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Animation palette : an interface for prototyping dynamic aerial motions Zhao, Peng 2004

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Animation Palette: An Interface for Prototyping Dynamic Aerial Motions by Peng Zhao B . E . , Tsinghua University, 2000 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Master of Science in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Department of Computer Science) We accept this thesis as conforming to the required standard The University of British Columbia August 2004 © Peng Zhao, 2004 I U B C L THE UNIVERSITY OF BRITISH COLUMBIA FACULTY OF GRADUATE STUDIES Library Authorization In present ing this thesis in partial fulf i l lment of the requirements for an advanced degree at the Universi ty of British Columbia , I agree that the Library shall make it f reely avai lable for reference and study. I further agree that permiss ion for extensive copy ing of this thesis for scholarly purposes may be granted by the head of my depar tment or by his or her representat ives. It is understood that copying or publ icat ion of this thesis for f inancial gain shall not be al lowed wi thout my writ ten permiss ion. ? t 0 Name of Author (please print) Date (dd /mm/yyyy) Title of Thesis: Degree: Depar tment of The University of British Co lumbia Vancouver , BC C a n a d a Year: Xoof grad.ubc .ca / fo rms/? formlD=THS page 1 of 1 last updated: 20-Jul-04 A b s t r a c t This thesis presents an interface for the interactive design of dynamic aerial stunts, such as platform diving, freestyle aerial ski jumps and half-pipe snowboarding. This has applications for the prototyping of sports motions or for computer character an-imation in video games. The user selects from a library of actions, such as "stand", "pike" and "extend", in order to create a motion. Some actions define a set of tar-get joint angles for proportional-derivative controllers, while others invoke balance controllers employing closed-loop feedback. A real-time physics based simulation determines the final motion. A motion can be created interactively in real-time, or edited off-line to allow for incremental refinement. Mot ion timings can be optimized automatically to produce desired outcomes. The interface can be used to explore questions such as "Is this new stunt possible?" or "What if the pike began earlier?" We demonstrate the interface using simulations of platform diving (29 unique dives), freestyle aerial ski jumps (13 unique jumps), and half-pipe snowboarding (4 unique jumps). i i C o n t e n t s Abstract ii Contents iii List of Tables vi List of Figures vii Acknowledgements ix 1 Introduction 1 1.1 Animat ion Methods 1 1.2 Motivat ion 2 1.3 A n Example 4 1.4 Contribution 5 1.5 Thesis Organization 5 2 Related Work 7 2.1 Physics-based Animat ion • 7 2.1.1 Constraint-based Approaches 8 2.1.2 Controller-based Approaches 8 i i i 2.2 Fini te State Machine Controllers 9 2.3 Interactive Interfaces for Character Animat ion 10 2.4 Summary . 11 3 The Animation Palette Interface 12 3.1 Interface and Workflow 12 3.2 Act ion Buttons 14 3.2.1 Kinematic Actions 15 3.2.2 Dynamic Actions 15 3.3 Switching Between Actions 16 3.3.1 Kinematic to Kinematic Transitions 17 3.3.2 Dynamic to Dynamic Transitions . 17 3.3.3 Kinematic to Dynamic Transitions 18 3.3.4 Dynamic to Kinematic Transitions 19 3.4 Summary 19 4 Prototyping Dynamic Aerial Motions 20 4.1 Mot ion Stages and Stage Parameters 20 4.2 Dynamic Controllers 24 4.2.1 Proportional-derivative Controller •. 24 4.2.2 Balance Controller 25 4.3 Offline Mot ion Refinement 28 4.3.1 Manual Adjustment 28 4.3.2 Automatic Optimization 30 4.4 Summary 32 iv 5 Implementation and Results 33 5.1 Dynamics Simulation 33 5.2 Character Models 35 5.3 Platform Div ing 36 5.4 Freestyle Aer ia l Ski Jumping 40 5.5 Half-pipe Snowboarding 45 5.6 User Experiences 46 5.7 Summary ; 47 6 Conclusions and Future Work 50 6.1 Improved Dynamic Controller Actions . . . 50 6.2 Natural Mot ion 51 6.3 GamePad Interface 51 Bibliography 52 Appendix A Dynamic Model Details 56 Appendix B Description of Virtual Buttons 60 v L i s t o f T a b l e s 5.1 Dimensions of kicker jumps 41 A . l Physical parameters of diver model. . . 56 A . 2 Joint strength of diver model. . . 57 A . 3 Physical parameters of skier model 57 A.4 Joint strength of skier model 58 A.5 Physical parameters of snowboarder model 58 A . 6 Joint strength of snowboarder model 59 B . l Description of diving buttons 60 B.2 Description of buttons for aerial ski jump control 61 B.3 Description of buttons for snowboard control 61 v i L i s t o f F i g u r e s 1.1 Example of animation created online using our system 4 3.1 Interface of Animat ion Palette 13 3.2 Control of kinematic motions 16 3.3 A kinematic action to dynamic action transition 18 4.1 Simulated platform diving and ski jumping 21 4.2 5 stages for forward somersaults pike 22 4.3 Three examples of stage parameters 23 4.4 Sagittal plane balance control in standing 25 4.5 Lateral balance control in standing 26 4.6 Lateral balance control in crouching 27 4.7 Interface for offline design 29 4.8 Dive entry before and after optimization of the time for extension. . 31 4.9 Ski landing before and after optimization of the time for stretch. . . 31 5.1 Degrees of freedom used for diving, snowboarding and skiing models. 35 5.2 States of Platform Diving 36 5.3 Platform diving: forward 1^ somersault pike wi th one twist 38 5.4 Platform diving: backward l i somersault pike 38 v i i 5.5 Platform diving: reverse I5 somersault tuck . 