Alexandre Bou
email: alexandre.bouenard@univ-ubs.fr

Samsara

Sylvie Gibet
email: sylvie.gibet@irisa.fr

Marcelo M Wanderley
email: marcelo.wanderley@mcgill.ca

Enhancing the visualization of percussion gestures by virtual character animation

Keywords: Gesture and sound, interface, percussion gesture, virtual character, interaction

A new interface for visualizing and analyzing percussion gestures is presented, proposing enhancements of existing motion capture analysis tools. This is achieved by offering a percussion gesture analysis protocol using motion capture. A virtual character dynamic model is then designed in order to take advantage of gesture characteristics, yielding to improve gesture analysis with visualization and interaction cues of different types.

INTRODUCTION

Designing new musical interfaces is one of the most important trends of the past decades. Efforts have constantly been made to elaborate more and more efficient devices in order to capture instrumental gestures. These technical advances have given rise to novel interaction opportunities between digital instruments and performers, and the creation of new sound, image or tactile synthesis processes. Our main guideline aims at providing a set of pedagogical tools for helping the study of percussion gestures. Among these, rendering real instrumental situations (interaction between performers and instruments) and exploring the gestural space (and its corresponding visual, gestural and sounding effects) are of great interest. Eventually, our final goal is to build new virtual instrumental situations, especially with gesture-sound interactions controlled by virtual characters. This paper offers a new tool for visualizing percussion gestures, which exploits both the analysis and synthesis of percussion gestures. The analysis process is achieved by capturing the movements of performers, while a physical model of virtual character is designed for the synthesis. The visualization is composed of different views of both the virtual character and the instrument. It is finally enhanced with interactions between graphics modeling, physics synthesis of gesture and sound replay.

The paper is organized as follows. In section 2, previous work and motivations are discussed. The analysis process of percussion (timpani) gestures is detailed in section 3. Visualization and interaction concerns are discussed in section 4. Finally, we conclude with further perspectives.

RELATED WORK

Previous works concern both percussion-related models and interfaces, and works combining virtual character animation and music.

Most of the work about percussion gesture and sound deals with the design of new electronic percussion devices, thus creating either new interfaces (controllers) and/or new sound synthesis models and algorithms.

On the one hand, new interfaces are based on increasingly efficient devices that are able to track gestures. Electronic percussions such as Radio Baton [START_REF] Boie | The Radio Drum as a Synthesizer Controller[END_REF], Buchla Lightning [START_REF] Buchla | Lightning II MIDI Controller[END_REF], Korg Wavedrum [START_REF] Rule | Keyboard Reports: Korg Wavedrum[END_REF] and ETabla [START_REF] Kapur | The Electronic Tabla Controller[END_REF] are digital musical instruments that are improving or emulating acoustic phenomena, by taking into account gesture cues such as position, touch and pressure. More recent work take advantage of various techniques, such as magnetic gesture tracking [START_REF] Marshall | The Virtual Bodhran -The Vodhran[END_REF], computer vision [START_REF] Mäki-Patola | The Augmented Djembe Drum -Sculpting Rhythms[END_REF] or the physical modeling of the drum skin [START_REF] Jones | Controlling a physical model with a 2D Force Matrix[END_REF].

On the other hand, it is also achieved by designing sound synthesis models and algorithms, ranging from purely signalbased to physically-based methods [START_REF] Dodge | Computer Music: Synthesis, Composition and Performance[END_REF]. These works rarely include the study of the instrumental gesture as a whole, especially regarding to its dynamical aspects or its playing techniques, even if some take into account real measurements [START_REF] Bresin | Experiments on gesture : walking, running and hitting[END_REF] and physical parameters mapping with percussion gesture [START_REF] Chuchacz | Physical Models and Musical Controllers: Designing a Novel Electronic Percussion Instrument[END_REF]. Playing techniques can be qualitatively observed and used ( [START_REF] Kapur | The Electronic Tabla Controller[END_REF] [12] [START_REF] Dahl | Playing the Accent: Comparing Striking Velocity and Timing in Ostinato Rhythm Performed by Four Drummers[END_REF]) for a better understanding of percussive gestures.

