO 2 ), sulfur dioxide (SO 2 ), hydrogen sulfide (H 2 S) among others. [START_REF] Atwood | Structural Aspects of Inclusion Compounds formed by Organic Host lattices[END_REF] The general formula of HQ clathrates is χG-3C 6 H 4 (OH) 2 , where G stands for the encaged guest species and χ is the occupancy factor (i.e., the fraction of cavities that are occupied). Note that the value of χ might theoretically vary from 0 for a guest-free clathrate (if all of the cavities are empty) to 1 (if all of the cavities are fully occupied).

HQ clathrates (denoted by β-HQ), discovered more than 150 years ago [START_REF] Woḧler | Ueber einige Verbindungen aus der Chinonreihe[END_REF] and considered for ages as just a fascinating scientific oddity, actually have very interesting properties: (i) these crystals can store large quantities of gases; [START_REF] Coupan | Kinetics of CO 2 Capture by Hydroquinone Clathrates[END_REF] (ii) can release (or absorb) energy when the guests enter (or exit) the clathrate structure; [START_REF] Mcadie | Thermal Decomposition of Molecular Complexes: II. β-Quinol Clathrates[END_REF] in the case of some systems, (iii) have a very high stability at ambient conditions that is ideal for applying analytical characterization techniques; 8 and (iv) can exist in a metastable state with no guests present in the lattice structure. [START_REF] Lee | Selective CO 2 Trapping in Guest free Hydroquinone Clathrate Prepared by Gas Phase Synthesis[END_REF]10 As a result, practical applications based on HQ clathrates have been proposed, including sequestration of hazardous substances, [START_REF] Chleck | The Preparation and Some Properties of Radioactive Quinol-Krypton Clathrate Compounds[END_REF] fractionation of organic compound mixtures, [START_REF] Hayes | Urea Complexation for the Rapid, Ecologically Responsible Fractionation of Fatty Acids from Seed Oil[END_REF] hydrogen storage, [START_REF] Han | Fast and Reversible Hydrogen Storage in Channel Cages of Hydroquinone Clathrate[END_REF][START_REF] Rozsa | Triple Guest Occupancy and Negative Compressibility in Hydrogen-Loaded β-Hydroquinone Clathrate[END_REF] and separation of CO 2 from different gas mixtures containing H 2 , [START_REF] Lee | Highly Selective CO 2 Extraction from a Mixture of CO2 and H2 Gases Using Hydroquinone Clathrates[END_REF] N 2 , [START_REF] Lee | Separation of CO 2 from Flue Gases using Hydroquinone Clathrate Compounds[END_REF] and CH 4 . 1717 In the late 1940s, Powell was the first ever to resolve an organic clathrate structure (HQ-SO 2 ) by X-ray crystallographic analysis, revealing one of the key elements for understanding the nature of these compounds. [START_REF] Powell | The Structure of molecular compounds. Part IV: Clathrate Compounds[END_REF] However, more than 75 years on, it is amazing to realize just how many simple and basic organic clathrate systems still remain unexplored, particularly among those formed with gases. [START_REF] Conde | Revisiting the Thermodynamic Modelling of Type I Gas-Hydroquinone Clathrates[END_REF][START_REF] Coupan | Experimental Determination of Phase Equilibria and Occupancies for CO 2 , CH 4 , and N 2 Hydroquinone-Clathrates[END_REF] For example, the detailed molecular structures of HQ-CH 4 and mixed (CH 4 -CO 2 )-HQ clathrates have still not been published. Indeed, this area has not yet been thoroughly studied and HQ clathrates could open up interesting new scientific avenues for exploration.

When different guests are encaged in an HQ structure (typically when a gas mixture is used instead of a pure gas), the resulting host-guest compounds are known as "mixed gas HQ clathrates". [START_REF] Coupan | Phase equilibrium properties of CO 2 /CH 4 mixed gas hydroquinone clathrates: experimental data and model predictions[END_REF] Mixed gas clathrates could be used in a number of practical applications such as gas separation by selective clathration. However, there is very little fundamental information on mixed gas HQ clathrates in the literature, except for recent physicochemical characterizations, and in spectroscopic and thermodynamic data. [START_REF] Lee | Selective CO 2 Trapping in Guest free Hydroquinone Clathrate Prepared by Gas Phase Synthesis[END_REF][START_REF] Lee | Preferential Occupation of CO 2 Molecules in Hydroquinone Clathrates Formed from CO 2 /N 2 Gas Mixtures[END_REF][START_REF] Park | Temperature-Dependent Release of Guest Molecules and Structural Transformation of Hydroquinone Clathrates[END_REF][START_REF] Coupan | A Characterization Study of CO 2 , CH 4 , and CO 2 /CH 4 Hydroquinone Clathrates Formed by Gas-Solid Reaction[END_REF] From a crystallographic point of view, even less information is available. Lee et al. studied the properties of (C 2 H 4 -CH 4 )-HQ and (C 2 H 4 -C 2 H 6 )-HQ clathrates and found that the lattice parameters a, b, and c (calculated from X-ray powder diffraction patterns) generally increase with the concentration of C 2 H 4 in the gas phase. [START_REF] Lee | Competing Occupation of Guest Molecules in Hydroquinone formed from binary C 2 H 4 and CH 4 gas mixtures[END_REF][START_REF] Lee | Highly Selective Enclathration of Ethylene from Gas Mixtures[END_REF] However, to the best of the author's knowledge, no detailed crystal structures of the kind organic clathrates form with gas mixtures have ever been reported.

Molecular dynamics (MD) simulations of clathrates have been described in the literature, although there are not as many of them as one might expect, considering the abundance and availability of certain host molecules such as water or HQ. Among the clathrates, gas hydrates are by far the systems that receive the most attention in simulation studies. Several reviews, those of Sum et al. [START_REF] Sum | Energy Science of Clathrate Hydrates: Simulation-Based Advances[END_REF] and Barnes and Sum, [START_REF] Barnes | Advances in Molecular Simulations of Clathrate Hydrates[END_REF] for example, offer detailed theoretical descriptions of their thermophysical properties and equilibrium phenomena simulated by MD. HQ clathrates have received far less attention in molecular dynamics studies, although they share many structural features with hydrate clathrates. To our knowledge, the first study was presented by Dang and Pettitt, [START_REF] Dang | A Theoretical Study of the Inclusion Complexes of β-Quinol[END_REF] in which they investigated the thermodynamics and guest dynamics of krypton (Kr) and argon (Ar) HQ clathrates. [START_REF] Dang | Thermodynamics of Diatomic Guests in β-Quinol Clathrates[END_REF] This study was promptly followed by a second one by the same authors on diatomic molecules. Santikary et al. [START_REF] Santikary | Molecular Dynamics Simulation of Clathrates: Noble Gases in the Cages of β-Hydroquinone[END_REF] studied the diffusion of noble gases (neon and argon) through rigid HQ lattices. Daschbach et al. [START_REF] Daschbach | Molecular Mechanisms of Hydrogen-Loaded β-Hydroquinone Clathrate[END_REF] and more recently Peŕez-Rodri ́guez et al. [START_REF] Peŕez-Rodríguez | Simulation of Capture and Release Processes of Hydrogen by β-Hydroquinone Clathrate[END_REF] investigated the behavior of H 2 as a guest molecule, whereas Nemkevich et al. [START_REF] Nemkevich | Mechanism of Concerted Hydrogen Bond Reorientation in Clathrates of Dianin's Compound and Hydroquinone[END_REF] studied HQ clathrates with Dianin's compound. Other guests including CO 2 , CO, H 2 S, and CH 4 were also previously modeled by Zubkus et al. [START_REF] Zubkus | Computer-Simulation Studies of β-Quinol Clathrate with Various Gases. Molecular Interactions and Crystal Structure[END_REF][START_REF] Zubkus | Molecular Interactions, Structure and Stability of β-Quinol Clathrate[END_REF] Recently, a study of HQ clathrates with CH 4 and CO 2 as guest molecules was presented, [START_REF] Comesanã | A Description of Hydroquinone Clathrates Using Molecular Dynamics: Molecular Model and Crystalline Structure for CH 4 and CO 2 Guests[END_REF] in which only the clathrates of the two guests in their pure state (not their mixtures) were investigated. In this study, a molecular dynamics model based in an optimized potentials for liquid simulations (OPLS) force field was tested and the solid native α phase and the β clathrate phases of HQ with CH 4 and CO 2 as guest molecules were reproduced with reasonable accuracy.

In the present study, we investigated the crystal structure of mixed (CO 2 + CH 4 )-HQ clathrates in a combined experimental and numerical approach. Single crystals were synthesized using CO 2 /CH 4 gas mixtures with different compositions ranging from pure CO 2 to pure CH 4 , and the crystal structure was resolved using X-ray diffraction (XRD). The main objective was to study how the lattice parameters of these mixed gas clathrates vary according to the proportion of CO 2 and CH 4 loaded in the crystal. The selectivity of the clathration (i.e., the capacity of the crystal to selectively encapsulate one of the two molecules present in the gas mixture used to form it) was also analyzed experimentally across the entire gas composition domain. In parallel, molecular dynamics simulations were performed on the same systems using state-of-the-art molecular models and force fields, namely, solving Newton's equations of motion for the individual atoms, coupled with a barostat and a thermostat to fix their thermodynamic conditions at the thermodynamic points of interest. Finally, the experimental and numerical results obtained were compared and discussed to offer salient conclusions regarding the structure and composition of these mixed gas organic clathrates.