39 5.6 Platform diving: bad entry for inward l\ somersault pike 39 5.7 States of Ski Jumping 40 5.8 Specification of ski-hil l 41 5.9 Dimensions of kicker jumps 41 5.10 Ski jump: double twisting double back flip 43 5.11' Ski jump: front pike single 43 5.12 Ski jump: back layout-tuck-layout 44 5.13 Ski jump: bad landing for a back-full-full 44 5.14 States of Half-pipe Snowboarding 45 5.15 Section view of half-pipe 46 5.16 Half-pipe snowboarding: back-grab ' 48 5.17 Half-pipe snowboarding: front-grab 48 5.18 Half-pipe snowboarding: back 360 49 5.19 Half-pipe snowboarding: crash landing for back-grab 49 v i i i A c k n o w l e d g e m e n t s First , I would like to thank my supervisor, Michie l van de Panne, for leading me into the world of computer animation. His guidance and encouragement was invaluable. I would also like to thank A l i a Sheffer and Jason Harrison for giving me useful comments to improve my thesis. Thanks to other members in Imager lab, who I was pleasant to work wi th . In particular, I wanna thank Hamish Carr for his suggestions on my thesis project, thank K e n Al ton for his help in my English, and thank Dave Burke for introducing me into the group of playing the Quake game. I am grateful to my friends here, including Shuzhen Wang, Xiaoj ing W u , Long L i , Pingdong A i , Yushuang L i u , Dan Xiao , L i n Zhong, Qian Huang, Kangkang Y i n , Chen Yang, Zhij in Wang and many others. They made my life in U B C a wonderful memory. Finally, I 'd like to thank my parents and my wife, Huanchun Ren, for their endless love and support. P E N G Z H A O The University of British Columbia August 2004 ix Chapter 1 I n t r o d u c t i o n Computer animation is a rapidly developing area in computer science, wi th appli-cations such as feature films, digital simulators, computer games and virtual'reality. Improved techniques are required to simplify and speed up the process of creating convincing animations. One key direction involves the use of physical simulation to generate physically realistic motions. This thesis presents an approach for the interactive design of dynamic aerial stunts. Before further discussing the motivation of our thesis, we wi l l first provide a brief overview of methods for creating human figure animations. 1.1 Animation Methods Broadly speaking, there are three widely used methods to make computer anima-tions: keyframing, motion capture and dynamic simulation. In keyframe character animation [3], the animator defines the position of al l parts of characters at specific points in time. These specified positions are known as keyframes. The computer then computes the in-between frames using an interpolation algorithm. Al though 1 keyframing is time consuming and requires significant ski l l , it remains the method of choice in many animated productions because of the complete control it offers the animator. A straightforward approach for generating realistic motion is to use a motion capture system [18] to record the 3D motion of a human actor and then map this motion onto an animated character. The ability to blend and transition between motions is very important for motion capture based animation system in order to provide adequate flexibility to create the wide range of desired animated motions required by video games, for example. Another key technology is that of retargeting the pre-recorded motions to an animated character having different dimensions from the person used to capture the motion, which is a common occurrence. One disad-vantage of this approach is that it is difficult to alter captured motions to realistically interact wi th environments different from the one in which they are obtained. Dynamic simulation [26] is a potentially powerful tool for making physically realistic animations. It has been used to both analyze and animate many classes of motion, including diving, running, and gymnastic motions. A major challenge in creating physically-based animation is that of solving for the required control to achieve desired behaviours, especially for complex models such as humans and many animals. Typically, this necessitates a great deal of trial-and-error in the design of the controllers for any given motion. 1.2 Motivation Presently, animators have used all three of the methods described above to produce high quality animations. For interactive applications such as video games, however, the animated characters need also respond to various environments, such as varying 2 terrains and interaction with obstacles. In this case, the simulation approach has advantages over the keyframing and motion capture. Also, the speed of today's computers now enables us to simulate a fully dynamic-based character in real-time. Recent games incorporate "rag doll" simulations which involve no active control. We believe this is due to the difficulty of designing controllers and that of defining appropriate interfaces between the game player and the game character. We present an interface which exploits the structured nature of acrobatic aerial movements to simplify the specification of physically-based prototypes of such motions. Specifically, we support platform diving, acrobatic ski jumping and half-pipe snowboarding based upon fully dynamic character simulations. Our system, called "Animation Palette", represents the required actions using a series of sequen-tially executed stages. For example, platform dives typically have the following sequence of actions: stand, crouch, takeoff, an aerial position such as a tuck or a pike, and extension prior to entry into the water. The complete diving motion can be created through the proper timing and execution of all these stages. Our interface maps each possible action for any given stage to an on-screen two dimensional virtual button. The timing of the button press represents when the specified action begins, and the exact location of the press on the button is used to represent two additional parameters which gives greater control over the action to be executed. When the interface is used in an online fashion, the simulation runs in real-time to produce the animation. As a result, the user is able to control a 3D character simulator in a fashion that is analogous to steering a plane via a flight simulator. The interface can also be used in an off-line fashion. For off-line design, we incorporate a timeline into the interface to represent the sequence of user inputs. 3 Virtual Buttons Control Parameters F i g u r e 1.1: E x a m p l e of a n i m a t i o n created on l ine u s i n g ou r s y s t e m . T h e user c a n refine the t i m i n g a n d l o c a t i o n parameters of p r e v i o u s o n l i n e i n p u t s a n d t h e n s imu la t e to see whe the r the desi red resul t is ach ieved . A l s o , g i v e n a m e t r i c to evaluate the q u a l i t y of a m o t i o n , e.g., the water en t ry angle for a p l a t f o r m dive , our sy s t em c a n a u t o m a t i c a l l y o p t i m i z e the t i m i n g of a speci f ied i n p u t to achieve the best ou tcome . 