A Saadi

M Becherif
email: mohamed.becherif@utbm.fr

D Hissel

A Aboubou

State space modeling of PEM Fuel Cell with a Moto-Compressor System

A proton exchange membrane fuel cell (PEMFC) system is composed of four main subsystems. In this paper, the air supply subsystem with the fuel cell is described by a nonlinear fourth order state space model. The model of the PEMFC is obtained from an equivalent electrical circuit; it combines the simplicity of an electrical circuit and attempts to model the physical phenomenon occurring inside the fuel cell. The effect of temperature variation and relative humidity on the cell are considered in this model. The compressibility of fuel, and oxidant fluids and condensation of water are also taken into account. The most used model in the literature is the nine state model proposed by Pukrushpan, thereafter reduced to the four states by Suh and Stefanopoulou, which was then reduced into three states by Talj and al. Despite the good results for average power, the major disadvantage of this last model is the obligation to start the simulation with the complete states space model due to the presence of a division over the moto-compressor speed in the model. This paper proposes an interesting dynamic model using a simple four order state space models for the moto-compressor group associated to the PEMFC stack which is suitable for purposes of control or diagnosis. The obtained simulation and experimental results for low power are successful and give the first step of the control purpose.

Introduction

Fuel Cells (FCs) can offer a highly efficient environment and friendly electrochemical transformation for energy conversion. They are widely considered as a potential alternative power source and have drawn much attention and intensive development for commercial stationary power generation, residential applications, transportation technologies and vehicles. The heart of FC is a device involving multi-physics coupling phenomena: mass transport (in the electrodes and electrolyte), charge transport (in the electrode), and electrochemical kinetics (at reactive sites). Problems are added to these phenomena which are thermal and distribution of reactive gases. Many mathematical models can locally describe these phenomena by means of partial differential equations involving space and time. These models are accurate, but they are, most of time, unusable for a system approach. That is the reason why other models appeared including dynamic models. Some of these models represent FC equivalent electrical circuit. This approach aims at establishing a simple and reliable model of the FC. Over the years, scientists have presented many FC electrical equivalent circuit models. For instance, [START_REF] Yuvarajan | Characteristics and modeling of PEM fuel cells[END_REF] includes the mass transport effect and the pressure regulator effect which is characterized by two transistors and a resistor. Both form a current limiting circuit that models the polarization of concentration, the parasitic resistance of the diode models the FC ohmic polarization. At the same level, the mass transport effect and the losses in FC are slightly differently presented by another equivalent circuit where two capacitors are used instead of one [START_REF] Yu | A novel circuit model for PEM fuel cells[END_REF]. The most used model in the literature is the nine states model proposed by Pukrushpan [START_REF] Pukrushpan | Control-Oriented Modeling and Analysis for Automotive Fuel Cell Systems[END_REF]. However, the large number of states restricts its use in control applications, due to the large number of the calculations. Hence, a reduced order is required. [START_REF] Suh | Analysis and control of Fuel Cell Hybrid power systems[END_REF] is a recent reduced order model for this application. The obtained one is of fourth state spaces order under some assumptions. [START_REF] Talj | A reduced-order model and a higherorder sliding-mode control of the air supply system of a proton-exchange-membrane fuel cell with experimental validation[END_REF] and [START_REF] Talj | Experimental validation of a PEM fuel cell[END_REF] propose reduction into four states by replacing the partial pressure of oxygen by the cathode pressure, under the assumptions that molar mass of oxygen, nitrogen and water have almost the same magnitude and the air-flow in the cathode. Then, a higher order sliding mode controller has been designed using super-twisting algorithm. But the major disadvantage of four states model is a division over the compressor angular speed. Thus the system is obliged to start with the complete model and is switched to the four states model [START_REF] Talj | A reduced-order model and a higherorder sliding-mode control of the air supply system of a proton-exchange-membrane fuel cell with experimental validation[END_REF]. In order to remedy to this and to synthesize a good control law, a comprehensive dynamic model is proposed in this paper. The modeling approach is based on the principles of conservation of mass, charge, momentum and energy. To get a brief overview of the FC electrical equivalent models, one is advised to go through [START_REF] Hernandez | Modeling and Fault diagnosis of a Polymer Electrolyte Fuel Cell Using Electrical Equivalent Analysis[END_REF] and [START_REF] Runtz | Fuel cell equivalent circuit models for passive mode testing and dynamic mode design[END_REF]. Moreover, the air supply subsystem with the FC is described by a nonlinear fourth order model where the state vector is composed of the oxygen and nitrogen partial pressures in cathode and the angular speed manifold. The stack current is traditionally considered as a measurable disturbance to the system while the control input is the compressor motor voltage [START_REF] Pukrushpan | Control-Oriented Modeling and Analysis for Automotive Fuel Cell Systems[END_REF]. The compressibility of fuel and oxidant fluids and condensation of water are also accounted for in this model. [START_REF] Hernandez | Modeling and Fault diagnosis of a Polymer Electrolyte Fuel Cell Using Electrical Equivalent Analysis[END_REF] proposed it for diagnosis purpose. The model has been validated in [START_REF] Becherif | Electrical Equivalent Model of a PEM Fuel Cell with Experimental Validation[END_REF] on a low power PEMFC. This paper proposes an interesting and simple four order state space model for the group moto-compressor with PEMFC which is suitable for the control or the diagnosis tasks. This paper is organized as follows. The second section gives a complete description of FC system model, which is composed of two parts; the electrical equivalent model of a FC and the moto-compressor model. The third section gives the validation of simulation results by comparing them with experimental results, and the final section is a conclusion.

Fuel Cell System Model

In order to produce energy, it is necessary to integrate the fuel stack with other components to form a fuel-based power generator system. Classically, four auxiliary systems can be considered: hydrogen supply system, air supply system, cooling system, and humidification system. In Fig. 1, it is assumed that a compressed hydrogen tank is used. Thus, the control of hydrogen flow is achieved simply by controlling the hydrogen supply valve to reach the desired flow or pressure. The air is assumed to be supplied by an air compressor which is used to increase the power density of the overall system.

Fuel cell electrical equivalent circuit model

The FC electrical equivalent model is obtained by setting an equivalent electrical component to account for the pneumatic behavior. This equivalence is based on the conservation principles of mass, charge and energy. Following the Bernoulli's laws of continuity, mass and energy flow are conserved in a pipe for an incompressible fluid; however, there will be losses due to friction and geometry of the pipes. The compressibility of the fluid adds a storing capacity to the pipes. Hence, the molar flow rates in a pneumatic system can be analogous to the flow of charge. The gases that are being passed through the channels are compressible. This later is determined by the volume that the channel can hold under given pressure and temperature conditions. This is analogous to a capacitor in an electrical system which is capable of accumulating charge under transient conditions and acts as an open circuit when steady state is achieved. Based on these information, [START_REF] Hernandez | Modeling and Fault diagnosis of a Polymer Electrolyte Fuel Cell Using Electrical Equivalent Analysis[END_REF] developed an equivalent electrical circuit which is shown in Fig. 2. See [START_REF] Hernandez | Modeling and Fault diagnosis of a Polymer Electrolyte Fuel Cell Using Electrical Equivalent Analysis[END_REF], [START_REF] Becherif | Three order state space modeling of proton exchange membrane fuel cell with energy function definition[END_REF] and [START_REF] Hernandez | Diagnostics of PEM Fuel Cells[END_REF] for more details.

dt dn Q  (2) With: out m in m in m Q Q Q , , ,   (3)
The gases that are being passed through the channels are compressible. This compressibility is determined by the volume that the channel can hold under given pressure and temperature conditions. This is analogous to a capacitor in an electrical system which is capable of accumulating charge under transient conditions and acts as an open circuit when steady state is achieved. The model is based on some assumptions listed as follows: All the gases are ideal gases. The interaction between different species is negligible ignored. The principle of superposition for electric circuits is applicable. The pressure changes produced by the velocity of the flow are negligible. The changes in the volume of channels are considered negligible. The flow is assumed to be laminar. The losses due to fuel and oxidant crossover are considered to be negligible. The only species that diffuse through the membrane are nitrogen and water. The water is introduced only on the cathode side.