■ EXPERIMENTAL SECTION

The gas clathrates are crystallized in a 168.0 ± 0.9 cm 3 highpressure jacketed reactor equipped with two viewing windows to watch the crystals growing during the experiment, two Pt-100 probes to measure the liquid and gas temperatures with an accuracy of ± 0.1 K, and a Keller pressure sensor (accuracy of ± 0.01 MPa). The protocol used here was previously used in another of the authors' studies to obtain CO 2 -HQ clathrate single crystals. [START_REF] Torre | CO 2 -Hydroquinone clathrate: Synthesis, Purification, Characterization and Crystal Structure[END_REF] In short, an oversaturated solution of HQ in absolute ethanol (EtOH), [START_REF] Li | Solubility of Hydroquinone in Different Solvents from 276[END_REF] typically 8 g of HQ in 11 g of EtOH, is first prepared in a small glass vessel containing a starshaped magnetic stirring bar. This vessel is placed inside the reactor in front of the viewing windows with the help of a clamp. The reactor is then closed, put under vacuum to eliminate any traces of air, and regulated to a temperature of 298 ± 0.1 K. The initial HQ/EtOH suspension is agitated with a magnetic stirrer situated beneath the reactor to properly dissolve the HQ and saturate the solvent. The agitation is stopped to perform the next operations in quiescent conditions. The reactor is pressurized either with pure CO 2 (or CH 4 ) or with a CO 2 -CH 4 gas mixture until the desired pressure of 3.0 MPa is reached. The temperature and pressure used in this work were chosen based on previous studies by the authors, particularly two: the first is a process evaluation of CO 2 /CH 4 separation by HQ clathrate formation in which a temperature of 298 K and a pressure of 3.0 MPa could be a relevant operating point for an industrial production gas separation unit using such a technology; [START_REF] Coupan | Hydroquinone Clathrate Based Gas Separation (HCBGS): Application to the CO 2 / CH 4 Gas Mixture[END_REF] the second presents a wide range of physical and chemical characterization results for (CO 2 -CH 4 )-HQ clathrates obtained at ambient conditions and 3.0 MPa but did not study crystal structures. [START_REF] Coupan | A Characterization Study of CO 2 , CH 4 , and CO 2 /CH 4 Hydroquinone Clathrates Formed by Gas-Solid Reaction[END_REF] Both temperature and pressure are maintained constant during crystallization. The crystals inside the reactor are observed using a commercial webcam (LiveCam Optia AF, Creative Labs), and all of the process data (i.e., pressure and temperature versus time) are recorded using a homemade LabVIEW interface with an acquisition frequency of 1 Hz. At the end of the synthesis, the composition of the gas mixture at equilibrium with the clathrates is analyzed by gas chromatography (GC). The reactor is then isolated (i.e., the gas supply valve is closed) and transported (under pressure) to the analytical room for XRD analysis. It is depressurized and opened to collect the clathrate crystals, and the XRD analysis is performed immediately at 100 K. Technical details on GC, XRD apparatus and methods, and information about the equipment used in this work are summarized in Tables S1 andS2 of the Supporting Information. Figures showing the crystal structure and the voids were obtained using Mercury 3.10.3. 39

■ NUMERICAL METHODS

For simulating the mixed gas HQ clathrate, we use a molecular dynamics technique based on molecular models and a methodology previously tested for pure CO 2 and CH 4 HQ clathrates. [START_REF] Comesanã | A Description of Hydroquinone Clathrates Using Molecular Dynamics: Molecular Model and Crystalline Structure for CH 4 and CO 2 Guests[END_REF] GROMACS software [START_REF] Bekker | GROMACS: A Parallel Computer for Molecular Dynamics Simulations[END_REF][START_REF] Berendsen | ROMACS: A Message-Passing Parallel Molecular Dynamics Implementation[END_REF] is used to carry out all MD simulations in the present work.

The initial coordinates of the HQ lattice are obtained from experimental crystallographic data acquired by X-ray diffraction analysis. [START_REF] Torre | CO 2 -Hydroquinone clathrate: Synthesis, Purification, Characterization and Crystal Structure[END_REF] The simulation boxes for the β-HQ clathrates are shown in Figure 1. The initial cell parameters of β-HQ are taken from the experimental values a = b = 1620.7 ± 0.6 pm, c = 578.0 ± 0.2 pm. We fill the β-HQ lattice with different concentrations of CO 2 and CH 4 , and each system is then equilibrated at the desired temperature and pressure values. We select the OPLS-all atom (AA) [START_REF] Jorgensen | Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids[END_REF] force field, somewhat modified for modeling the HQ lattice and guest molecules. In the model used here, the C6 rings in the HQ molecules are rigid, as are the CO 2 and CH 4 guest molecules, but the OH moieties have some freedom to rotate. All of the molecules are supposed to be nonpolarizable, meaning that the atoms are modeled as point particles with fixed relative positions and point charges.

The modifications made to the OPLS-AA force field used in this study concern the atomic equilibrium positions and charges recalculated from quantum mechanics (QM) instead of the default values in the force field tables. To ensure compatibility with the original OPLS-AA parameterization scheme, equilibrium geometries of HQ, CO 2 , and CH 4 are obtained using Becke's three-parameter hybrid functional B3LYP (Becke, Lee-Yang-Parr) [START_REF] Becke | Density-Functional Thermochemistry. III. The Role of Exact Exchange[END_REF][START_REF] Lee | Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density[END_REF] with the 6-31+G(d,p) Pople basis set implemented in Gaussian 09. [START_REF] Frisch | Gaussian 09[END_REF] Atomic point charges are recalculated with the help of the CHELPG scheme developed by Breneman and Wiberg [START_REF] Breneman | Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis[END_REF] in Gaussian 09 too.

The initial simulation boxes are prepared (optimized and equilibrated) in the canonical (NVT) ensemble, coupled with the thermostat by Bussi et al. [START_REF] Bussi | Canonical Sampling Through Velocity Rescaling[END_REF] When the simulation boxes are stabilized, we calculate the lattice parameters of the mixed gas HQ clathrate crystal structures by performing independent simulations with different relative concentrations of guest molecules in the isothermal-isobaric (NpT) ensemble. The pressure is stabilized at selected values by means of the Parrinello-Rahman barostat [START_REF] Bussi | Canonical Sampling Through Velocity Rescaling[END_REF] using anisotropic compressibility to take into account the rhombohedral symmetry of the HQ clathrate crystal. As usual, three-dimensional (3D) periodic boundary conditions are used in conjunction with the minimum image convention. The interaction potentials are truncated so that the explicit interactions remain inside the simulation box. Cutoff values of 110 pm are used for both the Lennard-Jones and Coulombic potentials. To evaluate these interactions, we chose the fourth-order particle mesh Ewald method [START_REF] Darden | Particle Mesh Ewald: An N• log(N) Method for Ewald Sums in Large Systems[END_REF][START_REF] Essmann | A Smooth Particle Mesh Ewald Method[END_REF] with a ratio mesh of 120 pm. To describe cross interactions, we use the Lorentz-Berthelot combining rules with a geometric mean. [START_REF] Good | Test of Combining Rules for Intermolecular Distances. Potential Function Constants from Second Virial Coefficients[END_REF]

■ RESULTS AND DISCUSSION

A summary of the experimental results obtained in this study is given in Table S3 of the Supporting Information, including CO 2 molar fraction in the gas phase in equilibrium with the solid phase measured at the end of the experiment, A and B parameters of the clathrate formula, crystal lattice parameters (a, b, c), tilt angle of the HQ molecule in the crystal (α), volume of the unit cell (V uc ), total occupancy of the guests in the clathrate (χ), CO 2 molar fraction in the crystal (x CO 2 ), ratio of the CO 2 and CH 4 molar fractions in the crystal (S CO 2 /CH 4 ), and separation factor (SF CO 2 /CH 4 ).

Crystal Structure. The modeled crystal structure is shown in Figure 2. Figure 3a-c shows general views of the host crystal structure for the mixed (CO 2 + CH 4 )-HQ clathrates obtained experimentally. The global rhombohedral structure (symmetry group R3̅ ) is the same whether the clathrates are obtained with mixed or pure gases (i.e., CO 2 and CH 4 ). The geometry is based on the formation of two interpenetrating, but not interconnected, networks of HQ molecules forming a cavity in which the guest molecules are encapsulated. The hydroxyl groups of HQ are linked by hydrogen bonding and form a planar hexagon defining the top and bottom of this cavity, whereas alternate HQ molecules pointing diagonally above and below each hexagon define the lateral parts of the cavity. Interestingly enough, we found that all of the clathrates analyzed in this study have the same crystallographic structure. The lattice parameters, however, strongly depend on the composition of the gas loaded into the clathrates, as discussed later on. In addition to the lattice parameters, the α angle (tilt angle of the O-O HQ molecule axis in relation to the c plane) shown in Figure 3d also characterizes the structure. In an attempt to get a better idea of the cavity shape, Figure 4 shows the voids present in the crystal, focusing on the solvent-accessible surface areas. With this approximation, the crystal is considered as a set of fused spheres with van der Waals radii. A probe sphere (of a defined radius) is then rolled over the van der Waals surface, and the accessible surface is mapped out by the center of the probe sphere to obtain a 3D view of the voids in the crystal. [START_REF] Turner | Visualisation and Characterisation of Voids in Crystalline Materials[END_REF] This method has already been used to characterize various materials such as salycilamide polymorphs, [START_REF] Johnstone | High-Pressure Polymorphism in Salicylamide[END_REF] L-alanyl-L-valine, [START_REF] Moggach | The Effect of Pressure on the Porous Peptide L-alanyl-L-valine[END_REF] gabapentin heptahydrate, [START_REF] Fabbiani | Searching for Novel Crystal Forms by in situ High-Pressure Crystallisation: the Example of Gabapentin Heptahydrate[END_REF] and adamantane hydrochloride salts. [START_REF] Mohamed | Using Crystal Structure Prediction to Rationalize the Hydration Propensities of Substituted Adamantane Hydrochloride Salts[END_REF] The HQ clathrate cavity exhibits a roughly spherical shape with pure CH 4 (see Figure 4a), whereas it is largely elongated toward the c-axis in the case of pure CO 2 (see Figure 4b). Interestingly enough, the cavity shape of the mixed (CO 2 -CH 4 )-HQ clathrates is halfway between those obtained with pure gases: the more CO 2 enclathrated in the cavity, the more deformed it is.