1.3 A n Example F i g u r e 1.1 shows an e x a m p l e of our interface for de s ign ing ac roba t i c a e r i a l m o t i o n s . T h e a n i m a t o r uses a mouse or s ty lus to choose w h a t a c t i o n the s i m u l a t e d charac te r 4 should do and how it should be performed by clicking at the appropriate position inside the vir tual button. Our system then maps the t iming and position parameters of these selections to controllers that compute the torque at each joint to drive the motion of the dynamic character. A physics-based simulation calculates the external forces such as gravity, and determines the final motion. Bo th the physical simula-tion and graphical rendering run in real time to provide the user wi th immediate feedback, displaying the animation as it is being created. 1.4 Contribution The primary contribution of this thesis is to provide a method for the interactive control of 3D physically-based characters. Specifically, we present an interface for prototyping dynamic aerial motions such as platform diving. Th is interface presents the control parameters of the simulation in an understandable manner, which allows the user wi th little knowledge of the underlying control mechanisms to make various of dynamic aerial motions in a short time. We develop a system that implements this interface technique and use it to design three types of stunts: platform diving, freestyle aerial ski jumps, and half-pipe snowboarding. This system demonstrates the feasibility of designing sports games based upon fully dynamic character simulations, as well as the possibility of creating useful tools for sports prototyping. 1.5 Thesis Organization The remainder of this thesis is structured as follows. After reviewing previous related work in Chapter 2, we provide an overview of the structure of our interface 5 in Chapter 3. Chapter 4 describes the components of our interface and the specific actions that our system currently supports. Chapter 5 demonstrates a variety of results obtained using our interface. Finally, Chapter 6 presents conclusions and future work. 6 Chapter 2 R e l a t e d W o r k The use of dynamic simulation to design animation is a topic of interest in the area of character animation. This chapter describes the work which is particularly relevant to ours. Firs t , we provide an overview of methods for producing physics-based animation. We then discuss the work specific to controllers based on finite state machines. Finally, relevant work on interactive control for character animation is reviewed. 2.1 Physics-based Animation Physical simulations can simplify the work required to generate realistic motions of passive objects, such as sliding blocks, bouncing balls, or clothing. However, for active objects such as humans and animals, we must also solve for the control mechanism to direct their movements. These must determine how the muscles act in order to produce desired motions. There are two different approaches to this problem, one is constraint-based and the other is controller-based. 7 2.1.1 Constraint-based Approaches Constraint-based techniques [2, 4, 16, 35] attempt to generate the animation through an optimization of a specified objective function subject to the constraints. T y p i -cally, the motions are defined as a trajectory with a collection of constraints imposed at specific times, such as the starting and ending positions. The physics is also im-posed as a constraint by adding the equations of motion as a constraint for each time step. The entire space-time trajectory is then optimized wi th respect to an objective, e.g., min imum control energy or minimum time, to achieve a unique "best" solution, thereby solving for a complete motion as a single optimization problem. The work of [8] presents an approach which can scale well to more complex characters using a set of objective functions and constraints that lead to linear time analytical first derivatives. More recently, this approach has been expanded upon in interactive techniques developed to control physical simulations of passive objects [23]. Space-time constaint techniques have several limitations. The solution de-rived by constraint-based techniques must be recomputed in new situations for which it was not calculated. Also, the available numerical methods often do not converge to acceptable answers because of spurious local minimum. 2.1.2 Controller-based Approaches Another approach, that of controller-based techniques, is to synthesize a controller that activates the muscles to perform some action. For instance, the locomotion of snakes [19] and the walking motion of cockroaches [17] have been produced wi th periodic controllers. In many cases, controllers are designed by hand [11, 36], which requires carefully fine-tuning the control parameters. There are also several meth-ods based on automatically synthesizing controllers [31, 32] using stochastic search 8 strategies. These automatic synthesis techniques work well only for finding con-trollers for simple creatures wi th a small number of degrees of freedom. This is because the space of possible controllers becomes exceedingly large as the degrees of freedom increase, which makes it difficult for the stochastic search method to locate useful solutions. One of the principle advantages of using controller-based techniques is that controllers are generally reusable and composable [6, 7, 27, 33]. A reusable con-troller can potentially be used to achieve a given motion wi th in different environ-ments. Composable controllers may be composed sequentially over time to generate a sequence of motions, which is what the user does wi th our system. Tha t is, the user chooses controllers for certain actions and arranges them in particular order to create the entire animation. 2.2 Finite State Machine Controllers Controllers can be based on finite state machines, which exploit the structured nature of certain motions, representing each phase of motion by a single state. The transitions between states can be time-based [31] that occurs after the controller has spent a prespecified time in a given state, or sensor-based [10] that occurs on a particular event. [11] created the animation of running, bicycling and vaulting using finite state motion control. These controllers are designed by hand which is difficult in that it requires specifying and testing many control parameters at each state. [31] presented an algorithm to automatically generate-and-test these parameters for relatively simple creatures and motions. The work of [14] uses a local stabilization technique upon a state machine model for the bipedal locomotion. The animations created in our system are similar to the work of [36], which 9 explored the creation of three simulated 10m platform dives. The controller in that work is also based on a finite state machine model, wi th al l the parameters tuned by hand. We provide a system for user based mid-level control, which significantly speeds up the creation of new motions by exposing all the key parameters in a readily accessible fashion, as shown in Figure 1.1. A s a result, we are able to rapidly author many new motions, as demonstrated by the set of 46 motions across 3 sports that we have authored to date using the system. 