The channel pressure for anode and cathode is taken to be the average of the inlet and outlet pressures.

Q Q Q Q Q v Q v Q v Q         , , , , , (4)
Q Q Q v Q v Q Q Q Q Q m N          , , , , (5)
  c or a i V Q R R V i i out i ch i out i Cf     ; (6)   c or a i V Q R V i Cf i in i in i in    ; (7)   a a out a ch a out m w m Cf V Q R R R V i in     , 5 . 0 (8) c or a i C Q dt dV i f i Cf i Cf   ; (9) m f m Cf m Cf C Q dt dV  (10) m N m N ca Q R V , ,  (11)
Where Vj denotes the molar volume of j where j={w for water, o for oxygen or h for hydrogen}. And i={a for anode, or c for cathode}.

Moto-Compressor model

PEMFCs can operate from pure oxygen (case of cells used in submarines and spacecraft for example). It is then stored in a pressurized tank. For terrestrial applications, stationary or embedded FCs are mostly supplied with ambient air. The use of a compressor is not without consequences on the overall system performance. It is powered by the FC and it takes a non-negligible power which can represent up to 25% of the electrical power supplied by the FC. The compressor is very important in FC system, and many technological barriers are resolved in this field. It must allow the air supply, dispose produced water without drying the membrane of the cell and ensure good system dynamics. The centrifugal volumetric compressors are among the compressor types commonly used in FC system. The air supply system, designed to feed in parallel two PEMFC, each is composed of a PMSM driving a volumetric compressor of type double screw. The air flow control problem is converted into a PMSM speed control problem [START_REF] Chang | An optimal speed controller for permanent-magnet synchronous motor drives[END_REF] that is composed of a cascaded control loop, where the outer loop controls the velocity and generates the reference of the quadratic current component ; and the inner loop controls the three-phase current and generates the desired control inputthe voltage that feeds the motor [START_REF] Genre-Grandpierre | Alimentation en air d'une pile à combustible: Conception du système, Caractérisation, Modélisation[END_REF]. For the inner loop, the desired direct component of the current is chosen to be . From and already defined as the output of the velocity controller, one can reconstruct the desired threephase current using the inverse Park transformation. Comparing with the measured three-phase current a simple hysteresis can be used to control the current and generates the voltage. The compressor motor torque is gives by the follow equation:

(

Where is motor constant and is the motor mechanical efficiency. The angular speed dynamics or acceleration is given by the following mechanical equation:

( ) (17)
Where J cp is the compressor motor inertia, and respectively denote the compressor motor torque and the friction torque.

(18) where is the compressor efficiency, is the ratio of specific heats of air, C p is the specific heat capacity of air and Wcp is the compressor mass flow rate. The supply manifold air pressure dynamics are defined by the (21) equation, where V sm is the supply manifold volume and T cp is the temperature of the gas leaving the compressor.

[( ) ] (19)
In commercial PEMFC systems, the following variables are available for measurement, and can be defined as output:

[ ] [ ] (20)
Where , and are the stack voltage and the supply manifold pressure. The air flow at the output of the compressor is a function of the angular speed of the compressor and the supply manifold pressure, given as follows [START_REF] Genre-Grandpierre | Alimentation en air d'une pile à combustible: Conception du système, Caractérisation, Modélisation[END_REF] ( )

Where is the volumetric efficiency. is the compressed volume per turn and is the air density.

The net power of the FC system, P net , which is the difference between the power produced by the stack, P st , and the lost powers due mainly to the auxiliaries. The majority of the lost power for an automotive FC system is spent on the air compressor.

(22) ( ) (23) (24)
It can be seen that the system state space equations are complicated, based on many parameters. For ease of comprehension, the constant parameters have been regrouped, and the complete dynamic model is of 4-th state space vector

  T x x x x x 4 3 2 1  (25)
Where x 1 and x 2 are the cathode and membrane pressures, respectively, x 3 is the angular speed of volumetric compressor and x 4 is the air pressure in the supply manifold. The control input is the motor's quadratic current. All the constant parameters C i , i=1,...,7 are depending on the FC physical parameters. The reader can refer to [START_REF] Becherif | Three order state space modeling of proton exchange membrane fuel cell with energy function definition[END_REF] for more details on the parameters C i . The complete system can be written as follows.

̇ ̇ (26) ̇ [( ) ] ̇

Validation of simulation results

The data used in the simulation are collected from a 20-cell PEMFC stack with 100 cm 2 area of each cell, membrane thickness is 25µm and the nominal power is about 400W. Many physical parameters involved in the stack can be measured. The inlet/exit measured magnitude are flow rates cathode and anode channel, inlet/exit air pressures of cathode and anode, average temperature and humidity of FC, the stack voltage and current which is traditionally considered as a measurable disturbance to the system. The equivalent electrical circuit model is based on modeling of anode, membrane and cathode. The stack current is traditionally considered as a measurable disturbance to the system. Moreover, the losses voltages: activation, concentration and ohmic are depend of the current. The hydrogen pressure is calculated as an intermediate step for calculating the thermodynamic voltage which is obtained by Nernst equation. The stack voltage is also the difference between thermodynamic and losses voltages. During these tests, different current steps are applied to the FC stack to exhibit the steady state and transient behavior. Firstly, the FC is turned on with a power of about 400W with a load that consumes a current of about 30 A shown in Fig. 3b. In the figure (a), the voltage of stack starts from the open circuit voltage (OCV). Apart from this zone, the simulation voltage is considerably close to voltage experimentally obtained, both are about of 14 V, and the error is less than 1.45% in the permanent regime.

The simulation powers are drawn on figure 4. This curve indicates the precision of the system's state space model. The stack power presents the sum of two powers; net and compressor power respectively. The compressor power is transferred into mechanical power which is provided in the form of motor speed.

Figure 1 .

 1 Figure 1. Fuel cell system description[START_REF] Pukrushpan | Control-Oriented Modeling and Analysis for Automotive Fuel Cell Systems[END_REF]

Figure 2 .

 2 Figure 2. Complete circuit of FC: anode, cathode and membrane

Figure 4 .Figure 3

 43 Figure 3. a) Simulated and experimental voltages; b) Simulated and experimental current

Conclusion

In this paper, the state space modeling of PEM fuel cell system with the motor-compressor group is achieved, the obtained nonlinear fourth order model interlaced with electrical equivalent FC circuit model is successfully validated. The obtained model is suitable for the control and the diagnosis purposes, unlike other developed models in the literature [START_REF] Talj | A reduced-order model and a higherorder sliding-mode control of the air supply system of a proton-exchange-membrane fuel cell with experimental validation[END_REF] and [START_REF] Talj | Experimental validation of a PEM fuel cell[END_REF]. The motor-compressor speed varies from zero value to desired value and the system is characterized by good performance stability and robustness. The transient and permanent regimes are providing satisfactory results and closeness to the experimental results. The proposed model is simpler compared to the complexity of the nine states model [START_REF] Pukrushpan | Control-Oriented Modeling and Analysis for Automotive Fuel Cell Systems[END_REF]. In addition, the simulation is not time consuming. The obtained results are good, and they establish an important stage towards control.