As both CO 2 and CH 4 are enclathrated, the formula of the mixed (CO 2 + CH 4 ) clathrate can be written as:

(ACO 2 + BCH 4 )•3HQ, with A + B = χ with (0 ≤ χ ≤ 1) and where A and B are defined as the CO 2 and CH 4 occupancy factors, respectively. These factors can be normalized by the global occupancy χ to give normalized occupancy factors x CO 2 = A/χ and x CH 4 = B/χ. The values x CO 2 and x CH 4 are the molar fractions of the CO 2 and CH 4 trapped inside the clathrate. The composition of the clathrate was calculated by structural analysis. For this purpose, the carbon and oxygen atom occupancies in the guest molecules were refined separately using two different variables. Given that the carbon atoms of both guest molecules are located in the same position, the variable for carbon atom occupancy gives the total occupancy of the guest molecules. The value of the oxygen atom variable reflects the CO 2 occupancy and the difference between the two variables gives the information pertaining to the CH 4 molecules. It has been proven that this technique gives occupancy values of the same order of magnitude as those obtained by TGA measurements. [START_REF] Torre | CO 2 -Hydroquinone clathrate: Synthesis, Purification, Characterization and Crystal Structure[END_REF] In this work, the occupancies and clathrate formulas determined by XRD analysis were crosschecked by elementary analysis. In addition, the reproducibility of the experiments, estimated based on three independent runs carried out in the same conditions using an initial 50:50 CO 2 /CH 4 gas mixture, is quite good as the average results obtained by structural analysis were A = 0.57 ± 0.03 and B = 0.22 ± 0.03 against A = 0.52 ± 0.12 and B = 0.19 ± 0.07 by elementary analysis.

The experimental values of parameters A and B of the clathrate formula (ACO 2 + BCH 4 )•3HQ are plotted in Figure 5 versus the molar fraction of CO 2 in the gas phase in equilibrium with the crystal. It is therefore very simple using these curves to obtain the clathrate formula for a given gas composition at 298 K and 3 MPa. Interestingly enough, both the crystal lattice parameters, i.e., a (=b) and c, obtained experimentally and by modeling appear to be directly correlated with the clathrate composition. The variation of the lattice parameters and the angle α versus x CO 2 are shown in Figures 6 and7, respectively. Note that as x CH 4 = 1x CO 2 , the variation of the lattice parameters versus x CH 4 can be deduced very easily.

When the clathrate became increasingly rich in CO 2 , we observed both a decrease in the a (= b) lattice parameter and an increase in the c parameter: the size of the unit cell is therefore strongly dependent on the composition of the gas encapsulated in the clathrate. With this particular binary gas mixture and in these conditions, the variation of the lattice parameters is monotonous (no extremum found). This trend clearly demonstrates that the HQ framework is highly adaptive.

We observed that MD estimates almost systematically deviate from experimental values, but, despite this, the performance of the HQ molecular model and the force field used can be considered quantitatively good. Let us recall that the HQ force field used combines two different approaches. First, the dispersive interaction parameters were originally computed in a group contribution scheme for substituted benzene derivatives in the OPLS force field. It is important to note that dispersive characteristic parameters are adjusted to reproduce experimental fluid-phase equilibrium data. The same applies for CO 2 and CH 4 force fields. The original HQ molecular model was then modified by recalculating the atomic point electric charges using QM calculations for an isolated molecule under vacuum. This means that the force field characteristic parameters were determined in conditions far removed from those studied for the present clathrates, underlining the remarkable transferability of force field parameters. The geometry of the HQ clathrate containing a single guest was found to be very similar to the results obtained in experiments, [START_REF] Comesanã | A Description of Hydroquinone Clathrates Using Molecular Dynamics: Molecular Model and Crystalline Structure for CH 4 and CO 2 Guests[END_REF] an encouraging first result. Because we are able to demonstrate that the clathrate structure is flexible enough to accommodate a mixed population of guest molecules, in keeping with the trend highlighted in experiments concerning the variation of a and c lattice parameters, these simulation results can be considered highly relevant in light of the hypotheses and simplifications used in the models (conventional, nonpolarizable, etc.). There was a certain drift in the estimated results, but the structural modification undergone by the clathrate with the change in guest composition is extremely subtle in experiments, and the simulations were able to very accurately capture this physical behavior.

Drawing on the analysis of the molecular dynamics simulation results, the shape of the clathrate cavities of the mixed clathrates can also be discussed. In the case of pure guest (CH 4 or CO 2 ) HQ clathrates, it is clear that all cavities have the same geometry, with a given set of lattice parameter values, regardless of the fluctuations in cage size due to the movement of the HQ molecules, which are bonded by labile hydrogen bonds only. Nevertheless, in the case of mixed guest clathrates, there is some controversy about the possible coexistence of clathrate cavities of different sizes for each type of guest molecule. Based on an analysis of the molecular dynamics simulation trajectory, a histogram of the α angle values for the pure CH 4 , pure CO 2 , and equimolar guest clathrate structures was calculated at 100 K and 0.1 MPa. The data obtained follow a normal distribution (see details of the statistical analysis in Table S4 of the Supporting Information).

The results presented in Figure 8 show a clearly monomodal cavity size distribution for the mixed clathrate too, which rules out the bimodal cage size distribution hypothesis. Molecular dynamics simulation results also support the case of a homogeneous crystalline structure with lattice parameters evolving continuously between the limiting values corresponding to the pure clathrates. This is an estimation result that might have been expected a priori, taking into consideration the reported flexibility of the hydrogen-bonded network of the clathrate structure, which is able to shrink or swell according to changes in guest occupancy rate or composition.

Clathrate Selectivity. The capacity of a clathrate crystal formed with a binary gas mixture to be more or less selective toward one of the two gases in presence can be discussed with the help of the separation factor (denoted SF), [START_REF] Linga | The Clathrate Hydrate Process for Post and Pre-Combustion Capture of Carbon Dioxide[END_REF] which considers both the composition of the enclathrated gas and the composition of the gas phase in equilibrium with the solid phase. This indicator, commonly used in chemical and process engineering studies to quantify clathrate selectivity toward one of the two gases, is expressed in eq 1 for the CO 2 /CH 4 binary mixture as (1)

where x CO 2 and y CO 2 are the CO 2 molar compositions of the gas present in the clathrate and in the gas phase in the CO 2 /CH 4 gas mixture, respectively. The higher the SF, the better the selective clathration toward CO 2 .

The composition of the clathrate itself can be simply assessed by the S CO 2 /CH 4 ratio of the molar fraction of the two gases (i.e., x CO 2 and x CH 4 ) present in the crystal, defined by eq 2

= S x x CO /CH CO CH 2 4 2 4 (2)
In our case, it is worth noting that S can also be directly calculated by the ratio of the A and B coefficients in the clathrate formula. Obviously, when S CO 2 /CH 4 > 1, the clathrate has more CO 2 than CH 4 .

The correlation curve between the composition of the solid and the gas at equilibrium is shown in Figure 9 for a temperature of 298 K. The corresponding values of S and SF versus the CO 2 concentration in the gas phase at equilibrium are plotted in Figure 10.

It is clear that in these conditions of synthesis pressure (3.0 MPa), temperature (298 K), and gas mixture composition (0 < y CO 2 < 1), the x CO 2 vs y CO 2 curve is always above the diagonal line of this chart (see Figure 9), demonstrating that the molar fraction of CO 2 in the solid phase is always higher than in the gas phase at equilibrium. In other words, the gas that could be recovered by dissociation of the clathrate is always richer in CO 2 than the gas used to form it. Therefore, the HQ clathrates formed from a CO 2 + CH 4 gas mixture are selective toward CO 2 for the entire gas composition range. This point is illustrated in Figure 10 by SF CO 2 /CH 4 values that are greater than 1, i.e., ranging from 2.7 to 4.2.

Actually, the SF values found in this work are different from those previously published in the literature. Coupan et al. [START_REF] Coupan | Phase equilibrium properties of CO 2 /CH 4 mixed gas hydroquinone clathrates: experimental data and model predictions[END_REF] calculated SF CO 2 /CH 4 values lower than 1 across the entire gas composition domain when the clathrate is crystallized from an HQ-saturated solvent solution formed at a very low pressure in conditions of three-phase equilibrium (e.g., T = 298.3 ± 0.3 K, P = 0.089 ± 0.013 MPa, and y CO 2 = 0.512 ± 0.002). This comparison might suggest that the clathrate selectivity toward CO 2 becomes much higher than 1 if the clathrate formation pressure largely exceeds the three-phase clathrate equilibrium pressure (in this study, the synthesis pressure is around 30 times higher than the equilibrium pressure). In addition, the SF values in this work were found to be about 3-10 times lower than those obtained by Coupan et al. (i.e., SF CO 2 /CH 4 from 10.1 to 18.8 at 293 K) [START_REF] Coupan | Hydroquinone Clathrate Based Gas Separation (HCBGS): Application to the CO 2 / CH 4 Gas Mixture[END_REF] and Lee et al. [START_REF] Lee | Selective CO 2 Trapping in Guest free Hydroquinone Clathrate Prepared by Gas Phase Synthesis[END_REF] who have also worked with CO 2 + CH 4 gas mixtures. These higher SF values could be explained by the fact that the mixed gas HQ clathrates found by Coupan et al. and Lee et al. were obtained (i) through a direct gas-solid reaction instead of crystallization from an HQ-saturated solvent, or (ii) through using an intermediate guest-free HQ clathrate (formed by using CO 2 ) identified as being particularly selective toward CO 2 . 10 However, even though the HQ clathrates were selective toward CO 2 across the entire gas mixture composition domain, it is very interesting to note in Figure 10 that the clathrate crystals contain more CO 2 than CH 4 (i.e., S CO 2 /CH 4 > 1) only when the molar fraction of CO 2 in the gas phase (y CO 2 ) is higher than around 0.2. We believe that these results could be very useful for practical applications, such as HQ clathratebased gas separation processes.