2.3 Interactive Interfaces for Character Animation There are many kinds of interactive interfaces for character animation. Most of them are based on kinematic approaches [15, 24], which copy particular joint angles from an input device, or copy things such as the positions of the hands or feet and then use inverse kinematics (IK) to compute joint angles. [21] developed a framework that used the two 6 -DOF tracking devices to control a 33-DOF character by layer-ing motions in several passes. [37] uses a foot pressure sensor pad to interactively control avatars. [28] demonstrates sketch-based interface for animating an articu-lated human character.. The system presented in [5] presents a novel mimic-then-act interface for creating animations. The increase of computer processor speed has made it possible to simulate the motion of articulated human models in real-time. This provides opportunities to extend the interactive control approaches used in flight and driving simulators to physically-simulated human figures. Ear ly work on the use of interactive control for physically-based character was presented in [29, 30], which proposed the use of manual manipulation to control the motion of bipedal characters. The work of [13] mapped the 2D movements of a mouse and keystrokes to control parameters in order 10 to design the motion of planar models. However the system d id not provide support for refining inputs and there are potential scalability problems for 3-dimensional motions. Our system employs additional levels of abstraction in the interface and allows for the control of 3D character motion. The timeline component of our interface further supports the refinement of t iming parameters. More recently, [22] demonstrates interaction wi th a partial dynamic 3D simulation for stepping motions. Our system is focussed specifically on dynamic-based aerial motions. More recently, NaturalMotion has developed an industrial software, called endorphin [1], for dynamic motion synthesis. This software allows users to instruct characters like directors instruct actors by choosing from an extensive list of available behaviours, such as balancing, jumping, and staggering. The A l and biomechanics techniques built in this system enable the simulated character to interact realistically wi th the environment. For example, when characters walk over a swaying bridge, they try to negotiate the bridge's movements for keeping balance. The motions created in our system depend mostly on user-based control which exploits the user's knowledge and intuition. The system-based control is only for maintaining balance during standing and crouching. 2.4 Summary We have presented the work from the computer animation literature that is related to our method. Our system builds on previous work in controller-based animation and interactive interfaces, as applied to 3D characters. The key ideas are embodied in our animation palette interface, which we describe in detail in the following chapter. 11 Chapter 3 The Animation Palette Interface The core of our animation system consists of an Animation Palette, which is intended to be analogous to a painting palette. Simply put, it provides a l ibrary of actions for the user to interactively select. The user can specify both when a particular action should happen and how it should be done, such as "walk quickly in this direction" and "fall to the left." This chapter presents an overview of this system, while the following chapter elaborates on the specifics of how it is used to create dynamic aerial motions. 3.1 Interface and Workflow Figure 3.1 shows an example interface of our system. The top part is a window displaying the animation that is being created. The inset-window i n the bottom left corner of the animation window serves to show information related to the current action, such as the action name and the target pose 1 . This inset-window is helpful for refining the motion offline, which is discussed in section 4.3.1. 1 This term will be defined shortly. 12 13 Below the animation window is a palette wi th 14 action buttons, one for each possible action. Each button defines an action and has two associated parameters that can be directly specified by the relative location of the user mouse-click or stylus-tap wi th in the action button. The meanings of the two parameters are defined according to the attributes of the action. The specific details of the palette and actions are presented later in sections 3.2 and 4.1. The bottom part of the interface is a timeline, which represents the sequence of user inputs. The user can adjust the t iming and parameters of previous action events and then replay or resimulate to see the result. For dynamic aerial motions, our system can automatically optimize the t iming of a specified input to achieve the best outcome. This process is described in further detail in section 4.3.2. A typical workflow starts by interactively creating an animation through the use of the action buttons. This is an online process,, that has the user specifying actions during an ongoing physics-based simulation of the character. The user then manually fine-tunes the motion offline using the timeline provided in our interface, or can resort to using the automatic t iming optimization feature. 3.2 Action Buttons There are two basic classes of actions in our system, kinematic actions and dynamic actions. Kinematic actions produce kinematically-generated animation, i.e., it in-volves a direct specification of positions and orientations over time and does not involve the use of a physics-based simulation. For dynamic actions, motions are the result of physical simulation, which models of the body mass and moments of inertia, internal and external forces and torques, and interaction wi th the environment. 