NOMENCLATURE


J-C Beugnot

S Lebrun

G Pauliat

H Maillotte

V Laude

T Sylvestre

Observation of surface acoustic wave Brillouin scattering in optical microfibers

We report the observation of surface-acoustic-wave Brillouin scattering (SAWBS) in a subwavelength-diameter fiber and show that this effect relies on the generation by the electrostrictive force of phonons confined at the surface of the microwire.

Brillouin scattering between sound and light waves has been extensively investigated in optical fibers. It is wellknown that silica optical fibers support many transverse and longitudinal elastic waves over a broad frequency range from 50 MHz to 11 GHz, that lead to guided-acoustic-wave Brillouin scattering (GAWBS) and stimulated Brillouin scattering (SBS), respectively [START_REF] Sylvestre | Nonlinear Fiber Optics[END_REF].

In this work, we demonstrate, for the first time to our knowledge, the generation of a new class of surface acoustic waves (SAW) in subwavelength-diameter optical fiber (SDOF) owing to the strong coupling between sound and light at interface between the optical microwire and the surrounding air. These SAW modes or Rayleigh waves cannot be optically excited in standard single-mode fiber (SMF), but they also have recently been evidenced in whispering gallery modes (WGM) microresonators and in silica microspheres [START_REF] Matsko | Optomechanics with Surface-Acoustic-Wave Whispering-Gallery Modes[END_REF][START_REF] Bahl | Stimulated optomechanical excitation of surface acoustic waves in a microdevice[END_REF]. In our experiment, we investigated a 8-cm long silica optical microwire drawn from a commercial single-mode fiber (SMF) by hydrogen flame. It has a waist of 1 µm and linear losses of 0.1 dB/cm at 1.55 µm. We then performed spontaneous Brillouin backscattering measurements at 1.55 µm using a standard heterodyne detection [START_REF] Beugnot | Complete experimental characterization of SBS in photonic crystal fiber[END_REF]. Figure 1(a) shows the spontaneous Brillouin spectrum for an input CW power of 100 mW. Several peak frequencies with different weights and linewidths can be seen in a frequency range from 6 GHz to 11 GHz. The highest frequency peak at 10.86 GHz comes from the standard SBS in the untapered SMF sections of about 2 m long. We can also observe in Fig. 1(a) three other acoustic frequencies centered at 8.33 GHz, 9.3 GHz and 10 GHz, respectively. Like in SMF, these three acoustic modes exhibit a spectral linewidth around 25 MHz in agreement with the acoustic phonon lifetime in fused silica. Two other acoustic resonances at lower frequencies around 6 GHz can also be observed in Fig. 1(a). To identify the physical origin of these elastic resonances, we performed numerical calculations of the phonon wave packets by solving the elastodynamics equation subject to an electrostrictive force (for detailed calculations, See Refs. [START_REF] Beugnot | Electrostriction and guidance of acoustic phonons in optical fibers[END_REF][START_REF] Laude | Generation of phonons from electrostriction in small-core optical waveguides[END_REF]). With this model, we are able to fully characterize the optoacoustic properties of our silica microwire including both the forward and backward Brillouin spectra without the requirement of a full band structure. We also consider in our model the phonon lifetime by taking into account the elastic losses assuming a complex tensor [START_REF] Thurston | Elastic waves in rods and clad rods[END_REF]. This loss model is compatible with the usual assumption that the product of the quality factor Q and the acoustic frequency is a constant for a given material (e.g., for silica, Q×f =5 THz). Figure 1(b) shows the normalized elastic energy distribution versus the acoustic frequency and for varying the waist diameter from 1 µm to 1.35 µm. The elastic energy distribution gives an overview of the theoretical Brillouin spectrum. As it can be seen, we retrieve most of the acoustic resonances experimentally observed in the waist region of the microwire. There is however a slight difference with experiment in frequency position that can be attributed to the nonuniformity of the microwire, but we can clearly identify the two modes around 6 GHz and the 3 other ones around 9 GHz. To go further into detail, we plot in Fig. 1(c) the spatial distribution of the optical mode intensity in the waist region at a wavelength of 1.55 µm. The black circle marks out the interface between the optical field inside the microwire and the strong evanescent field outside the wire. A large portion of this evanescent field enables the diffusion of light by surface acoustic wave and the highly confined optical field into the microwire induces an electrostrictive force 20 times larger than in SMF [START_REF] Laude | Generation of phonons from electrostriction in small-core optical waveguides[END_REF]. Figure 1(b) shows this electrostrictive force distribution, which was numerically calculated from our model. The kinetic energy density or elastic energy of the two surface acoustic waves at 5.382 GHz and 5.772 GHz are plotted in Figs. 1(e,f) for a waist of 1.05 µm. The elastic energy is mainly localized at the surface of the microwire, unlike the longitudinal acoustic waves, shown in Figs. 1(g,h), for which the generated phonon wave packet is guided inside the microwire's core by the optical force. Thus these SAW modes can only be excited in sub-wavelength waveguides exhibiting a strong evanescent field. They propagate along the surface with an acoustic velocity of 3410 m/s, which is lower than both the shear velocity (3740 m/s) and the longitudinal velocity (5960 m/s) [START_REF] Thurston | Elastic waves in rods and clad rods[END_REF].

To summarize, we demonstrated in an optical microfiber with a 1 µm waist the efficient generation of surface acoustic wave Brillouin scattering (SAWBS) at new frequency around 6 GHz. This work should contribute to a further understanding of the intriguing nonlinear opto-acoustic interactions in sub-wavelength optics. In addition, SAWBS could be used in various sensor applications since the SAW frequency should strongly depend on the material surrounding the optical microwire.

This work is supported by the Université de Franche-Comté and the ANR LABEX ACTION.

Figure 1 :

 1 Figure 1: (a) Experimental Brillouin scattering spectrum measured at 1.55 µm in 8-cm long silica optical microfiber with a waist of 1 µm and for a CW pump power of 100 mW. (b) Computed elastic energy of phonon wave packet (i.e., the theoretical Brillouin spectrum) versus the acoustic frequency and for a microwire waist varying from 1 µm to 1.35 µm. The black line shows the SBS phase-matching condition (K=2Kp). (c-g) Numerical results for a 1.05 µm silica rod diameter. (c) Optical power in the fundamental TE-like mode at a wavelength of 1.55 µm (neff = 1.1887). (d) Spatial distribution of the electrostrictive force with 1 W optical power. (e,f) Elastic energy density of resonant surface acoustic waves at 5.382 GHz and 5.772 GHz, respectively. (g,h) Elastic energy density of longitudinal acoustic modes at 8.37 GHz and 9.235 GHz.


Hayet Hammami

Gaëlle Calvary

Meriem Riahi
email: meriem.riahi@ensit.rnu.tn

Faouiz Moussa
email: faouzimoussa@gmail.com

Sara Bouzit

Comparative Evaluation? Yes, But With Which Alternative UI?

User's feedback provides valuable information suitable to help designers to improve their work. In this paper, we present a study on user's feedback when evaluating a User Interface (UI) by comparison. Our aim is to define the properties that the alternative UI must satisfy to maximize the benefits of comparative evaluation.