■ CONCLUSIONS

Single crystals of mixed (CO 2 + CH 4 )-HQ clathrates formed with different CO 2 /CH 4 gas mixtures were synthesized experimentally and underwent XRD analysis to obtain information on the crystal structures and on the occupancy of the guests enclathrated in the crystal. Molecular dynamics simulations were also performed on the same structures. From the results obtained, it was concluded that mixed (CO 2 + CH 4 ) clathrates have the same rhombohedral crystal structure whatever their composition is (i.e., from pure CO 2 to pure CH 4 ) and that their homogeneity and concentration depend on cavity size. However, the lattice parameters of the crystal and the size of the cavity vary with the gas mixture composition: when the proportion of CO 2 increases in the crystal, the lattice parameters a and b decrease while c increases, in a monotonic way (without extremum). The more CO 2 there is in the crystal, the more elongated the cavities toward the c-axis. The molecular dynamics simulations very accurately predicted this tendency of the crystal structure to vary according to the gas composition. The lattice parameters obtained in experiments and numerically were in very good agreement, demonstrating that the modeling strategy chosen and the simplified assumptions used are relevant. Interestingly enough, we were able to deduce from the statistical analysis of cavity sizes obtained by simulations, a key aspect of the clathrate structure that is very difficult to process in experiments: even if two different guests are present in the structure (i.e., CO 2 and CH 4 ) in variable proportions, mixed HQ clathrates have just one cavity size that varies as a function of the composition of the gas encapsulated in the crystal. Calculation of clathrate selectivity demonstrated that, in these conditions (synthesis at a pressure of 3.0 MPa and a temperature of 298 K), HQ clathrates are always selective toward CO 2 whatever the gas composition is:the gas loaded in the clathrates is always richer in CO 2 than the gas used to form it. However, it is worth noting that although the clathration was selective toward CO 2 , we found that the clathrates became richer in CH 4 when the CO 2 molar fraction in the gas at equilibrium dropped below ∼0.2. We believe that these results concerning clathration selectivity are highly important for practical applications using organic clathrates, particularly CO 2 /CH 4 gas separation processes based on HQ clathrates. It could be useful to perform additional work at different pressures and temperatures with this particular gas mixture and others.

■ ASSOCIATED CONTENT

* S Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b04081.

Analytical techniques, methods and materials used in this study, the snapshot of the rhombohedral simulation boxes for the β-HQ clathrate, the summary of the experimental data obtained, and the statistical analysis of the tilt angle (α) data obtained by simulation (PDF)

Accession Codes CCDC 1913196-1913204 contain the additional crystallographic data.

■ AUTHOR INFORMATION

Corresponding Author *E-mail: jean-philippe.torre@ensiacet.fr. Phone: +33(0)5 34 32 37 10.

Figure 1 .

 1 Figure 1. Snapshot of the rhombohedral simulation boxes for the β-HQ clathrate, containing as guest molecules (a) CH 4 , (b) an equimolar concentration of CO 2 and CH 4 , and (c) CO 2 . The views were taken along the z-axis, so the clathrate channels are perpendicular to the page plane. Each channel, consisting, for this system size, four aligned cells, shows the superimposition of all of the guest molecules it contains.

Figure 2 .

 2 Figure 2. Detailed view of the molecular dynamics simulation structure for the β-HQ clathrates, showing only three consecutive cells of a given channel. (a) Channel containing CH 4 as a guest molecule, (b) channel containing CO 2 + CH 4 , and (c) channel containing CO 2 . In each case, a vertical (along the z-axis) and a side (along the x-axis) view are presented.

Figure 3 .

 3 Figure 3. General views of the crystal structure of mixed (CO 2 -CH 4 )-HQ clathrates obtained experimentally: (a) view down the crystallographic c-axis; (b) view down the crystallographic a-axis; and (c) 3D view. Blue dotted lines are hydrogen bonds forming the planar hexagons at the top and bottom of the cavity. (d) HQ molecule is represented with its oxygen-oxygen axis tilted at an angle α to the c plane (0001). The structures presented in this figure were built with the clathrate (0.59CO 2 -0.23CH 4 )-3HQ (CDCC-1913200).

Figure 4 .

 4 Figure 4. Representations of typical cavities in HQ clathrates (down the crystallographic a-axis) obtained from a crystal structure analysis by XRD. The "solvent-accessible voids" are visualized using a probe sphere of 1.2 Å and a grid spacing of 0.2 Å. (a) CH 4 -HQ clathrate. (b) CO 2 -HQ clathrate.

Figure 5 .

 5 Figure 5. Variation of A and B (parameters of the clathrate formula (ACO 2 + BCH 4 )•3HQ) as a function of the molar fraction of CO 2 in the gas phase at equilibrium with the crystal. Experimental data were obtained with clathrates synthesized at T = 298 K and P = 3.0 MPa and analyzed with XRD at T = 100 K and P = 0.1 MPa. The blue and green lines are guides for the eye.

Figure 6 .

 6 Figure 6. Variation of the lattice parameters of the (CO 2 + CH 4 )-HQ clathrate crystals as a function of the molar fraction of CO 2 in the solid phase. Experimental data were obtained with clathrates synthesized at T = 298 K and P = 3.0 MPa and analyzed with XRD at T = 100 K and P = 0.1 MPa. Modeling data were obtained at T = 100 K and P = 0.1 MPa. The orange and purple lines are guides for the eye.

Figure 7 .

 7 Figure 7. Variation of the α angle (tilt angle of the HQ molecule axis in relation to the c plane) as a function of the molar fraction of CO 2 in the solid phase. Experimental data were obtained with clathrates synthesized at T = 298 K and P = 3.0 MPa and analyzed with XRD at T = 100 K and P = 0.1 MPa. Modeling data were obtained at T = 100 K and P = 0.1 MPa. The red lines are guides for the eye.

Figure 8 .

 8 Figure 8. Distribution of the HQ molecule tilt angle (α) in the clathrate structure for three values of CO 2 molar fractions in the solid phase (x): x = 0 in blue (CH 4 -3HQ); x = 0.5 in red (0.5CO 2 + 0.5CH 4 )-3HQ; x =1 in green (CO 2 -3HQ), each computed from 576 data points obtained by molecular dynamics simulations at 100 K and 0.1 MPa. Distribution histograms have been plotted with a class size of 0.2°. The solid curves correspond to the normal distribution calculated from the data points.

Figure 9 .

 9 Figure 9. Equilibrium between the CO 2 and CH 4 molar fractions in the HQ clathrate (x CO 2 and x CH 4 ) and the CO 2 and CH 4 molar fractions in the gas phase (y CO 2 and y CH 4 ). The green and blue lines are guides for the eye.

Figure 10 .

 10 Figure 10. Variation of the ratio of the molar fraction of the CO 2 and CH 4 present in the crystal (S CO 2 /CH 4 ) and of the separation factor (SF) as a function of the molar fraction of CO 2 in the gas phase. The dashed blue line represents the value SF CO 2 /CH 4 = 3.6. The dotted green lines show the value of the CO 2 gas fraction (y CO 2 ∼ 0.2), which corresponds to S CO 2 /CH 4 = 1. The rose line is guide for the eye.

DOI: 10.1021/acs.jpcc.9b04081

Author Contributions

The manuscript was written based on the contributions of all the authors. All of the authors have approved the final version of the manuscript.

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We would like to acknowledge the CNRS (Centre National de la Recherche Scientifique) for supporting this study. We would also like to thank Joseph Diaz and Mathieu Chabod for their assistance with the experimental apparatus. M.M.P. acknowledges the CESGA (www.cesga.es) for providing access to computing facilities and the Ministerio de Economi ́a y Competitividad in Spain for its financial support [Grant ref FIS2015-68910-P cofinanced by European Regional Development Funds (ERDF)].

SUPPORTING INFORMATION

Insights into the Crystal Structure and Clathration Selectivity of Organic Clathrates formed with Hydroquinone and (CO 2 + CH 4 ) Gas Mixtures Jean-Philippe TORRÉ 1, * , Heinz GORNITZKA 2 , Romuald COUPAN 3 , Christophe DICHARRY [START_REF] Atwood | Structural Aspects of Inclusion Compounds formed by Organic Host lattices[END_REF] Martín PÉREZ-RODRÍGUEZ 5 , Antonio COMESAÑA 5 , Manuel M. PIÑEIRO [START_REF] Woḧler | Ueber einige Verbindungen aus der Chinonreihe[END_REF] 1 . Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France. [START_REF] Sloan | Clathrate Hydrates of Natural Gases[END_REF] . Laboratoire de Chimie de Coordination LCC-CNRS, Université de Toulouse, CNRS, UPS, Toulouse, France. [START_REF] Hammerschmidt | Formation of Gas Hydrates in Natural Gas Transmission Lines[END_REF] . Total Research & Technology Feluy, Zone Industrielle Feluy C, B-7181 Seneffe, Belgium. [START_REF] Atwood | Structural Aspects of Inclusion Compounds formed by Organic Host lattices[END_REF] . CNRS/TOTAL/UNIV PAU & PAYS ADOUR/E2S UPPA, Laboratoire des Fluides Complexes et leurs Réservoirs-IPRA, UMR5150 -avenue de l'Université, 64000 Pau, France. [START_REF] Woḧler | Ueber einige Verbindungen aus der Chinonreihe[END_REF] . Departamento de Física Aplicada, Facultade de Ciencias, Universidade de Vigo, 36310, Spain.

S2

Table S1. Analytical techniques and methods used in this study.

Method Details

GC

The gas composition at the end of the synthesis is obtained by gas chromatography (GC).

The analysis is performed using a gas chromatograph (GC Agilent, model 7820A) equipped with a high-pressure sampling system, a 30-m capillary column (model HP-PLOT-Q) with an inner diameter of 0.32 mm (comprising a stationary phase of polystyrene/di-vinylbenzene coating, 20 µm thick), and a thermal conductivity detector. Hydrogen, supplied by a hydrogen generator (model NMH2), is used as a carrier gas. The GC is calibrated with different commercial CO2/CH4 gas mixtures. The method allows quantitative measurements with a relative uncertainty of 0.3%, and retention times for CH4 and CO2 of 0.64 ± 0.05 and 0.80 ± 0.05 minutes respectively.

XRD

The X-Ray Diffraction (XRD) analysis were performed using oil-coated shock-cooled crystals on a Bruker-AXS APEX II diffractometer with MoKa radiation (λ = 0.71073 Å).

S3

Table S3. Summary of the experimental data obtained in this study. Variables: CO2 molar fraction in the gas used for the synthesis (y CO2 init), CO2 molar fraction in the gas phase in equilibrium with the solid phase measured at the end of the experiment (y CO2 ), A and B parameters of the clathrate formula (A CO2 -B CH4 -3HQ), crystal lattice parameters (a, b, c), tilt angle of the HQ molecule in the crystal (), volume of the unit cell (Vuc), total occupancy of the guests in the clathrate (), CO2 molar fraction in the crystal (x CO2 ), ratio of the CO2 and CH4 molar fractions in the crystal (S CO2/CH4 ), and separation factor (S.F. CO2:CH4 ). The uncertainty ±  is within the 95% confidence interval of the mean, under the assumption of normality, estimated from 3 repeat experiments (CDCC 1913199-1913201). [START_REF] Steed | Core Concepts in Supramolecular Chemistry and Nanochemistry[END_REF] if the p-value is > 0.05, the assumption of normality cannot be rejected (i.e. the data follow normal distribution).