14 3.2.1 Kinematic Actions Our system supports two types of kinematic actions, keyframe-based and motion capture-based. The first allows the user to specify parameterized keyframes. For instance, a "Point" action may use the x and y vir tual button parameters to indicate the direction of the finger pointing, thus various pointing actions could be specified by clicking different positions of a "Point" button. A n alternate technique for kinematic animation is the use of motion capture clips. In this case, the two parameters are used to offer high level control over the motion sequence. Figure 3.2 shows two examples of this. The "Walk" button tells the character to walk, and the click position of this button controls the direction (9) and speed (v = k • r, where A; is a constant) of walking. Likewise for the "Fal l" button, the y position specifies the forward distance of the fall and the x position indicates the direction of the fall relative to the current walking direction. 3.2.2 Dynamic Actions Dynamic character motions include both passive "rag doll" simulation and the use of active controllers. For passive simulations, the x and y parameters specify the environment properties such as the gravity and ground elasticity, or some inactive attributes of the character such as the joint stiffnesses. In our system, the majority of action buttons for prototyping dynamic aerial motions implement active controllers. The x and y parameters of click position are used to parameterize the controllers, such as the target pose for proportional-derivative controllers, and the target lean angle for balance controllers. The details of this wi l l be elaborated in section 4.1 and Appendix B . 15 t l t 2 Figure 3.2: Control of kinematic motions. 3.3 Switching Between Actions When action A is in progress and a user then selects action B, we need a method for transitioning between these two types of actions. A s stated above, our interface sup-ports both kinematic actions and dynamic actions. This section discusses the four types of transitions that can occur during animation, namely kinematic to kinematic transitions, dynamic to dynamic transitions, kinematic to dynamic transitions, and dynamic to kinematic transitions. 10 3.3.1 Kinematic to Kinematic Transitions Transitions between kinematic actions in our system are computed by blending from one animation to another over a period of 0.5 seconds. We blend the global position, global orientation, and joint angles using a linear interpolation method. This can work well when the new motion is sufficiently similar to the current motion. Other issues need to be solved to expand the range of motions between which we can make realistic transitions, such as the footskate cleanup. We do not solve this problem because the focus of our work is on generating and controlling dynamic aerial motions. 3.3.2 Dynamic to Dynamic Transitions Transitioning between dynamic motions is straightforward because it involves a sim-ple substitution of controllers. The continuity of the motion is guaranteed because the state of the system (positions and velocities) is preserved when the new dynamic action begins. The new controller begins control over the simulated character imme-diately upon the user choosing a new dynamic action. For example, the "landing" action of ski jumps happens once the user selects it and drives the character to-ward the pose preparing for landing. Note that the new controller does not provide a guarantee of a successful motion. Rather, it relies on the user's experience and perception to determine whether the character can successfully perform landing. De-veloping "automatic landing" controllers for actions which are difficult to reliably achieve is not wi th in the scope of this thesis. 17 Kinematic Motion I Dynamic Motion Switch to Dynamic Simulation Figure 3.3: A kinematic action to dynamic action transition. 3.3.3 K i n e m a t i c t o D y n a m i c T r a n s i t i o n s During kinematic to dynamic transitions, current positions and computed velocities for the degrees of freedom of the character become the ini t ia l states of the physical simulation which is initiated. Thus, the animated characters w i l l ini t ia l ly preserve their linear and angular momentums immediately after the transition, which results in a natural-looking motion. Figure 3.3 shows an example of this. The character in red represents the first animation frame after the transition from a kinematic motion to the dynamic simulation. After that point the character can have physically-realistic interaction wi th the environment, such as the collisions w i th the block and the tree. 18 3.3.4 Dynamic to Kinematic Transitions The dynamic to kinematic transition is a hard problem which requires a large library of motion clips and adaptive blending algorithms. In our system, we simply stop the physical simulation and do a straight cut to the kinematic action, which thus results in a visible discontinuity in the motion. 3.4 Summary The animation palette interface provides a l ibrary of parameterized actions for the user to choose. These actions can be kinematic or dynamic. The user can inter-actively select among them to create a motion sequence, or refine them offline to improve upon a previous animation. In the next chapter, we wi l l discuss in detail the use of dynamic actions for prototyping acrobatic aerial motions. 19 Chapter 4 P r o t o t y p i n g D y n a m i c A e r i a l M o t i o n s Interactively controlling 3D dynamic characters is challenging due to the number of degrees of freedom (DOF) and issues such as the difficulty of maintaining balance. The interface should ideally be sufficiently expressive for the user to create a large variety of motions while sti l l being tractable to learn. The animation palette provides a generic framework for creating animations, and we shall use it to design dynamic aerial stunts. Figure 4.1 shows two examples of the types of simulated motions that can be rapidly constructed using our interface. 