They can also be quantified thanks to capturing techniques [START_REF] Tindale | A Comparison of Sensor Strategies for Capturing Percussive Gestures[END_REF], among which the most used is motion capture by camera tracking. But whichever method is used to reproduce the quality of the instrumental gesture, it generally fails to convey its dynamic aspect. That is why we explore in this paper the possibility to physically animate a virtual character performing percussive gestures so that its intrinsic features are available to our interface.

As for previous work combining virtual character animation and music, very few studies are available, especially in a mean of taking advantage of virtual character animation for helping the visualization of gestures. The DIVA project 1 used virtual character animation for audiovisual performances output driven by MIDI events [START_REF] Hanninen | Virtual concert performance -synthetic animated musicians playing in an acoustically simulated room[END_REF]. Hints about motion capture characteristics towards the quality of re-synthesis of the movement [START_REF] Peinado | Towards Configurable Motion Capture with Prioritized Inverse Kinematics[END_REF] have been proposed. The influence of music performance on virtual character's behavior [START_REF] Taylor | Using Music to Interact with a Virtual Character[END_REF] has also been emphasized. Some work aims at extracting expressive parameters from video data [START_REF] Camurri | Multimodal analysis of expressive gesture in music and dance performances[END_REF] for enhancing video analysis. Eventually, a solution consists in directly animating virtual models from the design of sound 2 . These studies are nevertheless out of the scope of virtual character animation as a gestural controller for enhancing the visualization and the analysis of instrumental situations.

TIMPANI PERFORMANCE

There are many classifications of percussion instruments, one of the most established typologies is based on physical characteristics of instruments and the way by which they produce sound. According to this classification, timpani are considered as membranophones, "producing sound when the membrane or head is put into motion" [START_REF] Cook | Teaching Percussion[END_REF].

Timpani Basics

Timpani related equipment is mainly composed of a bowl, a head and drumsticks (Figure 1). In general, timpanists have to cope with several timpani (usually four) with bowls varying in size [START_REF] Peters | Un-contestable Advice for Timpani and Marimba Players[END_REF]. As for timpani drumsticks, they consist of a shaft and a head. They are designed in a wide range of lengths, weights, thicknesses and materials [START_REF] Cook | Teaching Percussion[END_REF] and their choice is of great importance [START_REF] Noak | Timpani Sticks. Percussion Anthology. The Instrumentalist[END_REF]. Timpani playing is characterized by a wide range of playing techniques. First, there are two main strategies for holding drumsticks (Figure 2, left side): the "French" grip (also called "thumbs-up") and the "German" grip (or "matched" grip).

1 DIVA project : www.tml.tkk.fi/Research/DIVA 2 Animusic : www.animusic.com Players commonly use three distinct locations of impacts (Figure 2, right side). The most used is definitely the onethird location, while the rim appears rather rarely.

A database of timpani gestures has been created and is composed of five gestures: legato, tenuto, accent, vertical accent and staccato. Each gesture is presented on Figure 3, showing the space occupation (Y-Z projection) of each drumstick's trajectory, and highlighting the richness of timpani playing pattern variations. Taking into account these various features, timpani gestures are thus characterized by a wide variability. Next session will concern the quantitative capture of these variations.

Motion capture protocol and database

We propose to quantitatively characterize timpani gestures by capturing the motion of several timpani performers. We use a camera tracking Vicon 460 system 3 and a standard DV camera that allow both the retrieval of gesture and sound.

The main difficulty using such hardware solutions is then the choice of the sampling frequency for the analysis of percussive gestures (because of the short duration of the beat impact [START_REF] Dahl | Spectral Changes in the Tom-Tom Related to the Striking Force[END_REF]). For our experiments, cameras were set at 250 Hz. With a higher sampling frequency (500 Hz and 1000 Hz), we could expect to more accurately retrieve beat attacks, but the spatial capture range is significantly reduced so that it is impossible to capture the whole body.