Basile Fraboni

Jean-Claude Iehl

Vincent Nivoliers

Guillaume Bouchard

Adaptive multi-view path tracing

Keywords: CCS Concepts, Computing methodologies → Computer graphics, Ray tracing, Visibility

a) Path tracing b) Ours -equal time

Introduction

Rendering noise-free images with path tracing often requires heavy computations and sampling thousands of paths through each pixel. Rendering a sequence of images is even more intensive despite the high similarity of consecutive frames. Reducing temporal noise also requires more samples to remove flickering. Several authors have proposed different ways of reusing a single path to compute several pixels. These methods have achieved interesting speedups, but they all share the same limitation. Paths are sampled starting from one camera and they are transformed to contribute to another camera. As we shall see, this transformation can increase the variance of the Monte Carlo estimation of light transport.

Our paper proposes a different approach to this problem. We make the key observation that light transport can be estimated at any point in space and time and that many of these points are observed by more than one camera. Contrary to previous works that construct an entire path for a given camera, we progressively build a path that significantly contributes to several cameras. To do so, we first cast a ray from a camera, and then importance sample a reflected direction at the intersected point which gives significant energy to several cameras. Our importance sampling technique restricts the magnitude of the transformation and thus controls the variance of the observations by only selecting a subset of the cameras observing the point. The rest of the light transport is then estimated with standard path tracing.

Decoupling observations and transport estimation also makes our definition of a camera fairly general: a camera observes a region of space and time. A moving camera in an image sequence creates an observation per frame. A stereo/VR camera makes 2 observations, etc. Our approach can be used in very different settings: stereo-pair/VR video, camera array/light field rendering, etc.

Previous work

Exploiting the similarity between coherent viewpoints has been investigated in the past. We briefly describe existing approaches reusing paths and integrating in the gradient domain.

Space-time coherence

Taking advantage of space-time coherence by using the same samples in multiple renderings is a widely used technique for interactive and real time applications. In the context of offline Monte Carlo integration, several techniques have been developed. Adelson and Hodges [AH93, AH95] directly exploit spatiotemporal coherence in the context of ray tracing. Their idea is to reuse samples by projecting them from one camera to another instead of sampling each camera separately. Samples on diffuse materials are reprojected, glossy and specular reflections are then simulated for each camera. These early approaches dramatically reduce the rendering time of nearby frames, like stereoscopic images or consecutive frames in animation sequences, but their efficiency decrease with the amount of glossy materials.

Bekaert et al. [BSH02]

introduce the concept of path re-use to compute a single frame. The image is divided in small square windows and pixels of each window share sampled paths. This first solution however shows highly correlated and structured noise before reaching convergence. A correction of these artifacts is given in [XS07] by using less structured pixel neighborhoods and by shuffling reused contributions. This technique has recently been extended to gradient domain rendering [BPE17]. Massively increasing the number of samples by reusing calculations leads to a better domain exploration, at the cost of correlation and structured artefacts. Our technique works on a different setting: instead of sharing pieces of paths generated for neighboring pixels on a single image, we sample and share full paths between different viewpoints. In this setting path re-use doesn't show structured noise.

Havran et al. [START_REF] Havran | An efficient spatio-temporal architecture for animation rendering[END_REF] discuss reprojection data structures and algorithms to efficiently render multiple animation frames over a time segment. They use clamping to remove negligible reprojected sample contributions which would otherwise increase the variance. Although this technique is appropriate for diffuse materials, reevaluating and clamping the brdf to reproject samples can lead to a poor importance function for glossy materials. Feliu et al. [FSSK06] improve on [START_REF] Havran | An efficient spatio-temporal architecture for animation rendering[END_REF] and introduce the normalization integral involved in the projection from one camera to another. The authors also introduce multiple importance sampling to further reduce variance while reprojecting samples to several cameras. Even though the normalization constant and its integration are fully derived in the paper, the authors use a simple approximation. They achieve better results when rendering glossy materials.

Henrich et al. [START_REF] Henrich | Accelerating path tracing by eye-path reprojection[END_REF] propose a hybrid architecture mixing CPU rendering with a simple and efficient GPU reprojection of path vertices on the screen. Artifacts created by this simplified reprojection are then reduced by filtering and downsampling. We use a more sophisticated technique to selectively reproject samples, and to account for the Jacobian of the reprojection, thereby limiting the amount of variance and removing the need to post process our results.

Our method is similar to these approaches in that we re-use samples for similar viewpoints. However, our key idea is the selection of the set of cameras which will share a sample path before generating the full path. This allows us to take all these cameras into account in the generation of the full path. Our paths are then combined using multiple importance sampling to reduce the variance in the result. * 15] propose a complex post-processing pipeline to jointly denoise and upscale animation sequences, both spatially and temporally. Images are decomposed into diffuse and specular components. Diffuse paths are re-used (through motion interpolation) while specular paths are re-evaluated with a temporal manifold exploration technique and then interpolated. We present a simple variance reduction technique which can be used to accelerate the computation of an animation sequence (same variance but faster), or to reduce noise (same time but lower variance). Our technique can also be used in different settings such as light field rendering or stereo/VR rendering.

Zimmer et al. [ZRJ

Gradient domain rendering

Gradient domain rendering is a recent approach computing both a coarse image and its gradient, and using Poisson reconstruction to obtain the final image. This approach has been successfully applied to Metropolis light transport [LKL * 13], path tracing [KMA * 15] and bidirectional path tracing [MKA * 15]. Paths are reused between neighboring pixels to compute the gradients. The correlation between the paths improves the variance in the gradient computations. This approach has been further extended to animated sequences [MKD * 16], computing temporal gradients as well to reduce flickering artifacts between consecutive frames. Paths are reused in a different manner: an original path is generated to provide a new sample for the image integral. The path is then deterministically shifted to a neighboring pixel or frame. Finite differences are finally used to estimate gradient values. Our method is not incompatible with gradient domain methods and merely allows to get more paths using reprojections, and gradient domain solutions could benefit from our approach. We also demonstrate the efficiency of our method in the context of motion blur with fast moving objects. In such a context, to our knowledge, no efficient methods exist to compute the gradients. Since motion blur is mostly due to the discontinuities in the visibility of the scene, such gradients could be difficult to estimate.

Background

We focus on improving the classical path-tracing algorithm. This algorithm computes realistic images by simulating light transport throughout a scene via Monte Carlo integration. Each rendered pixel j of a camera k is computed as the integral over the light reaching the pixel [START_REF] Veach | Robust Monte Carlo Methods for Light Transport Simulation[END_REF] and the exposure interval [t 0 t 1 ] of the camera:

I k j = t k 1 t k 0 Ω(t) f j ( X)dµ( X)dt (1)
where Ω(t) is the union of all light paths X of finite lengths at time t, f j is the light contribution carried through the path and µ is the product of the measures of the differential area elements at each path vertex [VG97]. Note that f j contains in particular the spatiotemporal pixel reconstruction filter, and will be 0 for a path not reaching the pixel. A path X is a finite sequence of points on the scene. For our purposes, we will decompose such a path in two parts X = {xy, z} where xy is a prefix which connects a camera vertex x and a visible scene point y, and z is a suffix path, which starts at a point z and carries the radiance flux to y from z (Figure 2). Path tracing approximates the integral Equation 1 by accumulating contributions from a set of sampled paths from the camera. A point x is generated on the exit lens and a ray is cast from x in the scene to find the first hit on the scene y. A suffix z starting from y is then generated using a stochastic process to generate a succession of bounce directions and points on the scene. The contributions f j of the paths Xi = {xy, z} for pixel j are then merged using their probability distribution functions (pdf) p :

Îk j = 1 n n ∑ i f j ( Xi ) p( Xi ) with p( Xi ) = p(xy)p(z|xy) observation p(z) (2)
This formulation highlights the fact that the light transport can be decoupled from the observation. Given a suffix z, its pdf p(z) and the radiance L(z → y) reaching y, computing a contribution for pixel j only requires the evaluation of the visibility, brdf and camera importance function.

Multi-view rendering

Our goal is to reduce the variance of multiple path-tracing generated images of the same scene. We share sampled paths between multiple integrals at a fixed time. Thus virtually increasing the number of samples per image without increasing much the cost per generated path. Each camera is described by a set of parameters (e.g. position, orientation, exposure interval, lens, focal distance) and corresponds to one integral. In the case of a camera rendering an animated sequence, each frame of the sequence is considered as a unique camera. Our method is applicable in the context of surface rendering, but does not consider the case of volume rendering and participating media.

We propose a two-step importance sampling technique for multiview path sampling. Each path is generated as follows :

1. Prefix step :

• a time t is sampled ;

• the camera and desired pixel i for the sample is importance sampled and a hit point y is found on the scene ; • if the point is not purely specular, a subset of similar cameras that could have sampled this point is determined (subsubsection 4.2.4);

2. Suffix step :

• a bounce direction is importance sampled using the subset of similar cameras ; • regular path tracing is used to generate the rest of the path ;

• the path contribution is merged with the integral of each selected camera using multiple importance sampling and the balance heuristic.

Sampling

Camera sampling

We use the thin lens camera model. Generating a path for a camera therefore requires two points : a point on the film and a point on the lens. Once the pixel i requiring additional paths is determined, a film point x i is generated in the pixel, and a lens point x is generated on the lens disk.

Time sampling

For static scenes, time is irrelevant. Each frame of each camera is therefore rendered as an independent observer, and any path can be reused. For animated scenes, paths are only reused at fixed time. Indeed reusing paths between different time points in such a case introduces bias, even for paths only hitting static objects, since moving objects could change the visibility between the points, or change the illumination received by static objects. For this reason, paths are sampled at a precise time, and only reused if the exposure interval of the observer contains that time. We therefore introduce no bias due to changes in visibility and illumination since the path is only used for a fixed time.

Multi-view integration

Once an initial sample is generated and a corresponding hit on the scene is found, a set of compatible cameras for sharing the path suffix is determined. The initial path prefix is transformed using a deterministic shift mapping, for each camera opened at the time of the path. The associated change in density is then evaluated through the Jacobian of the transformation. A selection probability is finally derived for the observer depending on both this Jacobian and the brdf at the hit point y.