The UIs considered in the study were designed using the CAMELEON Reference Framework (CRF), covering variations at each level of abstraction. We study the impact of each variation on users' feedback. We show that when the alternative design refers to the same task model as the original one but using a different abstract UI, the number of negative returns is significantly higher, making the comparative evaluation more productive.

HCI. UI Design. UI Evaluation. Feedback. CAMELEON reference framework.

INTRODUCTION

Users' feedback is important for the design process. Critiques, opinions and suggestions are valuable information to improve the design [START_REF] Nguyen | Fruitful Feedback:Positive Affective Language and Source Anonymity Improve Critique Reception and Work[END_REF], (Hui, 2015). B. Gates tells that "We improve our products, based on feedback, until they're the best". Traditionally when asking for users' feedback, designers present only one User Interface (UI), the one to be tested. However, as demonstrated in (Tohidi, 2006) providing several design alternatives to the assessor increases the amount of feedback and facilitates comparative reasoning. However, to the best of our knowledge, there is not yet any research studying the characteristics that the alternative design must satisfy in order to maximize the benefits of the evaluation.

This research aims to improve the comparative assessment by producing the optimal alternative design, i.e. maximizing returns to the original UI. In this paper, we report an experiment, where we use the CAMELEON Reference Framework to generate UIs depending on different classes of variations of a design and we study their impact on users' feedback through a comparative evaluation. This study is expected to support the definition of criteria that the alternative design must meet to maximize feedback on the UI of interest.

In this paper, we describe our approach and experiment. First, we provide a discussion on related work. Then, we present preliminary studies for conducting the experiment. Finally, we report the experiment and discuss the evaluation results.

RELATED WORK

Testing many is better than testing one

Working with examples has proven to have several benefits for both the learning process and the outcome (Lee, 2010). Accordingly, designers often use examples for inspiration, which offers contextualized illustrations of how form and content integrate. According to [START_REF] Herring | Getting inspired!: understanding how and why examples are used in creative design practice[END_REF], examples are crucial to design activities. They support both the generation of new ideas and the selection of interesting ones. Examples enable to identify limitation of previous designs, as well as reinterpretation and recombination of ideas (Masson, 2011).

Besides using alternative designs and examples during the design process, it has been proved that using multiple designs can also improve the results of the design evaluation. Creating multiple prototypes facilitates comparative reasoning, grounds team discussion, and enables situated exploration (Tohidi, 2006).

In [START_REF] Wiklund | Does the Fidelity of Software Prototypes Affect the Perception of Usability? In procedings of[END_REF], Wiklund et al. studied the impact of the fidelity of software prototypes on the perception of usability. The result of their research lead to this observation:

In studies such as this one, we have found subjects reluctant to be critical of designs when they are asked to assign a rating to the design. In our usability tests, we see the same phenomenon even when we encourage subjects to be critical. We speculate that the test subjects feel that giving a low rating to a product gives the impression that they are "negative" people, that the ratings reflect negatively on their ability to use computer-based technology, that some of the blame for a product's poor performance falls on them, or that they don't want to hurt the feelings of the person conducting the test. [START_REF] Dicks | Mis-Usability: On the Uses and Misuses of Usability Testing[END_REF] show that when people are shown multiple prototypes, they could feel less pressured to impress the experimenters by praising a particular design. Being presented with multiple alternative designs may allow for a more accurate comparative evaluation.

Tohidi et al. (Tohidi M. W., 2006) examined the differences that would occur between a usability test that exposed users to a single design, and one where they were exposed to three different alternatives. This study showed that designs are rated higher when seen alone than they would be when seen in comparison with other designs. Additionally, the number of designs given to evaluate can influence the quantity, quality, and responsiveness of the feedback.

However, in their study, there was no discussion about how to choose the alternative designs given to users during the usability test.

In our work, we investigate the impact of the alternative design given during the comparative evaluation on the user's feedback. We believe that the choice of this UI could remarkably influence the feedback received from users.

CAMELEON reference framework

CAMELEON is a Reference Framework (CRF) for the development and execution of UIs in multiple contexts of use, a context of use being defined as a triplet <User, Platform, Environment>. It structures the design process into four levels of abstraction for ensuring UIs consistency by design, and thereby saving costs of development and maintenance (Calvary, 2003). The four levels of abstraction are (Figure1):

 Task and domain is the top level that describes the users tasks the interactive system must support, together with the information (the domain concepts) that are manipulated by these tasks,  Abstract User Interface (AUI) makes design decision about grouping and navigation,  Concrete User Interface (CUI) makes design decisions about rendering. It defines how the UIis perceived and can be manipulated by users,  Final User Interface (FUI) is the running UI.

Design decisions are about the programming or mark-up language to be used.

Figure 1. A simplified version of the CAMELEON Reference Framework

These four levels of abstraction are structured with a relationship of reification (going from an abstract level to a concrete one) and/or abstraction (going from a concrete level to an abstract one) (Calvary, 2003).

PRELIMINARY STUDIES

We conducted an experiment in which participants had to evaluate different designs. Each design is generated depending on a different variation of the first three abstract levels of CRF: task and domain, AUI and CUI.

Our goal is to identify which UI influences user's feedback the most and then to define the criteria that alternative UIs must meet to maximize returns on the UI produced by the designer.

We assume that these variations affect the user's feedback as follows:

H1: The choice of the alternative design conditions the user's return to the original one.

H2:

The comparative evaluation will be more productive with a design that has the same task model but a different abstract UI.

Method

We start by creating different designs for the same application following CRF. Therefore, we first define the variations:

 At the Task and concepts level, there are three classes of possible variations:

-Structure of tasks, e.g. by factorizing tasks and/or concepts, -Operators between tasks, e.g. by replacing a choice operator by a sequence one, -Task decorations, e.g. by declaring a task as being frequent.

 At the Abstract UI level, there are two classes of variations:

-Grouping, e.g. by putting together all frequent tasks to separate them from nonfrequent ones, -Navigation, e.g. by launching the interactive system on the dialog space devoted to frequent tasks and by forcing non-frequent tasks to be accessible through frequent tasks.

 At the Concrete UI level, there are two classes of variations:

-Interactors, e.g. by preferring graphical widgets (radio buttons, check boxes, etc.) to vocal interaction, -Parameters, e.g., by setting colour, size, position, etc. of grapical widgets.

We did not consider variations at the Final UI level of abstraction as we decided to work with paper-based prototypes, quick and thereby inexpensive to make.

Case study

The case study is about checking and managing security of houses remotely. The motivation is that such an application is widespread, and thereby easy to explain.

Three main tasks were proposed to the user: (1) control the access to the house, (2) control the security cameras and (3) manage the alarm system. Controlling the access to the house allows the user to remotely lock or unlock the doors and other entries of the house. The user can watch the feed from the security cameras (in real time or recorded), send or delete them. Finally managing the alarm system allows the user to program it and to stop the alarm when triggered.

Design alternatives

The Task models below (figures 2 and 5) are designed using Flexilab, a multimodal editor created by (N. Hili, 2015). Figures 3 and4 present two alternatives of AUI related to Task model 1. Figure 6 proposes an AUI for Task model 2.

Participants

We recruit a total of 28 participants: PhD students, recent graduated doctors, master students, engineers and other students in computer science.