In order to retrieve beat impacts, markers have also been placed on the drumsticks. The smaller timpani (23") has been used to emphasize sticks rebounds. Three performers (c.f. Figure 4) were asked to perform our timpani-dedicated capturing protocol, yielding our timpani gestures database. Table 1 proposes a summary of the playing characteristics for each subject that has performed our capturing protocol. The differences between performers namely lie in their degree of expertise (Professor or Master student), the grip strategy that is used (French or German), their dominant (Left or Right) hand, and their gender. Master stud. G Right F

Each performer has been asked to perform a single stroke roll of each gesture variation (legato, tenuto, accent, vertical accent and staccato) presented in section 3.1. And for each 3 Vicon : www.vicon.com of these gestures, the performer has been asked to change the location of the beat impact according to Figure 2 (right side). Finally, our database is composed of fifteen examples of timpani playing variations for each subject, and to each example corresponds five beats per hand. This database will be used when studying in detail the variations of the timpani gesture.

The use of widespread analysis tools integrated in Vicon software allow for the representation of temporal sequences as cartesian or angular trajectories (position, velocity, acceleration), but one can easily observe that such a representation isn't sufficient to finely represent the subtility of gesture dynamics, and cannot be easily interpreted by performers.

In the instrumental gesture context, we are mainly interested in also displaying characteristics such as contact forces, vibration patterns, and a higher-level interpretation of captured data (space occupation, 3D trajectories, orientation of segments).

VISUALIZATION

Our visualization framework proposes the design of a virtual instrumental scene, involving the physical modeling and animation of both virtual characters and instruments. Timpani gestures are taken from the database and physically synthetized, making available both kinematic and dynamic cues about the original motion.

Virtual instrumental scene

A virtual instrumental scene is designed using both graphics and physics layers. The OpenGL graphics API is used for rendering the virtual character, the timpani model, and rendering motion cues of these entities. It also allows users to explore the virtual instrumental space and to visualize the scene from different points of view.

The ODE physics API [START_REF] Smith | Open Dynamics Engine[END_REF] is used for the physical simulation the virtual character and collisions. These graphics and physics layers build the primary visualization framework. It is possible to enrich this visualiza-tion with both meaningful kinematic and dynamic motion cues since the overall gesture is available.

Kinematic cues

Kinematic motion cues can be of different types. Firstly, positions and orientations of any joint and segment composing the virtual character can be visualized (Figure 5) in real-time by the rendering of coordinate references.

Temporal trajectories describing the motion can be traced (Figure 6). These include position, velocity, acceleration, curvature trajectories, as well as plane projections, position/velocity and velocity/acceleration phase plots of segments and joints. Although temporal trajectories (Figure 6) convey helpful information about the motion, they cannot be visualized for the moment at the same time as our virtual instrumental scene rendering. We propose the real-time visualization of 3D trajectories and their corresponding bounding boxes (Figure 7). This helps in identifying the gestural space actually used during the performance.

In addition of these kinematic cues, we offer the visualization of dynamic characteristics of percussion gestures by physically modeling, simulating and controlling a virtual character.

Dynamic cues

The aim of the visualization of gesture's dynamic profiles is to facilitate the visualization of the interaction between the virtual character and the percussion model. Interaction information is available, thanks to physical modeling and simulation of instrumental gestures.

Virtual character modeling and simulation

The dynamic simulation of instrumental gestures has been achieved by firstly proposing a dynamic model of a virtual character, and secondly by putting this physical model into motion through a simulation framework.

The virtual character is both modeled by its anthropometry and its physical representation. As for the anthropometry, it directly comes from motion capture. The physical representation of the virtual character is composed of segments (members) articulated by joints, each represented by its physical parameters (mass, volume, degrees of freedom).

The simulation framework is composed of two modules. The first one is the simulation of motion equations. Equations 1 and 2 describe the evolution of a solid S of mass m. The acceleration of a point M of the solid S is aM and FM is the resulting force applied on S at point M . The inertia matrix of S expressed at the point M is IM , while ΩS represents the angular velocity of S. Finally τM is the resulting torque applied on S at the point M .

m.aM = FM

(1)

IM . ΩS + ΩS.IM .ΩS = τM (2)
Once the joints and members of the virtual character can be simulated by the emulation of motion equations, we offer a way to physically control the virtual character with motion capture data thanks to a Proportionnal -Integral -Derivative (PID) process (Figure 8).