Transforming the prefix of a path

For the generation of a prefix from a thin lens camera , both a point x i on a pixel i and a point x on the lens are sampled, thus obtaining a unique ray direction and a hit y . Given another camera k, a point x k on its lens is required to determine a point x j on its film to reuse the path suffix. We define this point deterministically as

x k = r k r x (3)
where r k and r are the respective lens radii of cameras k and . This transformation does not introduce bias in the integral for k since x k uniformly samples the lens of k. Given y and x k the point x j on the film of k is uniquely defined. We denote T →k the transformation of a path X for observer to a path Xk for observer k (Figure 3):

T →k : {x y , z} → {x k y , z} . (4)
By construction, T → is the identity, and T k→ = T -1 →k . Every transformed path cannot or should not be reused. We therefore perform the following tests:

• check whether x j is in the rectangle of the image k;

• run a Russian roulette on our selection probability (Eq. 13, 17);

• check the visibility on the segment [x k , y ].

Transforming densities

Every observer of a primary hit point y is an importance strategy to sample both y and suffix paths z. Let us consider an observer k and a pixel j for this observer. The integral for this pixel at a time t is

I k j (t) = Ω(t)
f j ( X)dµ( X).

(5)

Remember that the path contribution function f j contains the pixel filter and will be 0 for paths not reaching j. We will omit t in the following since every path reuse is done at fixed t. Given a second observer , this integral can be split in two parts depending on whether the path could have been provided by observer or not. If Ω is the set of paths reaching observer and Ω →k = T →k (Ω ), we can write

I k j = Ω →k f j ( X)dµ( X) + Ω\Ω →k f j ( X)dµ( X). ( 6
)
For the part of the integral over Ω →k a second strategy exists to compute the integral using paths from observer . This corresponds to the following change of variables :

Ω →k f j ( X)dµ( X) = Ω f j (T →k ( X ))|T →k |dµ( X ) (7)
where |T →k | is the determinant of the Jacobian of T →k . As detailed in Appendix A the pdf associated with this integral for Monte Carlo estimation is

p →k ( X ) = p ( X )|T →k |V k (T →k ( X )) K →k (8)
K →k = Ω p ( X )|T →k |V k (T →k ( X ))dµ( X ) (9)
where V k checks the visibility of the transformed path.

The Jacobian determinant of the transformation can be efficiently computed as a special case of [START_REF] Marschner | Manifold exploration: a markov chain monte carlo technique for rendering scenes with difficult specular transport[END_REF] [LKL * 13], since the primary hit point y is assumed non specular and the suffix path is identical for each viewers:

|T →k | = ∂x k ∂x ∂y ∂x i ∂y ∂x j -1 = r 2 k r 2 g(x , y) g(x , x i ) g(x k , x j ) g(x k , y) (10)
where x i and x j are respectively the film points at pixel i and j, and

g(a, b) = | ω ab • n b | b-a 2 .
For thin lens cameras, the Jacobian determinant is then:

|T →k | = r 2 k r 2 cos θ y y -x 2 d 2 cos 3 θx i y -x k 2 cos θ k y cos 3 θx j d 2 k ( 11
)
where d is the distance between the camera origin and the film plane (cf. Figure 4) and r is the lens radius of the camera. Given a hit generated from any observer, we first determine the set of observers who could have generated the same hit. Then for every observer in this set, we compute the pdf from the other observers and add the contribution of the path using multiple importance sampling. This strategy however may cause problems because importance functions associated with other observers can be very poor and slow down or prevent the convergence. We therefore add two selection probabilities on other observers in the multiple importance sampling framework to dampen the poor importance strategies.

Similar importance selection: Jacobian

The transformation of a path depends on the visibility and implies a change in density. Both the visibility and the Jacobian determinant appear in the pdf and in the normalization term. Two problems arise.

First, the evaluation of the normalization term of a pdf is an integral over the whole film of the observer potentially providing a path for the pixel. Computing multiple importance sampling weights requires comparing the pdfs of all the different strategies :

w →k ( X ) = p →k ( X ) ∑ j p j→k (T → j ( X )) . ( 12
)
We would therefore have to evaluate K →k (Equation 9) for each observer involved, which is a considerable overhead.

Second, the Monte Carlo estimation of integrals suffers from bias if a subdomain is insufficiently sampled due to a finite number of samples. We observe such situations in areas where large changes in density occur. This is due to the inefficiency some cameras to generate samples in such areas. Although no visibility problems occur, no sample is generated on one observer because the probability of generating one is small with respect to the sample budget. This bias results in strong artifacts in motion blur (cf. Figure 5).

To overcome these limitations, we ensure that the reused samples have an importance similar to that of native samples. We perform a stochastic selection (Russian roulette) of the prefixes using the Jacobian determinant as a similarity probability.

p jacobian ( X , Xk ) = T →k -1 if T →k > 1 T →k otherwise (13)
The Russian roulette accepts native samples with a probability of 1 ( T → = 1) and rejects samples with high or nearly zero Jacobian determinants. We show in Figure 5 that this selection strongly reduces the relative standard deviation of the normalization terms. We therefore consider the normalization terms as constants independent of the observer, and cancel them in multiple importance sampling weights without introducing noticeable bias.

Similar importance selection: material

For the integral to be correct, the contributions of the paths must be computed using the exact brdf with the right observer. Importance sampling is used to accelerate the convergence rate of the integral, by sampling paths proportionally to their contribution to the final integral. Using paths from other observers changes the importance function used. On glossy materials, this can slow down or prevent the convergence. We therefore use a second term in our selection probability for observers to ensure that their importance functions are compatible.

We thus propose a heuristic to select a subset of similar observers regarding the material parameters. Since the glossy importance functions fr(• → y → x), denoted ρ, are distributions over the hemisphere we can use distance metrics to evaluate their similarity. Several distances between distributions exists, but most of them requires a numerical integration (e.g. Kullback-Leibler, Hellinger, Wasserstein) and are not always normalized. Precomputing distance tables for all material variations of a scene is costly and hardly feasible. We therefore use the total variation (TV) distance which can be evaluated on-the-fly for microfacet distributions. The TV distance δ is the maximum difference between the pdf for the same random variable.

δ(ρ , ρ k ) = sup ω∈S |ρ (ω) -ρ k (ω)| (14)
The microfacet theory describes glossy lobes concentrated around the mirror direction for a given incident direction [CT82]. The mirror direction corresponds to the maximum intensity of a lobe and hence the maximum pdf value. The TV distance between two lobes is then computed by comparing the absolute difference of the pdf values regarding the peak of the initial distribution.

δ(ρ , ρ k ) = |ρ (ω ) -ρ k (ω )| with ω = argmax(ρ ) (15)
We can normalize the TV distance by the maximum of each distribution leading to a simpler formula. Thus, a TV distance close to zero means that the distributions are similar ; on the contrary, a value close to one indicates a high dissimilarity.

δ(ρ , ρ k ) = ρ (ω ) ρ (ω ) - ρ k (ω ) ρ k (ω k ) = 1 - ρ k (ω ) ρ k (ω k ) (16)
As a consequence, we select similar cameras by comparing each visible camera k to the initial camera that sampled y on the scene (cf. Figure 6). Figure 6: Given an initial observation direction (thick arrow), the probability for selecting other prefix directions decrease with their distance to the initial distribution. We show the distribution of probability (cf. Equation 17) over the hemisphere (left), and the pdf of the initial direction for GGX (right).

In this way, we ensure to add a substantial contribution to the initial camera and minimize the inadequate importance sampling for the others. Since the dissimilarity of glossy distributions increases with the roughness (or shininess), we found that elevating the distance to a power leads to a better fit to the reference. Figure 7 shows convergence plots of the estimators for several roughnesses using 12 cameras. The probability for selecting a camera k similar to camera finally reads:

p material ( X , Xk ) = 1 -δ(ρ , ρ k ) 1 α (17)
where α is the roughness of the surface at y. We perform the selection before testing the visibility of the prefix by coupling the Jacobian selection and the brdf selection in the same Russian Roulette step. Figure 8 shows that using this additional selection probability indeed improves the result by reducing the variance. Hence the pdf of a prefix is multiplied with the selection probabilities. After selecting the subset of similar viewpoints we uniformly sample the mixture of their lobes to continue the path. The pdf of the sampled brdf direction is then:

p(ω) = ∑ j p(ω|x j y). (18)
The path suffix is finally constructed using the classical recursive path tracing.

Adaptive sampling of the image space

Sharing paths between cameras leads to inhomogeneous sample density over the film due to occlusions and our selective path reuse. This is a classical drawback when reusing paths as pixels lacking samples cannot be predicted. For this reason we use a simple multipass adaptive strategy to fill in under-sampled areas (Figure 9).

We first proceed with a pilot iteration which distributes samples uniformly over all pixels. We then compute an error estimation Figure 7: RMSE of the integration of the GGX distribution for one direction among 12 observation directions with varying roughnesses. We compare the standard integration (purple), the multiview integration by sampling a mixture of all distributions (light blue), and the multi-view integration by first selecting a subset of similar directions and then sampling the mixture (green). The RMSE with the reference shows that our selection performs equivalently to the best strategy. It is interesting to note that the mixture without selection increases the variance of the estimators when alpha decreases. based on the χ 2 divergence [START_REF] Rigau | Refinement criteria based on f-divergences[END_REF] for each pixel. We evaluate a total variation noise estimate of the error gradient, similar to the metric proposed by Heitz et al.

[HHM18] (cf. Section 4.2). Finally, we use this noise estimate to redistribute samples during the next iteration. This scheme is iterated until a time limit or a target error is reached.

The described noise estimation highlights noisy areas and high gradients, which have been proved correlated with the variance [MKD * 16]. The adaptive scheme both redistributes samples in under sampled areas, making them imperceptible, and slightly reduces the noise in areas where error is important. However, any adaptive strategy which focuses on under-sampled areas can be used. The error estimate simply drives the maximum number of samples allocated to the pixel. Slow converging, high error pixels will get more samples than fast converging, low error pixels. Figure 10 presents the results of using the aforementioned noise estimation and Figure 11 shows the evolution of the RMSE for a given samples budget.