EXPERIMENT

We first start by briefly introducing the study. We then explain the security house application and its main functionalities. Finally, we give each participant two designs and a questionnaire. We no not enforce any time limit; the participants take their time to observe each UI.

The questionnaire given to each participant within the two designs is divided in two parts. The first part is composed of 11 questions based on a 5-point Liker scale. This first part is meant to rate the design. These questions are about three main aspects: Content (organization), navigation (structure/navigation tool) and design (visual). In the second part of the evaluation, the participants are asked to give their opinions concerning these six dimensions of design evaluation: navigation, aesthetics, readability, consistency, exportability and learnability.

We divide the participants into 3 groups. The first group is asked to evaluate UI_1 with UI_2. The second group evaluates UI_1 with UI_3, and the third group evaluates UI_1 with UI_4. The UIs are selected as presented below: The aim of the experiment is (1) to identify which variant gives more feedback, and (2) to see the impact of each abstraction level variations on the user's feedback, in order to define which alternative design to use during UI evaluation.

EVALUATION RESULTS

Categorization of user's feedback

In order to classify the users' statements (critique, opinion and suggestion), we use the taxonomy elaborated in (Tohidi, 2006) In our study, we only consider "comments" and "suggestions", comments being classified as either "positive" (Easy and convenient navigation), or "negative", (there is too much information in the interface).

Impact on user ratings depending on the choice of the alternative design

In order to assess the impact of comparing UI_1 to different designs (same task model but different AUI; same task model and AUI, but different CUI; different task models), we first calculate the average overall score of UI_1 based on the participant's rating given in the questionnaire.

Then, for each different prototype, we compare the score assigned to UI_1 when seen with each of the other design. Finally, we calculate the number of statements about UI_1 each time when given with a different UI.

The first observation is that the choice of the second UI conditions the user returns and opinion to the first one. For example, when comparing UI_1 to UI_2, a user did not comment about the interface navigation, but when comparing UI_1 to UI_3, the user started criticizing the navigation or the widgets.

The number of statements when comparing UI_1 to UI_3 was higher than when comparing UI_1 to UI_2, and UI_4. Also, the average score given to UI_1 when seen with a design with a different AUI was lower than when seen with the other designs (Table1).

These results support our hypotheses: (1) the comparative evaluation is more productive with a UI that has the same task model but a different abstract UI;

(2) the number of suggestions to improve is significantly higher when comparing UI_1 to UI_3 than when comparing UI_1 to UI_2 or UI_4.

An observation that we did not expect is that when evaluating the UI with one design that has a different Task model, the number of positive feedback is significantly lower.

CONCLUSION AND FUTURE WORK

As demonstrated in (Tohidi, 2006), user's feedback is affected by the number of design alternatives they are exposed to. In this paper, we report a study to observe the user's feedback depending on the alternative UI given for comparison. The aim of this research is to define the criteria that the alternative UI must meet to maximise returns on the original one. We used the CRF to characterise the UIs variations. We observe that the user's opinion about the UI under study is remarkably affected by the choice of the alternative design presented. Analyzing the feedback, we found that the AUI variants affect the users' feedback the most in terms of rating (score) and of the number of statements.

In the next step, we will explore further criteria, and once well defined, we will develop a tool for generating the best alternative UI for supporting comparative evaluation at low-cost and for highbenefit.

Figure 2 .Figure

 2 Figure 2. Task model 1

Figure 7 .

 7 Figure 7. Choice of the alternative design

  but we adapt it to our needs. In their work, Tohidi et al. divided the user's statements as shown in Figure8where comments are facts or personal opinions about the design. Suggestions are propositions for change to improve . The comments were either positive or negative. As for the suggestions there were classified as substantial or superficial. Substantial suggestions include ideas for improvement that were original (new), as well as ideas borrowed from other interfaces.

Figure 8 .

 8 Figure 8. Categorization of User Feedback according to Tohidi et al.

Figure 9 .

 9 Figure 9. Categorization of User Feedback

Table 1 .

 1 Impact on user ratings depending on the choice of the alternative design


Michaël Ortega
email: michael.ortega@univ-grenoble-alpes.fr

Wolfgang Stuerzlinger

Pointing at Wiggle 3D Displays

Keywords: 3D Interaction Technique, Pointing, Eye Tracking. Index H.5.2. Information Interfaces and Presentation: User Interfaces -Interaction styles, Input devices and strategies

This paper presents two new pointing techniques for wiggle 3D displays, which present the 2D projection of 3D content with automatic (rotatory) motion parallax. Standard pointing at targets in wiggle 3D displays is challenging as the content is constantly in motion. The two pointing techniques presented here take advantage of the cursor's current position or the user's gaze direction for collocating the wiggle rotation center and potential targets. We evaluate the performance of the pointing techniques with a novel methodology that integrates 3D distractors into the ISO-9241-9 standard task. The experimental results indicate that the new techniques are significantly more efficient than standard pointing techniques in wiggle 3D displays. Given that we observed no performance variation for different targets, our new techniques seem to negate any interaction performance penalties of wiggle 3D displays.

INTRODUCTION

Today, virtual 3D environments are used in many industrial and educational domains. For example, in medicine, and more specifically in anatomy learning, the students spend a large amount of time in exploring 3D models of bones, muscles and tendons. In this context, the depth perception provided by perspective projection is a critical component for constructing a correct cognitive model of these anatomical structures.

Monoscopic perspective projection already provides important depth cues from occlusion, relative size, and texture distortion. Other cues, such as binocularity and motion parallax further improve depth perception [START_REF] Gibson | Motion parallax as a determinant of perceived depth[END_REF] [START_REF] Frank | Visual comfort of binocular and 3d displays[END_REF]. While most forms of binocular display requires specific devices, such as Head Mounted Displays [START_REF] Pfeuffer | Gaze + pinch interaction in virtual reality[END_REF], the need for an external device makes it less accessible to a general audience (students). Motion parallax, and more specifically automatic motion parallax, also called wiggle stereoscopy or short Wiggle 3D display, as illustrated in Figure 1, is a better candidate to convey strong depth cues. Automatic motion parallax can easily be used on every person's laptop, desktop or tablet computer.

A basic task in interactive 3D environments is to click on a 3D point to designate/select it for further operations. Yet, one of the biggest drawbacks of wiggle 3D display is that most potential targets points are continually in motion, which substantially Author Version of paper published at IEEE VR 2018. decreases potential pointing performance, and could even make each selection stressful and tiresome. In this paper, we present two new techniques that stabilize potential targets by taking advantage of the cursor's current position or the user's gaze direction. To our knowledge, such selection has never been evaluated in wiggle 3D display systems.

Other related work has investigated gaze-based pointing techniques in virtual environments, both with 3D environments [START_REF] Tanriverdi | Interacting with eye movements in virtual environments[END_REF] or on 2D displays [START_REF] Velloso | An Empirical Investigation of Gaze Selection in Mid-Air Gestural 3D Manipulation. 15th Human[END_REF]. The most recent work uses HMDs with integrated eye-tracking capabilities [START_REF] Pfeuffer | Gaze + pinch interaction in virtual reality[END_REF].

Our contributions are:

•
Two new pointing techniques for wiggle 3D displays,

•
An evaluation of the techniques in a novel experimental design that integrates distractors into the ISO 9241-9 task [START_REF] Soukoreff | Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI[END_REF].