The PID process translates the motion capture trajectories into forces and torques. Knowing angular targets from motion capture ΘT and ΘT , and knowing the angular state of the virtual character ΘS and ΘS, the PID computes the torque τ to be applied. Kp, Ki and K d are coefficients to be tuned. This process ends the simulation framework and makes the virtual character able to dynamically replay instrumental timpani sessions.

The interactions between the virtual character, percussion model and the sound are then discussed. It is achieved by taking advantage of the dynamic characteristics that are available thanks to our virtual character dynamic model.

Interaction

In order to account for the interaction between the virtual character's sticks and the timpani model, we suggest to render a propagating wave on the membrane of the timpani when a beat impact occurs. Although the rendering of such a wave isn't the theoretical solution of the wave equation, this model can take into account the biomechanical properties of the limbs and the properties of the sticks. Once the collision system detects an impact, kinematic and dynamic features -such as the velocity and the impact force -can be extracted. These features instantiate the attributes of the propagation of the wave making it possible the visualization of the position and the intensity of the impact (Figure 9).

Once kinematic and dynamic features of motion and physical interactions are obtained, we can set up strategies of sound production. In this paper, we limit ourselves to the triggering of pre-recorded sounds available from motion capture sessions. These sounds are played when the impacts of the virtual character sticks are detected on the membrane of the timpani model.

One can notice that the time when the sound is played doesn't depend on motion capture data, but depends on the physical simulation and interaction between the virtual performer and the percussion model. This provides an exten-sive way of designing new gesture-sound interactions based on both kinematic and dynamic gesture features.

CONCLUSION

We have presented in this paper a new interface for visualizing instrumental gestures, based on the animation of a virtual expressive humanoid. This interface facilitates the 3D rendering of virtual instrumental scenes, composed of a virtual character interacting with instruments, as well as the visualization of both kinematic and dynamic cues of the gesture. Our approach is based on the use of motion capture data to control a dynamic character, thus making possible a detailed analysis of the gesture, and the control of the dynamic interaction between the entities of the scene. It becomes therefore possible to enhance the visualization of the hitting gesture by showing the effects of the attack force on the membrane. Furthermore, the simulation of movement, including preparatory and interaction movement, provides a mean of creating new instrumental gestures, associated with an adapted sound-production process.

In the near future, we expect to enrich the analysis of gesture, by extracting relevant features from the captured motion, such as invariant patterns. We will also introduce an expressive control of the virtual character from a reduced specification of the percussion gestures. Finally, we are currently implementing the connection of our simulation framework to well-known physical modeling sound-synthesis tools such as IRCAM's Modalys [START_REF] Ellis | Modalys Demonstration[END_REF] to enrich interaction possibilities of this framework. A similar strategy to existing frameworks, such as DIMPLE [START_REF] Sinclair | Extending DIMPLE: A Rigid Body Simulator for Interactive Control of Sound[END_REF], using Open Sound Control [START_REF] Wright | Open Sound Control: The State of the Art[END_REF] messages generated by the simulation engine, is being considered.

Figure 1 :

 1 Figure 1: Timpani player's toolbox: bowl, head and drumsticks.

Figure 2 :

 2 Figure 2: Left: French (top) and German (bottom) grips; Right: Impact locations on the drumhead.

Figure 3 :

 3 Figure 3: Timpani playing variations -Tip of the drumstick trajectories (Y-Z projection). Legato is the standard up-and-down timpani gesture. Tenuto and accent timpani variations show an increase in velocity and a decrease in space occupation (in the Y direction). Vertical accent and staccato timpani variations also show an increase in velocity, and are characterized by an increase of space occupation (in the Y direction) for a more powerful attack and loudness.

Figure 4 :

 4 Figure 4: A subject performing the capturing protocol. The number of markers and their positions follow Vicon's plug-in Gait indications.