4.1 Motion Stages and Stage Parameters The structured nature of acrobatic aerial motions makes it possible to represent the required actions using a series of sequentially executed stages. For example, platform dives can typically be represented by the following sequence of actions: stand, crouch, takeoff, an aerial position such as a pike or a tuck, and extension. A 20 Figure 4.1: Simulated platform diving and ski jumping. user can create the complete diving motion through specifying the proper t iming and execution of al l of these stages. As an example, Figure 4.2 illustrates the stages for forward somersaults in a pike position for platform diving. The simplest of our presented motions have 4 stages, while the most complex have 8 stages. Throughout the remainder of the thesis, the words stage and action w i l l be used interchangeably. We use one action button for controlling each possible action. The t iming of the button selection represents when the associated action takes over the control of the simulated character, while two action parameters are given by the x and y location of the selection within the button. These action parameters serve to parameterize the action to make a variety of motions. The following list describes the types of action parameters used in our system. • Target joint angle: Sets the desired angle of a single joint for proportional-derivative controllers discussed in section 4.2.1. For example, the x-location of the takeoff button specifies the desired bend angle of the waist during a takeoff jump. • Target body position: Indicates the desired position of several joints. For 21 Stand Crouch Takeoff Pike Come-out Forward Arms-Up Forward Figure 4.2: 5 stages for forward somersaults pike. instance, the x-location of the open pike button click represents the target angle of the pike, which is a combination of the waist and hip angles. • S t i f f n e s s o f j o i n t : Designates the stiffness of one or more joints for the proportional-derivative controllers, which is helpful to create jumping motions wi th different heights. • C e n t e r o f m a s s : Denotes a target position for the center of mass relative to the location of ankles. This is an important parameter for the standing and crouching actions and preparing the body for a somersault, as illustrated in section 4.2.2. • S p e e d o f p e r f o r m a n c e : Specifies how fast the character w i l l reach the given target pose. It is important for most aerial actions like pike or tuck and it is discussed in detail in section 4.2.1. • I n i t i a l s t a t e : Represents the starting locations of the motions. For example, in the case of ski jumps, this parameter specifies the starting height on the h i l l leading towards the ski jumps. Figure 4.3 shows three examples of action buttons used in our platform diving interface. The two key parameters for the crouch action are the lean angle and 22 (a) Crouch (b) Takeoff (c) Open Pike Figure 4.3: Three examples of stage parameters. the height of crouch, which are mapped to the x parameter and the y parameter respectively. The lean angle is determined by the position of center of mass relative to the location of ankles, and is implemented in our system by setting the target lean angle of the balance controller discussed in section 4.2.2. The height of crouch is determined by the target hip and knee angles. The important attributes for the takeoff action are the ini t ia l rotation momentum, as determined by the target waist bend angle while taking off (x), and the height as determined by the stiffness of the hips and knees while jumping (y). For the open-pike action, the controllable parameters are the target angle of pike (x), which is a combination of the waist and hip angles, and the speed to reach this pose (y), which is determined by the interpolation duration of the target angles discussed in section 4.2.1. A complete summary of the set of buttons used for the platform diving, acrobatic ski jumping, and snowboard control is given in Appendix B . 23 4.2 Dynamic Controllers In order for a given dynamic action to be realized, we need to determine low-level controllers that compute how much torque each joint should exert in order to achieve the desired result. There are two classes of controllers used in our system, one for driving the character toward target poses and another class of controller for maintaining balance. We now discuss each of these in turn. 4.2.1 Proportional-derivative Controller The joint torques that drive joint angles toward their desired values are computed using proportional-derivative (PD) controllers: T = kp • (8* desired @current) ^d ' ^ i where r is the torque applied at the joint, Qdesired is the desired joint angle, 0current is the current joint angle, 0 is the relative angular velocity of the two links connected by that joint, and kp, kd are proportional and derivative control constants. The values of kp and kd control the strength of the actuator for each joint, which should be strong enough to achieve particular desired actions. Appendix A gives the specific control constants used for our dynamic models. For the hip, knee, and ankle joints, their control constants are different across various actions. For example, the "stand" action usually requires higher kp and kd values at the ankles than the "pike" action. Linear interpolation of the target angles, i.e., ^desired-, is used between target-angle poses in order to produce smooth transitions between the most recent pose and a newly chosen pose. The duration of the interpolation is exposed as one of the motion parameters for many actions, such as pike and tuck. 24 C O M Figure 4.4: Sagittal plane balance control in standing. 4.2.2 Balance Controller Maintaining balance is crucial for stages that preceed and follow the aerial portions of the motion. Balance control can depend on many factors, such as the distance between two feet and the placement of two feet. In our system, we focus on the balance during a regular stance with the feet being spaced at shoulder width . According to [34], balance in the sagittal plane can be modeled as an inverted pendulum about the ankle joint, as shown in Figure 4.4. The torque due to gravity is M-g-h- sin(/9) KM -g-h-9, where M is the mass of the character, g is gravitational acceleration, h is the height from the ankle to the Center Of Mass ( C O M ) , and 6 is the leaning angle as measured in radians. The torque exerted by the spring muscle at the ankle is r = kp • 8. A s long as kp > M-g-h, the ankle wi l l be sufficiently strong to maintain the equilibrium position. The addition of damping in the ankle joint torque ensures that the body 25 Figure 4.5: Lateral balance control in standing. wi l l eventually stop near the target leaning angle, which is set by the x parameter of the "Stand" and "Crouch" buttons. The body can no longer maintain balance when the lean angle is such that the projection of C O M onto the ground plane falls outside the support polygon of two feet. However, such a body position is required before a jump in order to initiate