Final reconstruction

Each camera selected to use the path contribution adds the contribution with the following MIS weight:

w →k ( X ) = n p →k ( X )p jacobian ( X , Xk )p material ( X , Xk ) ∑ j n j p j→k ( Xj )p jacobian ( Xj , Xk )p material ( Xj , Xk ) (19
) where n and n j are the number of samples generated on the respective pixels by our adaptive sampling strategy. With our approximation that the normalization term K →k in Equation 9 does not depend on , p →k can be computed as:

p →k ( X ) = p ( X )|T →k |V k (T →k ( X )).
(20)

Results & discussion

We implemented our method into a prototype CPU path tracer supporting multi-threading in C++. All scenes were rendered on a dual Intel(R) Xeon(R) CPU E5-2640 v3 @ 2.60GHz, with 64Gb of memory running Linux. We built on top of Intel(R) Embree kernels and use the Spatio-Temporal BVH [WAB17] to load multiple animation segments at once. All test materials are modeled with a glossy lobe with GGX roughness varying from 0.5 to 0.001.

We showed the influence of the similarity selection on a test scene, a specially crafted Cornell Box, with fast moving cubes and glossy materials. This sequence is complex to render since cameras may see tangent geometry while cubes are moving, which implies large variations of the Jacobian and temporal visibility changes.

We rendered a 100 frames barbershop animation sequence with 100 cameras. The cameras shutter intervals overlap to highlight the noise reduction in motion blur, which is reconstructed using a simple triangle filter. Our method compares favorably with equal time path tracing, and achieves a good reduction in noise level with no Various statistics on the barbershop sequence are depicted on Figure 12. Figure 12a illustrates the ratio between the number of image contributions and the number of paths. This is the average number of reused paths which increases linearly with the number of observers. Please note that our prototype path tracer doesn't use coherent visibility requests and the performance illustrated in Figure 12b may not be representative of a more optimized renderer. Visibility requests and observer selection eventually cost more than building a single path. This cost is scene and renderer dependent (ray request, suffix path length, material evaluation and sampling, etc). Figure 12c illustrate the effects of the selection. Simple geometric tests filter candidate paths down to selected paths and the last visibility test filters out half the total candidates. Figure 12d compares the RMSE of the teaser image computed with different exposure intervals. These intervals provide candidate paths to select and reuse. The best results are achieved with a large exposure interval, as expected. Without temporal overlap our technique performs exactly like a path tracer in this degenerate case.

Limitations

Considering multiple observers has an overhead. Asymptotically, the overhead depends quadratically on the number of observers. Evaluating the selection probabilities is required for every observer on every path prefix. We then trace a visibility ray for each selected observer. For a large number of observers, this exhaustive observer loop will need to be replaced by a fixed sampling of the observers coupled with a proximity cache to benefit from coherency.

The efficiency of our algorithm also depends on the whole scene setup:

• the proximity of points of view: our similarity selection will not share paths between distant cameras (both spatially and directionally) ; • the scene materials: on glossy scenes many paths will not be shared ;

• the scene complexity, which directly affects the cost of visibility queries ; • the path length which changes the cost of tracing a path, and therefore decreases the relative overhead of our method.

We use a selection probability such that the importance of reused paths is similar to that of the initial one. This directly affects the number of samples we can reuse at a given time. In cases when very few or no projections occur, our method may produce poorer results than the classical one since we have an overhead, to finally obtain the same result. This is the case on the Cornell video in the supplemental, on the highly specular back wall.

Our similarity selection of brdf lobes is derived in an empirical manner and a more formal work is needed to assess its quality. A material selection proportional to a statistical measure, such as the moments of the integral could further improve the convergence of our estimators [SHSK18].

Conclusions and perspectives

We have discussed an adaptive and multi-view path tracing technique. The main contribution is an importance sampling heuristic to robustly reuse paths. Compared to previous methods, our heuristic robustly identifies and reuses similar paths with a better control over the variance of the result. Our approach builds on standard path tracing and leaves the overall pipeline unchanged. This heuristic is however derived in an ad-hoc manner and a more formal study of the brdf similarity ad its impact on the variance of the result is necessary.

Combining our simple heuristic with the different path reuse techniques is also an interesting research area.

Figure 2 :

 2 Figure 2: An example path in the traditional configuration

Figure 3 :

 3 Figure 3: Transformation from camera to camera k

Figure 4 :

 4 Figure 4: Geometric configuration for the Jacobian determinant

Figure 5 :

 5 Figure 5: Top row shows the relative standard deviation of the normalization constants (Equation9). Performing the Jacobian selection strongly reduces their variations (right). Bottom row highlights a detail of the animated Cornell Box. From left to right, the biased result without selection due to the large variations of the constants, our result with the selection, and the reference.

Figure 8 :

 8 Figure 8: At equal sample count, using our material selection (left) results in less noise on glossy materials than no selection (right).

Figure 9 :

 9 Figure9: We rendered 10 images, camera 1 (top left) and 9 camera 2 (bottom left), using our algorithm with and without adaptive sampling. Areas where visibility is not shared exhibit some high level noise in the case of uniform sampling. Adaptive sampling redistributes samples in such areas, making them imperceptible. Right insets show a comparison at equal sample count.

Figure 10 :Figure 11 :

 1011 Figure10: A Cornell box rendered with or without adaptive refinement and the associated sample map. Our noise estimate focuses well on penumbrae, speckles, indirect lightning, motion blur and gradients. For a given sample budget (256 in this case), the adaptive refinement exhibits less noise on complex areas.

Figure 12 :

 12 Figure 12: Overhead induced by path reuse

c 2019 The Author(s) Eurographics Proceedings c 2019 The Eurographics Association.

Appendix A: General Monte Carlo multiple integration

Let f A and f B be two functions integrated over a measure space Ω with given measure µ. Each integrand is non zero over a subset of Ω that we respectively denote Ω A and Ω B . Using Monte Carlo integration, these integrals can be estimated by sampling random variables in the sub-domains associated with each integral. For f A ,

The variance of this estimation can be improved using importance sampling, with a probability density functions (pdf)

Overlapping region of the integration domains (in red), which we exploit to increase the sampling of both f A and f B .

(respectively p B ∝ f B ). Suppose now that we have an injective map T such that Ω A and T (Ω B ) overlap (Figure 13). The integration can then be divided in two parts:

A change of variable in the second term gives

where |T | is the jacobian determinant of T . The pdf of such transformed samples is:

where p B (x B ) is the pdf of the sample, V A (T (x B )) is a visibility function which is zero when applied to a point out of Ω A and K is a normalization constant. This constant is not trivial and requires a numerical integration as well.

Two Monte Carlo estimators can now be used to integrate over Ω A ∩ T (Ω B ) : sampling can be done either from Ω A or from Ω B using T and a visibility test. A robust strategy to weight both estimators and reduce the variance is the balance heuristic [VG95]:

Finally, the Monte Carlo estimators of ÎA is:

and similarly for ÎB . The weight w B→A equals zero when samples can not be generated from domain Ω B and w A→A is 1 in this case.

Both functions can now be jointly integrated with Monte Carlo estimators and samples can be shared where domains overlap. This approach generalizes well to N integrands and N associated importance functions.


Dhriti Khandal

Christophe Bliard

X Coqueret

Pierre-Yves Mikus

Patrice Dole

Stephanie Baumberger

Jeremie Soulestin

) C Bliard

) X Coqueret

) P Y Mikus

) P Dole

) S Baumberger

) J Soulestin

M F Lacrampe

LignoStarch Tailored modification of starch by radiation-grafting of lignin

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The research was carried out in 4 domains: Method development, Mechanical Properties, Surface Properties, and Radiation-induced modifications.

Concept

Surface hydrophilicity decreases of the starch lignin blends after irradiation.

Mechanical Properties can be modified in presence of Ligninlike additives. Radiation-induced grafting of aromatic additives competes chain scission. Final blend properties depend on blend composition and radiation parameters.

-Hydrophobic surfaces can be obtained with q water >110° -Mechanical properties can be modified in presence of lignin-like monomers despite the ever existing chain scission -Deformation breaking mechanisms monitored by videotraction -Composition (plasticizer, aromatic additive

  ) and radiation parameters determine final properties -Aromatic additives exert strong protective effect against scission -Starch molecular architecture can be tailored as desired Salient Results xxx@xxx.fr CONTACT : Prof. Xavier Coqueret, Institut Chimie Moleculaire de Reims, URCA Reims xavier.coqueret@univ-reims.fr Amylose: Linear polymer chain with a (12010 conference, Bethesda MD Invited conferences at IMRaP 2011, Tihany Radiation Conference 2011, Gordon Research Conference on Radiation Chemistry 2012 Baumberger et al., J. Agric Food Chem, 1998, 46, 2234-2240 Lepifre et al., Biomacromolecules, 2004, 5, 1678-1686 Khandal et al., Radiat. Phys. Chem. 2012, Vol 81, No. 8 (2012), 986-990 Khandal et al., Radiat. Phys. Chem., in press 3 other publications are in process of review or submission Conferences and Publications Modifications at Molecular Level -Grafting of aromatic additives overcome chain scission -Radiochemical yields G(S) and G(X) determined f ( [arom] ) -H-bonding and supramolecular interactions affect reactivity


Guillaume Touya

Jean-François Girres

Generalising Unusual Map Themes from OpenStreetMap

Introduction

Research on generalisation algorithms mainly focused on the most prominent themes of a topographic map, namely roads, buildings, hydrography, terrain and land use. Now that many efficient algorithms exist for such prominent themes (Stanislawski et al. 2014), minor themes like ditches [START_REF] Savino | Pattern recognition and typification of ditches[END_REF] or swamp patches [START_REF] Anderson-Tarver | Fuzzy modeling of geometric textures for identifying archipelagos in Area-Patch generalization[END_REF]) gain interest from the research community. In OpenStreetMap (OSM), the loose specifications resulted in a large range of unusual themes, e.g. electric lines (Figure 1c), and generalising maps out of OSM data requires to handle such unusual themes. Moreover, another particularity of OSM is the very high level of detail that can be found for some features, compared to traditional geographical databases, e.g. airports, port sites (Figure 1a) or parks (Figure 1b). The unusual details contained in such areas also require specific algorithms to preserve the structure and the relations between the components. Generalising OSM data is a challenging task [START_REF] Sester | Integrating and Generalising Volunteered Geographic Information[END_REF] but this paper only focuses on the generalisation of those map themes or areas exhibited in OSM. The second part of the paper describes algorithms to generalise airports and their components. The third part focuses on railways generalisation. The last part concludes and presents some perspectives.