Figure 5 :

 5 Figure 5: Real-time visualization of segments' orientations.

Figure 6 :

 6 Figure 6: Example of kinematic trajectory plot. Tip of the drumstick : position/velocity phase along the Z axis.

Figure 6

 6 Figure 6 shows an example of such plots, the trajectory represents the position/velocity phase (projected on the Z axis) of the drumstick.Although temporal trajectories (Figure6) convey helpful information about the motion, they cannot be visualized for the moment at the same time as our virtual instrumental scene rendering. We propose the real-time visualization of 3D trajectories and their corresponding bounding boxes (Figure7). This helps in identifying the gestural space actually used during the performance.In addition of these kinematic cues, we offer the visualization of dynamic characteristics of percussion gestures by physically modeling, simulating and controlling a virtual character.

Figure 7 :

 7 Figure 7: Real-time rendering of 3D trajectory and bounding box -drumstick tip trajectories helps in identifying the gesture space that is actually used.

Figure 8 :

 8 Figure 8: PID process. From motion capture data targets (angles ΘT and angular velocities ΘT ), joints' current state (angles ΘS and angular velocities ΘS) and coefficients (Kp, Ki and K d ) to be tuned, torques τ are processed to physically control the virtual character.

Figure 9 :

 9 Figure 9: Dynamic cues about beat impact: visualization of the location and magnitude of the attack by the propagation of a wave.

Table 1 :

 1 Timpani gestures data.

	Subject	Expertise	Grip Handedness Gender
	S1	Professor	F	Right	M
	S2	Master stud.	G	Left	M
	S3

ACKNOWLEDGMENTS

The authors would like to thank the people who have contributed to this work, including Prof. Fabrice Marandola (McGill), Nicolas Courty (VALORIA), Erwin Schoonderwaldt (KTH), Steve Sinclair (IDMIL), as well as the tim-pani performers. This work is partially funded by the Natural Sciences and Engineering Research Council of Canada (Discovery and Special Research Opportunity grants), and the Pole de Competitivite Bretagne Images & Réseaux.


Alexandre Bouënard

Marcelo M Wanderley

Sylvie Gibet

Analysis of Percussion Grip for Physically Based Character Animation

This paper presents the analysis of percussion technique for the simulation of virtual timpani playing situations. The analysis has been processed for two subjects performing with two types of grips (French and German), yielding to the extraction of percussion technique parameters from a motion capture database. These parameters are shown to be necessary for specifying the control and extending the expressivity of the simulation process.

Introduction

The present contribution aims at combining the assets of both the dynamic control of virtual characters and the analysis of percussion instrumental gestures, for synthesizing novel physically responsive and sounding instrumental situations. The physical simulation is indeed of great importance for taking into account the physical parameters of the strike (tension, forces) that influence the dynamics of the gesture and the produced sound, while the analysis of percussion grips gives a level of control and different modes of playing to the virtual character.

Either for the physical simulation or the analysis parts, the interest of using motion capture data appears crucial and twofold. Firstly, it provides realistic examples of the human motion under study for driving the virtual character simulation. Physically-based character animation techniques provide a solution to the limited reuse of motion capture data (due to the uniqueness of the capture conditions), and results in synthesizing adaptative behaviors towards environment changes through the simulation of dynamic laws. Secondly, motion capture data allow the specification of the virtual character control by understanding the body characteristics and expressive components that are at stake during the motion. Moreover, the possible alteration of the original motion by the simulation process emphasizes the importance of a comprehensive and useable analysis of the original motion.

This paper presents the extraction of percussion grip parameters that can be used as gesture inputs for the dynamic control of virtual characters performing different technical percussion styles. It is organized as follows. Section 2 reviews previous work about physically-based character animation using motion capture data, stylebased computer animation and the analysis of instrumental gestures. Section 3 introduces the overall context and the method used for extracting parameters that characterize percussion grips. The grip influence, in terms of end-point trajectories and angular constraints, is presented in section 4. Section 5 discusses the benefit of such parameters for our synthesis framework. Eventually, section 6 concludes with further perspectives.

Previous Work

Data-driven computer animation techniques have widely been studied in the past few years, taking advantage of the increasing availability of quantitative representations of the human motion thanks to the proliferation of acquisition systems.

Music-related contributions for virtual character animation often use a sound-driven approach, such as MIDI-driven [START_REF] Hanninen | Virtual concert performance -synthetic animated musicians playing in an acoustically simulated room[END_REF] or performance-driven [START_REF] Taylor | Using Music to Interact with a Virtual Character[END_REF]. However, these finally prove a lack in taking into account the dynamic aspect of instrumental gestures.