angular momentum. The front-back balance controller thus does not only serve to maintain balance, but also to prepare the body for somersaults. Using the ankles for lateral stability is not very stable because the width of foot is much smaller than the length of foot. Thus, other joints must be used to help keep lateral balance. The hip abductor and adductor moment can move the Center Of Pressure ( C O P ) between two feet, which draws the C O M back to the equilibrium position. For human during the quiescent stance, the lateral balance is dominated by this hip load-and-unload strategy [34]. Figure 4.5 shows the character in the frontal plane, in which the equilibrium position is the point midway between 2G Figure 4.6: Lateral balance control in crouching. the two feet. The torques of the hip abductor and adductor are computed using a spring-damper model: T — /up * X ' 35 where x is the distance between the C O M and its equilibrium position and x is the velocity of the C O M . In the crouched position, a knee-based strategy is used for lateral balance. Similar to the hip strategy, the knee flexor and extensor also serve to move the location of the C O P in order to control the C O M . For example, extending the left knee and flexing the right knee wi l l move the C O M to the right. Figure 4.6 illustrates a crouching character, using knee joints to maintain lateral balance. Maintaining balance is a challenging part of creating dynamic character mo-tions. The mechanisms discussed above can only solve the balance problem in some cases. For complex problems, such as the landing of the skier and the snowboarder, 27 we need to develop more adaptive controllers. This is discussed as future work in Chapter 6. 4.3 Offline Motion Refinement Our system supports both online and offline authoring of aerial motions. Online use of the interface enables the creation of simulated animations in real time through the use of the action buttons during an ongoing simulation. Offline adjustments can be used to refine the resulting motions, through either manual adjustment or automatic optimization. 4.3.1 M a n u a l A d j u s t m e n t Manual adjustments are useful for producing a motion through iterative refinement and is supported through the use of a timeline included at the bottom of the inter-face panel. Each vir tual button press introduces an event that is displayed on the timeline, as shown in Figure 4.7. The t iming of this event can be adjusted directly on the timeline by dragging wi th the mouse. Selecting any event marker on the timeline also allows for the associated action parameters to be altered, as specified by the selection point within the associated vir tual button. In Figure 4.7, the red cross-hairs drawn on the "Takeoff" button illustrate the current parameter settings associated wi th a selected takeoff action. These parameters can be adjusted wi th a mouse or stylus press at the desired location wi th in the button. Once a set of desired adjustments has been made, the user hits a "Resimulate" button in order to review the newly refined motion. Unlike during online creation, manual adjustments offline have no real-time feedback of the animation. Nevertheless, there are several useful feedback signals 28 Selected Action Timeline Cursor 1 Inputs Optimization Result Figure 4.7: Interface for offline design. 29 that can help the user wi th the motion refinement. A simple-but-helpful cue is showing the target pose while the user adjusting the parameters associated wi th a button. This provides the user with immediate feedback of what k ind of action is specified. As shown in Figure 4.7, the inset-window in the bottom left corner of the animation window serves this purpose. Another useful form of visual feedback is to display the animation frames while the user drags the timeline cursor. This is especially helpful for adjusting the t iming of inputs. Since some aerial motions pass by too quickly for the user to catch particular events, such as the specific time instant when the skier reaches the top of the kicker jump, offline scrolling through the animation is the best way to handle this. 4.3.2 Automat ic Optimizat ion To further speed the creation of successful simulated aerial motions, our system can automatically optimize the t iming of a specified input to achieve the best outcome. Accomplishing this requires a metric to evaluate the quality of a motion and a fast function evaluator, which in our case consists of a simulation that determines how changes in t iming affect the given metric. Numerical methods which exploit deriva-tive information wi l l generally require the fewest function evaluations. However, this requires differentiable optimization metrics, which may be difficult to achieve in the face of non-linear effects such as joint limits and other discontinuous events that may occur during the course of a simulation. In the face of these difficulties, we perform the optimization by discretely sampling the t iming parameter in question at regular intervals that bracket its current value. Function evaluations are then carried out using a dynamic simulation from that point in time forward to the time 30 Figure 4.8: Dive entry before and after optimization of the time for extension. Figure 4.9: Ski landing before and after optimization of the time for stretch. where the metric is evaluated. The previous motion is used to start each of these simulations from the appropriate dynamic state. Our optimization metric for platform diving is computed by integrating the error of the water entry angle for the body: t2~h where C is the total error which needs to be minimized, t\ is the time at which the diver first touches the water, ti is the time at which the upper body is fully under water, and E(t) is the error of the entry angle at time t which is defined in terms of the angular deviation from the vertical. A component measuring twist errors could 31 also be added, although we have not experimented wi th this. Figure 4.8 illustrates several frames from a diving motion before and after the optimization of the t iming parameter associated wi th the extension action, which is the last action prior to water entry. Similarly, the optimization metric for ski jumping is calculated by integrating the error of the landing angle for the body, from the time the skier first contacts the ground tp the time it reaches the end of the landing area. Figure 4.9 shows the landing motions before and after the optimization of the t iming for the stretch action, which is the last action prior to landing. 