WIGGLE 3D DISPLAY

Classic perspective projection uses the pinhole camera principle: a fixed viewpoint where light from the scene passes through onto the projection plane. It provides many important depth cues such as occlusion or relative size. Yet, it is a projection of a 3D environment onto a 2D image and thus information about the third dimension is at least partially lost. Wiggle 3D display is a perspective projection where the viewpoint permanently rotates back-and-forth around a fixed 3D point (P). Wiggle 3D display provides a dynamic monoscopic perspective image, yielding changes in parallax and object occlusion, thereby providing more depth cues than the classic static projection [START_REF] Gibson | Motion parallax as a determinant of perceived depth[END_REF].

P is a point in the 3D scene, around which the viewpoint rotates back-and-forth. P is usually situated in the centre of the 3D content, and the viewpoint rotation is typically horizontal. As a rotation pivot, P stays stable on the screen, as are all points situated on a 3D vertical line passing through P. The range of movement of any given point of the object (po) then increases proportionally to the horizontal distance between po and P (see Figure 2). However, the difficulty of selecting any such point po then also increases with the horizontal distance to P: points that move faster (further from P) are more difficult to select [START_REF] Ortega | Hook: Heuristics for selecting 3D moving objects in dense target environments[END_REF][8] [START_REF] Pavlovych | Assessing Target Acquisition and Tracking Performance for Moving Targets in the Presence of Latency and Jitter[END_REF]. In the dynamic environment investigated by Ortega et al. [START_REF] Ortega | Hook: Heuristics for selecting 3D moving objects in dense target environments[END_REF], targets have unpredictable movements, which leaves the user only with the strategy of following the target until (s)he reaches it, which might never happen, when the target is too fast. With more predictable target movements [START_REF] Pavlovych | Target following performance in the presence of latency, jitter, and signal dropouts[END_REF] [START_REF] Pavlovych | Assessing Target Acquisition and Tracking Performance for Moving Targets in the Presence of Latency and Jitter[END_REF], which is similar to the backand-forth movements in wiggle 3D displays, an efficient pointing strategy might also be to follow the target movement. Yet, when the target moves too fast, another strategy is to position the cursor on a specific point of the target path, and then wait until the target is under the cursor. With both predictable and unpredictable target movements, the user has to change their pointing strategy, which affects pointing performance negatively.

In contrast to previous work that changes the shape of the cursor [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF], our new techniques do not change the cursor, but change the display of the scene to make the point that the cursor is over better visible to the user.

For wiggle 3D to be useful for general applications, it is crucial to create pointing techniques that can match the pointing performance with the level of a static image, while maintaining the benefits of wiggle 3D display in terms of enhanced depth perception.

TECHNIQUES

Design Rationale

We propose two techniques for pointing in Wiggle 3D displays, which maintain the depth cues provided by this kind of display. The techniques aim to stabilize a target point during the continuous back-and-forth rotation of the viewpoint. In this context, we investigate the co-location of the 3D rotation pivot (P) with the target. As mentioned above, P and all the points situated on the vertical line passing through P stay stable on the screen. A target that coincides with P (see Figure 2) is then stable on the screen plane. Based on this insight, we propose two methods for computing P.

Gaze Pointing (GPT) and Mouse-based Pointing (MPT)

Both new techniques compute P in real time, based on the wellknown ray-casting principle: a point on the screen (SP) and the viewpoint position (the center of projection or origin of the view for the 3D scene projection) creates a ray whose intersection with the scene is a 3D point: P. Changing SP, along the 2D screen, causes P to travel in 3D across the (visible parts of the) 3D scene surface(s). In the proposed techniques, if the ray-casting does not intersect the scene, P stays at its last computed 3D position.

As one of our motivations is commonly available, low-cost hardware, such as laptops, desktops or tablets, we propose two techniques for determining SP with no or low-cost, and then compute P.

In the first technique (called MPT: Mouse Position Technique) SP is simply determined by the mouse cursor position. This technique can then be used on classical computers, with no additional material, and with the mouse as an efficient pointing device.

In the second technique (called GPT: Gaze Position Technique), SP is the screen location where the user is gazing at. The technique requires an eye-tracker device, nowadays a low cost and widespread device, for knowing the gaze direction. Such an approach could be used on a computer, but also on a tablet. For tablets, hovering is typically not supported, which means that the finger cannot act as a mouse. Thus, MPT cannot be used and GPT is the only technique that could stabilize a target on a tablet. As both techniques only change the visual feedback of the scene by modifying the rotation pivot of the view, the sequence of actions in a pointing task is identical to everyday pointing: move the mouse/the finger onto the target and click/touch it.

USER EVALUATION

Here we describe the general procedure and apparatus used in the experiment as well as the analysis of the results. In this study, we evaluate the performance of GPT and MPT against the status quo for wiggle 3D displays, which uses a fixed rotation pivot at the centre of the screen. We call this condition fixed pivot, FPT.

Hypotheses

From previous work we know that selecting a moving target is more difficult than selecting a static one [START_REF] Ortega | Hook: Heuristics for selecting 3D moving objects in dense target environments[END_REF][8] [START_REF] Pavlovych | Assessing Target Acquisition and Tracking Performance for Moving Targets in the Presence of Latency and Jitter[END_REF]. We thus first hypothesize that performance will be better for both MPT and GPT than for FPT. More specifically, MPT and GPT will show on average faster pointing and fewer errors (H1).

However, with FPT targets close to the vertical midline of the screen could match with P and thus be static on the screen. H1 should thus be correct "in general", but not for all the targets. We examine this in more detail in the results below.

Moreover, as a target acquisition task typically requires the user to first look at the target before actuating the cursor button [START_REF] Zhai | Manual and gaze input cascaded (MAGIC) pointing[END_REF], we assume that the target should be stabilized earlier with GPT than with MPT. We thus hypothesize that GPT will provide better performance than MPT (H2).

Distractors

GPT and MPT compute P in real time, for any new position of SP, determined respectively by the gaze or the cursor position. Then, during a pointing task, while SP travels on the screen, on a flat line in between the 2D projection of the starting point and the 2D projection of the target, P travels onto the visible faces of the 3D scene, which could be a 3D path with many depth changes. The oscillation amplitude of a final target is thus potentially continuously changing during a pointing movement. This makes our new techniques performance highly dependent on the 3D scene and thus on the presence of distractors, i.e., potential targets along the pointing path [START_REF] Blanch | Benchmarking pointing techniques with distractors: adding a density factor to Fitts' pointing paradigm[END_REF].

In order to accurately measure the performance of GPT and MPT, our software apparatus thus has to simulate such an environment. In other words, only displaying the starting point and the final target does not yield an ecological environment for the task we are interested in. For our experiment, we thus decided to create a new solution for integrating distractors into a pointing task onto the (visible) surface of a virtual environment, and we decided to combine targets in a ISO 9241-9 circle (see Figure 3) with a distractor scene, which is then displayed in a wiggle 3D display system.

In the ISO 9241-9 task, all targets are arranged on a circle (Figure 3), and each circular configuration correspond to an index of difficulty (Fitts' law ID). However, in a wiggle 3D display the pointing difficulty depends on the pointing amplitude, the target's width, and also the target's oscillatory movements (speed and amplitude). As the oscillatory movements could change with the target's depth, we decided to put all the targets of an ISO circle at the same depth. We then consider that each ISO 9241-9 circle has a unique ID, even if the wiggle rotation implies different target movements according to their distance to P. [START_REF] Soukoreff | Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI[END_REF]. Eleven targets are placed in a circular configuration, and the pointing sequence is fixed. In the study, the angle variable (in degrees) is the angle between the vector made by two consecutive targets and the right vector (horizontal, from left to right).