The combination of a motion capture database and physically-based methods yields to frameworks that are well-suited for modeling human-like interactive bodies, since the capture of real movements and the simulation of dynamic laws intrinsically provide physically realistic and adaptative results. The use of physical models for dealing with motion capture data has been involved in motion editing, retargetting and generating transitions between motion clips ( [START_REF] Popovic | Physically Based Motion Transformation[END_REF] [START_REF] Abe | Momentum-based parameterization of dynamic character motion[END_REF]). Hybrid methods have also been explored, composing data-driven kinematic and dynamic controllers ( [START_REF] Faloutsos | Composable Controllers for Physics-Based Character Animation[END_REF] [14] [START_REF] Zordan | Dynamic Response for Motion Capture Animation[END_REF]), based on the design of PD controllers ([8] [START_REF] Zordan | Motion Capture-Driven Simulations that Hit and React[END_REF]) which is also the approach of our work [START_REF] Bouënard | Enhancing the Visualization of Percussion Gestures by Virtual Character Animation[END_REF].

Regarding stylistic aspects of virtual character animation, previous works concentrate its efforts on extracting and generating expressive motion from motion capture data, and proposes methods based on signal processing ([4] [START_REF] Amaya | Emotion from Motion[END_REF]), statistical models ( [START_REF] Urtasun | Style-based Motion Synthesis[END_REF] [START_REF] Shapiro | Style Components[END_REF]), or the optimization of physical models [START_REF] Liu | Learning Physics-Based Motion Style with Nonlinear Inverse Optimization[END_REF]. The robustness of these approaches however calls upon complex methods that move away, in a musical perspective, from a useable and comprehensible data analysis of the variability and the particularity of instrumental gestures. Such data analysis of instrumental gestures mostly rely on trajectory analysis [START_REF] Dahl | Playing the Accent: Comparing Striking Velocity and Timing in Ostinato Rhythm Performed by Four Drummers[END_REF] and classification/recognition methods of trajectory parameters ( [10] [12]).

Method

The analysis of timpani performance is directed by the present methodology (Figure 1), taking advantage of a timpani performance database and yielding to the extraction of gesture parameters that can be used as gesture inputs for the control of physically-based humanoids. A motion capture database was created, where three timpani players were asked to perform the capturing protocol designed for taking into account various tim-pani playing situations: drumstick grips, beat locations and musical varations. The motion was originally recorded using a Vicon 460 system with 6 cameras, sampled at 250 Hz. Markers have been placed both on the whole body of the performer (according to the Plug-in Gait model) and drumsticks. Each motion capture session results in the processing of the motion for a skeleton model (BVH format), including the position and orientation of the 19 joints composing the skeleton model.

The analysis of timpani instrumental gestures is achived by a two-level scheme considering task and constraint spaces. The task space can be defined as the 3D cartesian space containing end-arm and drumstick trajectories. The constraint space can be defined as the angular strategies that affect the physical components which condition the behavior of the performer, as angular trajectories and their derivatives can directly be correlated to joints' physical parameters such as stiffness or viscosity.

The parameterization of these spaces (task and constraint parameters) can be used as gesture inputs for the dynamic control of virtual characters [START_REF] Bouënard | Enhancing the Visualization of Percussion Gestures by Virtual Character Animation[END_REF] by task planning and constrain setup. In this paper, we focus especially on this parameterization step for studying the effect of drumstick grips on timpani instrumental gestures for the subjects S1 and S2.

4 Grip Effect: from the Tip of the Drumstick to Arm's Articulations

Variations in timpani playing range from drumstick grips, beat locations, to musical variations [START_REF] Bouënard | Enhancing the Visualization of Percussion Gestures by Virtual Character Animation[END_REF]. The present paper focuses specifically on the effect of french (F) and german (G) grips on timpani instrumental gestures, based on the analysis of beat attacks performed by two subjects S1 (French grip) and S2 (German grip). We focus on spatial and temporal differences that emerge from the analysis of the vertical component of the tip of the drumstick, as well as informations about arm articulations (shoulder, elbow, wrist) explaining these diffferences.