Generalising Airports

Modelling Airports

Airports are composed of specific features that are generally well captured in OSM: runways, taxiways, aprons and terminals, for instance (Figure 2). Additional features like helipads, hangars or windsocks are omitted here to focus on the main features. These features can either be polygons or lines, and when scale decreases, generalisation is clearly required to typify these features (Figure 2). In order to generalise airports properly, airports are modelled as complex objects composed of these features, that sometimes can either be lines or polygons (Figure 3). Several algorithms are proposed to generalise these features: runway collapse, taxiway collapse and typification, apron and terminal amalgamation, and algorithms change whether the taxiways/runways are lines or polygons. Figure 4 show a simplified version of the proposed generalisation guidelines for OSM airports, into a ScaleMaster [START_REF] Brewer | Framing Guidelines for Multi-Scale Map Design Using Databases at Multiple Resolutions[END_REF]. Airport features are mainly large scale features, as all should be removed at the 1:200k for instance (only the extent with a ponctual symbol should be represented from these scales). The algorithms described in the next subsections can be used gradually to increase the generalisation level as scale decreases. Only runway and taxiway algorithms are presented here for the sake of brevity.

Runway Collapse

Runways are long straight polygonal lanes that need to be collapsed into straight lines when scale decreases. Rather than complex skeletonizing algorithms, we use the longest segment that can be drawn inside the runway polygon that is parallel to the orientation of the polygon [START_REF] Duchêne | Quantitative and qualitative description of building orientation[END_REF]) (Figure 5). As the general orientation algorithm is based on the minimum bounding rectangle of the runway polygon, it is not so sensible to the granularity of the geometry. As a consequence, the algorithm obtains good straight generalised runways for airports found across the world in OSM.

Taxiways Collapse and Typification

Taxiways can have either polygonal geometries or linear geometries. When geometries are polygons, taxiways have to be collapsed, beginning by the thin parts, and then including all taxiways as scale decreases. A complete collapse algorithm like the one by [START_REF] Szombara | Unambiguous collapse operator of digital cartographic generalisation[END_REF] could be used, but we chose a two-steps process: first thin parts are identified by erosion, and then the thin parts are skeletonized.

To skeletonize taxiways, a three-step process is proposed. Polygonal taxiways in OSM are generally represented through a complex assembly of connected polygons. Thus, adjacent borders of neighboring polygons (of taxiways and runways) are firstly detected (Figure 6a) in order to preserve the structure of the taxiway network. To collapse taxiways, the skeleton is obtained using Voronoi diagrams extracted from a triangulation (Figure 6b) in each polygon. Diagrams are then connected through adjacent borders detected in the first step, and finally pruned and filtered in order to generate linear taxiways, as exposed in Figure 6c. For instance, in the example of the generalisation of taxiways on Blagnac airport in Figure 6, a minimal length of 100 meters is needed to preserve linear taxiways. Figure 6. Three-step process to collapse taxiways on Blagnac airport. ©OpenStreetMap When taxiways are lines, two algorithms are proposed: crossroad typification and stroke-based selection. Complex crossroads are identified using graph and shape measures (Figure 7) and collapsed by creating a simple connection, like branching crossroads can be collapsed in a road network. More precisely, three types of complex crossroads are identified in all studied airports with linear taxiways: simple branchings (in red in Figure 7), branchings with a central connection (in pink), and double branchings (two connected simple branchings, in blue). For instance, the simple branchings are the taxiway graph faces with three edges and three degree-3 nodes, that have a triangular shape. Then, the edge to keep is identified by angle considerations, and the node that is not connected to this edge to keep is extended to reach the edge (Figure 7). Similar methods are applied to both other types of complex crossroads. Figure 7. Linear taxiway complex crossroads are identified (coloured areas) and collapsed.

Then, strokes are computed and only the longest ones are selected. Length threshold are related to the scale of the generalised map. For instance, taxiway strokes smaller than 0.4 map mm are removed. If a stroke connects two other strokes that are above the threshold, it is kept to preserve connectivity.

Results

Figure 8 shows some 1:25k generalisation results in three airports in different countries (Lyon, Vienna and Rio) to show robustness across countries. In this case, all three airports had linear runways and taxiways so generalisation algorithms were triggered on taxiway lines, aprons and terminals.

Generalising Railways

Railway networks are composed of main railway lines and sidetracks, isolated or grouped in triage areas. Main tracks can simply be generalised by a stroke-based selection [START_REF] Thomson | Generalisation of geographic networks[END_REF]. But, due to OSM heterogeneity, main tracks are sometimes divided in two or more parallel lines corresponding to the rail lanes (Figure 9). In this case, a collapse into a single lane is necessary before stroke-based selection can be applied.

Collapsing Main Railways

To collapse such parallel railway lines, the first step is the identification of the railway portions where such a structure appears. Using the spatial relation model from [START_REF] Touya | Towards an ontology of generalisation constraints and spatial relations[END_REF], the sections where two railways are close and parallel are identified, and then collapsed using a computed average line between both sections (Figure 10). When more than two sections are involved (Figure 9), the average is computed between all the sections. Figure 10. Results of main railways collapse (collapsed line in pink).

Two types of junctions can occur for parallel railway lines: parallelism ends with one or more lines turning in a different direction, or the lines intersect (Figure 11). The intersection case is easy to handle with the intersection point used as the final point of the collapsed line. When some lines change directions, the lines are reconnected at the point with parallelism ends (Figure 11).

Sidetracks Typification

When grouped in a triage area or a train station, sidetracks are grouped in a particular structure that needs to be preserved by typification as scale decreases (Figure 12). Sidetracks are identified when a line is tagged by both "railway" and "service" tags. Triage areas are then identified by grouping sidetracks by connexity. Strokes [START_REF] Thomson | Generalisation of geographic networks[END_REF] are computed inside each triage areas and sorted according to length by descending order. As long as it is bigger than a minimal length, long strokes are selected and the surrounding strokes (that are shorter) are removed from the list to avoid symbol overlap. Finally, if the selected strokes are not connected to the main railways, features enabling connection are selected. Results can be seen in Figure 12 for a generalisation to 1:25000 scale.

Discussion

Due to the varying expertness of contributors, and the imprecision of some capturing methods (e.g. recognition on satellite imagery), the quality of OSM data is very heterogeneous [START_REF] Girres | Quality assessment of the french OpenStreetMap dataset[END_REF][START_REF] Haklay | How good is volunteered geographical information? a comparative study of OpenStreetMap and ordnance survey datasets[END_REF]. This heterogeneity has an impact on generalisation processes that are mostly designed for good and homogeneous data. Regarding, the unusual themes presented in this paper, some railroad sections might be disconnected to their neighbours, for instance, which makes the proposed algorithms useless. We believe that one way to tackle the heterogeneity is to provide correcting pre-processes with each algorithm, which correct the data regarding the algorithm requirements. For instance, our railway algorithms require a planar graph (the OSM specification recommend to capture the railways as a planar graph). So the algorithms are combined with a pre-process that makes the railways network a planar graph.

Despite this quality heterogeneity, most airports are similarly captured across countries (Figure 13), because of the unique set of specifications, and airports can be captured from aerial photos by european contributors all over the the world. So a generalisation process set up with european airports is quite applicable elsewhere in the world.

Figure 12. Airports in different parts of the world: they are captured similarly. ©OpenStreetMap [START_REF] Touya | Detecting Level-of-Detail inconsistencies in volunteered geographic information data sets[END_REF] shows that there is also a level of detail heterogeneity in OSM. Geographical features are not always captured at the same level of detail for different themes (e.g. cadastral buildings vs. forests from Corine LandCover dataset), and even in the same theme, as objects may be captured with sources (GPS tracks, satellite imagery) at different levels of detail. Taxiways are a good example of this level of detail heterogeneity as it is sometimes captured with details at complex junctions (e.g. Chicago in Figure 12), and sometimes with simplified representations (e.g. Dakar in Figure 12). As a consequence, similar objects do not require the same degree of generalisation for a same final scale, as the initial level of detail may differ (i.e. there no need for complex junctions collapse in Dakar airport).

Traditional generalisation orchestration seeks to analyse the geographical context of an object (or a group of objects), in order to find the best suited algorithms and parameters for this object regarding its context. With OSM, we believe that orchestration also has to analyse the quality and level of detail of the objects to generalise, in order to choose the best suited algorithms.

Conclusion and Further Work

To conclude, making maps out of OSM data requires the development of new algorithms either because new type of geographical features are included in the dataset, or because new geographical structures to generalise emerge from the high details OSM data can have in some active areas. In this paper, algorithms are proposed and tested in OSM data, for airport features and railways.

Map generalisation is not only about algorithms, and the main difficulty is to orchestrate the use of the algorithms in an automatic process. So, to go further, the proposed algorithms have to be included in orchestration processes like CollaGen [START_REF] Touya | CollaGen: Collaboration between automatic cartographic generalisation processes[END_REF] or the ScaleMaster2.0 [START_REF] Touya | ScaleMaster 2.0: a ScaleMaster extension to monitor automatic multi-scales generalizations[END_REF]. Moreover, other types of unusual map themes, such as the ones presented in Figure 1, have to be tackled, in order to improve automatic mapping from OSM data.

Figure 1 .

 1 Figure 1. Sites with unusual detail ((a) a port and (b) a park), and unusual map theme ((c) electric lines) found in OpenStreetMap. ©OpenStreetMap

Figure 2 .

 2 Figure 2. Highly detailed airport: when zooming out (pictures on the right), such details require generalisation. ©OpenStreetMap

Figure 4 .

 4 Figure 4. ScaleMaster (Brewer & Buttenfield 2007) modelling of airports generalisation.

Figure 5 .

 5 Figure 5. Principles of the runway collapse algorithm and results on Blagnac airport on the right. ©OpenStreetMap

Figure 8

 8 Figure 8. 1:25k generalisation of three airports in Lyon, Vienna and Rio.

Figure 9 .

 9 Figure 9. Three, then four parallel railway lines. ©OpenStreetMap

Figure 11 .

 11 Figure 11. Results of main railways collapse (collapsed line in pink).

Figure 12 .

 12 Figure 12. Results of sidetracks typification around the main station of Pau. ©OpenStreetMap