Adding distractors means creating a 3D environment that places potential targets along the pointing path and challenges the user during the pointing action as could happen in a real application setting. In our context, such a 3D environment should respect three main constraints:

1. potential targets (ptargets) should have different depths, to simulate a (potentially) arbitrary 3D scene. 2. inspired from [START_REF] Blanch | Benchmarking pointing techniques with distractors: adding a density factor to Fitts' pointing paradigm[END_REF], ptargets should respect Fitts' law along the pointing path. Each ptarget should have an ID "equal" to the final target's one. However, due to their depth differences, their movement amplitudes are different. Thus, a distractor's real ID then "slightly" changes from the target's one. For distractors, we consider this deviation to be not critical, as the average ID is still correct. 3. both the distractors density (called rho [START_REF] Blanch | Benchmarking pointing techniques with distractors: adding a density factor to Fitts' pointing paradigm[END_REF]) and their depth amplitude are limited, as they cannot cause the target to be occluded. From these constraints, we developed a distractor 3D shape (illustrated in Figure 4) with the following properties:

1. ptargets are circles around the starting point, with specific line widths. 2. The width of ptargets are the same as the circle's line width. This width increases according to both the distance to the starting point and Fitts' law. We compute the width with the formula from previous work that scaled distractors accordingly [START_REF] Blanch | Benchmarking pointing techniques with distractors: adding a density factor to Fitts' pointing paradigm[END_REF]. 3. ptargets alternate between closer or farther from the viewpoint. Visual constraints require that farther ptargets be at the final target's depth (otherwise they may be invisible). Other ptargets are closer to the user and their visual depth is chosen to follow an empirical linear function: depth = distance_to_start_point/5 (Figure 5). Moreover, the density of the ptargets, has to be carefully chosen to avoid that ptargets occlude the final target. 4. in order to be more ecological (simulate the viewing of real objects) the gaps in between the potential targets are filled with cones, which makes the depth change smoothly from one ptarget to another along the path.

To keep visual consistency, all the targets of an ISO 9241-9 circle cannot be displayed at the same time. Indeed, some of them will be hidden by the distractors shape. Thus, we display only the next target. This is different from the ISO 9241-9 task, but we consider that this does not influence the results, as after a training step we can assume that every user knows the pointing sequence and does not hesitate about where the next target is.

Apparatus and Software

The study was conducted on an 15" Apple Macbook Pro Retina, with 2.6GHz Intel Core i7 and an NVIDIA GeForce GT 650M 1024M. We used a 22" monitor, at 1600x1024@60Hz (Apple Cinema Display). Eye tracking was done with a Tobii 4C. The monitor was positioned vertically, with the eye-tracker mounted at the bottom of the screen. We used a traditional mouse as a 2D pointing device. Mouse acceleration was disabled, and the gain was set to 3.54: 1cm movement with the mouse made the cursor move about 3.54 cm on the screen.

The software was written in Python, with PyOpenGL, using shaders in GLSL 3.30. The wiggle 3D display was created by rotating the viewpoint according to the current rotation pivot (P) (computed differently for each pointing technique). The viewpoint made back-and-forth rotations with a range of 18 degrees. This is equivalent to 20 cm of lateral head movements at 70 cm from the screen. We used a sinusoidal function for smoothing the changes of direction, and the viewpoint made complete back-and-forth loops in 0.8 secs. These values were established through observation of many wiggle 3D displays that one can find on the internet as well as pilot experiment.

The cursor icon was unchanged. We kept the traditional arrow cursor that is typical for desktop operating systems.

Participants and Procedure

We recruited 12 participants (mean age 28 years, SD 3.4) from the local university. Participants first started with the eye-tracking calibration step. Next, the experimental context was introduced by presenting the wiggle 3D display principle.

To compensate for the lack of familiarity with the different conditions, participants were asked to perform 4 practice trial "circles" with each condition. This was enough to enable participants to feel comfortable with our simple task. Participants were instructed to select the green highlighted target as quickly and accurately as possible, and to only rest after finishing a complete ISO circle. The distractors shape was not displayed during the resting period, making this period easy to identify.

Design

The study used a 3x4 within-subject design. The first independent variable is the technique: 3 techniques GPT, MPT and FPT. The next variable is the combination of ISO circle and distractor shape, from Fitts' law IDs and rho (distractor density). The radius of the ISO circles was fixed, for a pointing amplitude of 766 pixels. Only the target width changed. In this study, 4 combinations of [ID, rho] were used: [3, 0.6], [4, 0.3], [5, 0.2], and [6, 0.1], which were created with target widths of 110, 51, 25 and 12 pixels, respectively.

Techniques were counter-balanced between participants while the [ID, rho] combinations were randomly presented. The first dependent variable was the movement time. It is the time between the previous click and the click on the current target. The second variable is the error rate, which expresses the number of missed target. The last variable is the throughput, in bits per seconds, computed following the procedure outlined by previous work [START_REF] Mackenzie | Fitts' throughput and the speed-accuracy tradeoff[END_REF].

3x4=12 different conditions were presented to each participant, with 10 trials per condition. Each ISO circle had 11 targets, which corresponds to 10 pointing tasks (the time to click on the first target cannot be controlled). Each participant completed a total of 3x4x10x10 = 1200 pointing tasks, for a total of 12x1200 = 14400 recorded trials overall.

After the experiment, which lasted about 30 minutes, participants were asked to rank the techniques in terms of preference, and to record their feelings in terms of performance, fatigue and usability.

Results

We analyzed the results with repeated measures ANOVA and report the outcomes for alpha = 0.05. As with many pointing experiments, the data was not normally distributed. We first filtered outliers beyond three standard deviations from the mean, and then used a log transform before performing the ANOVA. The data then also passed Mauchly's sphericity test.

Quantitative

Technique had a significant effect on movement time, F(2,22) = 19.14, p < 0.0001, error rate F(2,22) = 26.35, p < 0.0001, and throughput F(2,22) = 21.27, p < 0.0001.

As identified by a post-hoc test, for all significant effects the FPT condition is significantly slower/has more error/less throughput than the group formed by both the MPT and GPT conditions. For example, MPT and GPT throughputs are 4.92 respectively 4.88 bps, which the FPT condition has only 4.19 bps (Figure 6). Movement angle had a significant effect on movement time, F(9,99) = 5.91, p < 0.0001, error rate F(9,99) = 8.81, p < 0.0001, and throughput F(9,99) = 19.23, p < 0.0001.

There is a significant interaction between technique with angle in terms of movement time F(18,198) = 3.69, p < 0.0001, error rate F(18,198) = 6.59, p < 0.0001, and throughput F(18,198) = 4.99, p < 0.0001.

In terms of throughput a Bonferroni Multiple Comparison Test identifies the following grouping of angles: (171°, 204°) with the lowest throughput, followed by (40°, 335°) and (139°, 237°, 302°), and (73°, 106°, 270°) with the highest throughput.

Considering only the angles at 73°, 106°, and 270°, i.e., movements that are predominantly vertical, there is no significant difference between the FPT, MPT and GPT conditions (throughputs between 4.55 and 5.28), F(2,22) = 2.654, p > 0.05. Figure 7 illustrates the differences between the techniques in terms of throughput for each angle.