Axis Convention

Vertical Component of the Tip of the Drumstick

Quantitative features (Table 1) processed on the vertical component of the tip of the drumstick show that S1 (French grip) performs the same timpani gesture with much more amplitude. The mean of the height of the tip of the drumstick for the subject S1 is about twenty centimeters higher than for S2 (German grip), with a variance twice as high. This fact is strengthened by the vertical range of motion of the tip of the stick for S1 that is about twice as high than its counterpart for S2. The mean of the height of the tip of the drumstick shows moreover that the of the stick is in average closer to the timpani membrane for S2. Characteristic local extrema can also be observed during the preparatory gesture of beat attacks. Figure 3 presents an example of the vertical component of the preparatory gesture between two beat attacks, and the identification of three characteristic extrema denoted E1, E2 and E3. These extrema are temporally (temporal apparition in percentage of gesture's duration) and spatially characterized in Table 2. Vertical extrema E1, E2 and E3 (Table 2) are temporally equi-distributed for S1 showing a continuous preparatory gesture, whereas local extrema for S2 denote three discontinuous parts. E1 corresponds to the reaction of the previous rebound, between E1 and E2 the tip of the drumstick seems to seek a rest position (during more than the half of the whole movement duration) just above the timpani membrane, while E2 and E3 correspond to the amplitude that S2 gives for the next beat attack. Table 2 quantifies also the effect of the french and german grips on the vertical amplitude of the extrema.

French and german grips influence spatial and temporal characteristics of height of the tip of the drumsticks. The rest position between the extrema E1 and E2 for S2 could be explained by the proximity of the tip of the drumstick to the timpani membrane.

Shoulder Constraints

The analysis of the range of motion (Table 3) of shoulder's orientation and elbow's position shows that the upper-arm articulations of S2 are much more constrained than for S1. The range of motion of shoulder angles of S2 is so limited (between two and seven times lower than for S1) that the position of the elbow is almost constant. This could explain why the vertical amplitude of the tip of the drumstick for S2 is lower than for S1. The stiffness of the upper-arm is influenced by the drumstick grip, and partly explains the difference in the amplitude of the drumstick. Elbow and wrist angle strategies also emphasize these differences.

Elbow and Wrist Constraints

Figure 4 shows the importance of the flexion of the elbow (S1) and the twist of the wrist (S2) angle trajectories. For both subjects, we can indeed correlate the temporal apparition of the extrema of these angles to the temporal apparition of the extrema quantified on the vertical component of the tip of the drumstick (Figure 3).

The relationship between elbow and wrist articulations for flexion and twist angle trajectories (Figure 4) shows morevover the trend of the wrist in amplifying different angles. For the subject S1, the flexion angle of the wrist is amplified towards the flexion angle of the elbow during the whole duration of the movement. Whereas for the subject S2, the twist angle appears more predominant as it is amplified towards the twist angle of the elbow during the whole duration of the movement. Due to this amplification relationship between elbow and wrist angles, we focus only on the elbow articulation for the flexion and twist angle trajectories for comparing S1 and S2 trajectories (Figure 5). For both flexion and twist angles, two different strategies can be put in evidence.

The flexion angle for S1 shows the same oscillatory motion as the drumstick, whereas S2 seems to lock the flexion angle to a low value for about the half of the movement, until the late preparation of the next beat attack.

As for the twist angle, two opposite strategies are used. On the one hand, for S2, the twist value at impact is very high, so that the interior of the forearm almost faces the timpani membrane. During the preparatory gesture, the twist angle is almost locked and the subject lately tends to gain momentum by decreasing this twist angle. On the other hand, S1 seems to less constrain the twist angle (attested by the variation during the preparatory gesture) and tends to gain momentum by increasing the twist angle between two beat attacks.

Benefit of Task and Constraint Parameterization for the Synthesis

Our system currently allows the simulation of virtual timpani instrumental situations, and the retrieval of kinematic and dynamic characteristics about timpani instrumental gestures (Figure 6). It takes directly angular trajectories as raw inputs from the motion capture database for the physical simulation of timpani instrumental gestures [START_REF] Bouënard | Enhancing the Visualization of Percussion Gestures by Virtual Character Animation[END_REF]. This input step thus does not discriminate between timpani playing styles that are inherent to performers.