Starting point

Qualitative

Taking the average of technique rankings, participants prefer GPT (8/12), followed by MPT (4/12), and finally FPT which was always ranked last. Eight participants felt fatigue with FPT, while two participants expressed that they experienced slight fatigue with GPT: they had the feeling they had to be more concentrated than with other techniques. All the participants felt fatigue about the experiment itself during the last condition: "the distractors shape is too geometric, and the rotational movements creates a visual fatigue effect" (P6).

Two participants thought that they were more efficient with GPT because they had the feeling that "the gaze arrives sooner on the target than the mouse cursor" (P5, P6).

Discussion

Our results highlight the benefits and potential of our two new pointing techniques in terms of time, errors, and throughput. Overall, the new techniques, GPT and MPT, which use the gaze respective mouse cursor, provide both similar results, which validates H1, as these techniques significantly outperform the status quo (FPT). As expected, this performance benefit does not exist for targets along the vertical midline of the screen, simply because in FPT these targets are stable by definition.

Still, even if targets are stable earlier with the gaze pointing technique GPT [START_REF] Zhai | Manual and gaze input cascaded (MAGIC) pointing[END_REF], results do not show a significant difference between GPT and MPT, which means that we have to reject H2.

Finally, GPT and MPT are clearly preferred, and all participants identified benefits in terms of comfort and performance. GPT was preferred by eight users, but MPT also receive very good reviews, while FPT clearly was the worst condition.

MPT OR GPT ?

We point out that our throughput results match the results for 2D pointing [START_REF] Mackenzie | Fitts' throughput and the speed-accuracy tradeoff[END_REF]. Moreover, as our new pointing techniques stabilize the targets, they enable the user to perform precise manipulations on a 3D object, such as translating a vertex, or rotating/extruding/drawing a specific face. Yet, the wiggle 3D display still provides more depth cues than a static projection.

GPT and MPT are statistically not significantly different, and GPT is preferred by most of the users. This validates that GPT is a good candidate for both tablet and laptop/desktop computers. On tablet computers, GPT is the only candidate. Indeed, MPT cannot be used on such screens, as there is no cursor on tablet systems (the finger hovering the screen is not detected). Moreover, on such computers, eye-tracking without additional devices is becoming available [START_REF] Holland | Eye tracking on unmodified common tablets: challenges and solutions[END_REF].

On laptop/desktop computers, a few participants complained about the use of eye tracking and the gaze point. Thus, we are not certain of GPT is a solution suited for long term use. Still, as the two techniques have the same core function: f(SP) = P, it could be interesting to provide both techniques to the user and to offer the user the possibility to switch between them. A longitudinal experiment could reveal which technique is better for long term use.

We could have investigated other techniques that freeze the viewpoint rotation. Some of the alternatives that seem feasible are freezing the rotation as soon as the mouse button is depressed, as soon as an additional button is depressed, or as soon as the mouse moves. Relative to the status quo, any of them might also improve pointing performance, as long as the image is frozen, to the level of a static image. However, freezing limits the number of targets that are accessible during a pointing movement. Compared to a static viewpoint, the back-and-forth rotation of the viewpoint enables the system to display more of object's surface area, such as the sides of the skull in Figure 1. These areas are potential targets, and any freezing-based pointing technique would force the user to wait for the target to become visible to start a pointing movement. This could have a significant impact on pointing performance, because the user now needs to anticipate the viewpoint rotation and to precisely know when to freeze the image so that the target is visible.

Moreover, on laptop/desktop systems the mouse is frequently also used for hovering without pointing. This is particularly useful for illustrating some aspect of the scene to another user. Automatic freezing during mouse hovering decreases the additional depth cues due to motion parallax during this specific task. In 3D user interfaces, inspecting a 3D object/scene is a very common task that is associated with pointing. Inspecting involves mainly travelling the gaze over a 3D shape for learning its shape or for looking at something on the surface. For this task, GPT and MPT do not act the same. With MPT, the gaze does not modify the wiggle rotation. The scene movements are predictable and there is no "Midas effect". However, when the 3D point that the user looks at is far from the cursor, wiggle movements could be very large, making accurate inspection potentially more difficult. The simple solution is to move the cursor. With GPT, the gaze modifies the wiggle rotation. There is a "Midas effect", but it is positive: the scene is stable at the gaze position, and all the rotation movements are thus in the non-central (i.e., peripheral) area of the human visual field of view, still providing depth cues. From this, GPT seems a better technique in general.

CONCLUSION AND FUTURE WORK

This paper presents two new pointing techniques for wiggle 3D displays that outperform the status quo in terms of performance and user preferences. This makes wiggle 3D display a good candidate for displaying 3D content on low-cost display devices, and potentially even for 3D design software.

In order to evaluate the effects of these new pointing techniques in longer term usage, we plan to implement them in a 3D design software package and then to perform a longitudinal evaluation with two categories of users: students in anatomy and 3D designers, and on two categories of computers: desktop and tablets.

Figure 1 :

 1 Figure 1: In Wiggle 3D Displays, the viewpoint permanently rotates back-and-forth around a fixed 3D point (P). In this figure, the left and center skulls present projections from the extremities of the wiggle 3D rotation. The continuous back-and-forth motion between these two extreme viewpoints enables the user to see the depth of each part of the skull or the protuberance up to the nose. This information is invisible in the frontal projection on the right.

Figure 2 :

 2 Figure 2: A wiggle rotation is made around a 3D point: P. The latter is computed from a screen position (SP). Here, SP1 is the screen location where the user is gazing at, and P1 is on the bone surface. The whole scene does small back-and-forth rotations around P1, which is behind the stable SP1. If the user is looking at a different screen position SP2, then the display changes to stabilize the target P2 in screen space.

Figure 3 :

 3 Figure3: ISO 9241-9 task[START_REF] Soukoreff | Towards a standard for pointing device evaluation, perspectives on 27 years of Fitts' law research in HCI[END_REF]. Eleven targets are placed in a

Figure 4 :

 4 Figure 4: a: Illustration of ISO 9241-9 circle (targets are the transparent red circles) displayed on the distractor shape. The participants never saw this image. The current target is the green circle. Potential targets/distractors are the concentric grey circles (centered around the previous target position), whose width varies to have the same ID as the target. One in two potential targets/distractors has the target's current depth, while every other is closer to the user, following a linear function: depth = distance_to_start_point/5. b: Distractors shape as the user see it. The cursor is on the previous target.

Figure 5 :

 5 Figure 5: Profile of distractor shape. One in two potential targets/distractors has the target's current depth, while every other is closer to the user. Their "height" follows the linear function: depth = dist / 5, where dist is the distractor's distance form the starting point.

Figure 6 :

 6 Figure 6: Mean and standard error of movement time, error rate and throughput for each technique. FPT is significantly slower, more error prone, and has lower throughput than GPT and MPT, which are statistically not different.

Figure 7 :

 7 Figure 7: Mean throughput per angle for each technique. FPT is highly dependent on the angle, while GPT and MPT do not vary significantly. FPT is equivalent to other techniques when the pointing angle is vertical, i.e up/down to the central pivot, but lower when pointing is horizontal, i.e distant and on both sides of the central pivot.

ACKNOWLEDGMENTS

We thank Özge Nilay and Junwei Sun for their assistance with a pilot study for this work. We thank Simon Chambonnet for its implementation of the first prototype and the first pilot study with the distractor shape. We acknowledge funding by NSERC for this research. We also gratefully acknowledge the support of ANR (French National Research Agency) (ANATOMY2020 ANR-16-CE38-0011, ISAR ANR-14-CE24-0013 and PERSYVAL-lab ANR-11-LABX-0025-01).