The parameterization step described in section 4 is the first step towards such a discrimination and the mod-elling of timpani gestures, in terms of providing control parameters for upper-limb postures and the planning of gestures. The two subjects S1 and S2 under study have shown different strategies, both at the task and constraints levels, underlining parameters that can be handled by our system. As for the task level, the local extrema that have been observed on the height of the tip of the drumstick are used as task control inputs to our system. Spatial and temporal characteristics yield the planning of timpani drumsticks motion during the simulation. As for the constraint level, the different strategies observed on the shoulder, elbow and wrist angles are used for the constraint setup of the degrees of freedom of virtual character joints. For S1, the oscillatory motion of the flexion angles for shoulder, elbow and wrist articulations is used for the simulation process. For S2, shoulder angles can be almost locked while the modelling and simulation of the elbow and wrist articulations involves twist angles.

Conclusion

We have presented in this paper the identification and the extraction of percussion technique parameters. The observation of differences on spatial and temporal characteristics of the height of the drumstick for two subjects with different grips has been explained by strategies involved in upper-arm stiffness, elbow and wrist angle trajectories. Such percussion style parameters can be used as inputs for our physically-based character animation framework for generating stylistic and expressive virtual timpani instrumental situations.

Future directions include the study of the effect of other timpani playing variations on the presented parameters, we aim namely at analysing the effect of beat locations and musical variations on timpani instrumental gestures.

Figure 1 :

 1 Figure 1: Methodology for the analysis of timpani performance.

Figure 2

 2 Figure 2 defines the XYZ global coordinate system that has been used during motion capture sessions. Every joint's position and orientation is later expressed towards this global frame. Special attention should be taken regarding the expression of joints' orientations. The geometric model issued from the motion capture software expresses orientations as XYZ euler sequences, the Z axis of an articulation being aligned

Figure 2 :

 2 Figure 2: Experimental setup and axis convention.

Figure 3 :

 3 Figure 3: Local extrema of the vertical component of the tip of the drumstick for S1 (top) and S2 (bottom) between two beat attacks.

Figure 4 :

 4 Figure 4: Intra-subject relationship between elbow (dark) and wrist (light) regarding flexion and twist angle trajectories for the subjects S1 (top) and S2 (bottom) between multiple beat attacks.

Figure 5 :

 5 Figure 5: Inter-subject comparison of elbow flexion (top) and twist (bottom) angle trajectories for the subjects S1 (dash) and S2 (plain) between multiple beat attacks.

Figure 6 :

 6 Figure 6: Retrieval of kinematic and dynamic motion cues thanks to the simulation framework of timpani instrumental gestures.

Table 1 :

 1 Vertical component of the tip of the drumstick.

	Subject (Grip)	S1 (F) S2 (G)
	Mean [mm]	1133	909
	Variance [mm]	111.2	46.1
	Range of Motion [mm] 434.2	178.6

Table 2 :

 2 Local extrema of the vertical component of the tip of the drumstick: average temporal (in percentage of gesture's duration) and spatial characterization.

	Subject (Grip)	S1 (F)	S2 (G)
	E1 [% / mm] 21.2 / 1255.6 12.0 / 916.95
	E2 [% / mm] 47.6 / 1059.9 68.3 / 881.58
	E3 [% / mm] 68.4 / 1258.9 85.2 / 1022.4

Table 3 :

 3 Shoulder and elbow range of motion.

	Subject (Grip)		S1 (F) S2 (G)
		rX 27.00	8.42
	Shoulder angle [ • ]	rY 21.81	2.97
		rZ 22.21	11.98
		X	98.2	13.3
	Elbow position [mm]	Y	133.5	31.9
		Z	68.5	9.8

Acknowledgments

The authors would like to thank Prof. Fabrice Marandola (McGill) and Prof. Sofia Dahl for helpful hints about percussion performance, as well as the timpani performers. This work is partially funded by the Natural Sciences and Engineering Research Council of Canada (Discovery and Special Research Opportunity grants), and the Pôle de Compétitivité Bretagne Images & Réseaux.