4.4 Summary In this chapter, we have presented the animation palette framework for prototyping dynamic aerial motions. The required actions are represented by a series of sequen-tially executed stages. We use one action button for controlling each possible action. PD-controllers compute the torque at each joint for driving the character to achieve a desired action. Balance controllers are responsible for actively maintaining the balance. Finally, offline motion refinement can serve to improve motions to achieve the desired result. In the following chapter, we wi l l describe implementation issues in detail and we present the resulting motions created using our system. 32 Chapter 5 I m p l e m e n t a t i o n a n d R e s u l t s We have implemented a system using our- interface ideas to design motions for platform diving, freestyle aerial ski jumps, and half-pipe snowboarding. The next two sections wi l l describe the dynamic simulation and the character models we used to make the aerial motions, and the remaining sections w i l l describe our results in detail. 5.1 Dynamics Simulation Our system makes use of the publicly-available Open Dynamics Engine ( O D E ) [26] for computing and integrating the equations of motion. One advantage of this simulation library is that models can be assembled on the fly. Links and joints can be added, removed or changed during the simulation. This feature makes O D E more flexible to use than some other libraries such as S D / F A S T [12] which requires pre-compiling the models before the simulation begins. The process of simulating the motions of rigid bodies through time has two parts. Dur ing each time step, the first part uses the equations of motion to determine 33 the instantaneous accelerations for al l the rigid bodies. The second part, namely the integration, advances the current time by a given step size and adjusts the state of al l the rigid bodies for the new time value. O D E uses a first order semi-implicit integrator, which includes both the implicit forces (i.e., constraint forces at the joints) and explicit forces (i.e., external forces applied by the environment and the applied joint torques). Since we use controllers to drive the character toward target poses and the external forces are explicit, the integration can become unstable when the system is stiff, i.e., when kp and kj are large. Reducing the simulation time step enhances the stability, but results in slower simulation speed. We limit the maximum torque that each joint can exert to avoid excessively-large control torques, which reflects the reality of limited muscle forces and also helps wi th the stability of the simulation. In our system, the maximum allowable torque at each joint is given by Tmax = 1.0 • kp, where kp is the spring constant for this joint. For collision detection, we assign each body a simple shape (e.g. sphere or box), and use the collision detection engine supplied wi th O D E to determine which bodies are in contact at each time step. The average time of this collision engine for intersection testing is 0(n) [26], where n is the number of objects. To simplify the control and increase the stability, we only process collisions between the character and the environment (e.g., ground), and we ignore the self-collision of different parts of the character model. The collision reaction forces in O D E are based on a penalty method and a Coulomb friction model is used to l imit the tangential component of the reaction forces. This is sufficient to simulate the interaction forces between the character and the ground. The ODE-based simulation runs in real-time on a 2.66 G H z P 4 P C . The fixed time step which we use to integrate the equations of motion is 0.001s. Wi thout 34 Figure 5.1: Degrees of freedom used for diving, snowboarding and skiing models. graphical display, our diving simulation can compute 3.7 simulation seconds in 1 wall-clock second. For skiing and snowboarding, the performance numbers are 1.68 and 1.69 respectively. The diving simulation requires significantly fewer collision detection computations and is faster as a result. 5.2 Character Models The character models are based on the anthropometric parameters used in [6]. We make changes to the original model according to the nature of each aerial motion. For example, the skier needs to bind each foot to a ski. In order to increase the speed and stability of dynamic simulation, we remove the wrist joints and the joint 35 Stand Crouch Forward Arms Up Stand Crouch Backward Arms Down Figure 5.2: States of Platform Diving . between head and neck. These joints have little effect on the simulation results and can make the simulation unstable, due to the large disparity between lightweight body parts such as the hands and the heavier links such as the torso. The structures of the three character models are shown in Figure 5.1. The diver model has 13 links and 26 Internal Degrees Of Freedom ( IDOF) . The snow-boarder is the same but wi th an extra D O F for each ankle. Lastly, the skier has fixed ankles, giving 13 links and 22 I D O F . The details of these dynamic models are given in Appendix A , including all the physical parameters of the links (e.g., mass and moment of inertia) and joints (e.g., joint strength). 5.3 Plat form Diving Platform diving is the least difficult motion to design because it does not need to solve the problem of balance upon landing, as is the case wi th ski jumping and snowboarding. We represent the motion of dives wi th 5 stages of actions: stand, crouch, takeoff, one or more aerial positions, and extension before entry into water. Our interface has 12 action buttons for the control of al l possible actions during diving. Figure 5.2 shows the actions and the possible transitions between them. 36 Table B . l illustrates the actions and x and y parameters associated wi th each button. We have used the interface to author 29 types of 5m platform dives, including all four takeoff methods a diver can use: forward, backward, inward and reverse dives. In the diving terminology of [20], we have authored dive types 101a, 101b, 101c, 103b, 103c, 105b, 107c, 201a, 201b, 201c, 203b, 203c, 205c, 301a, 301b, 301c, 303b, 303c, 305c, 401a, 401b, 401c, 403b, 403c, 405b, 405c, 407c, 5132d. Figures 5.3, 5.4 and 5.5 show three of them, while Figure 5.6 illustrates an unsuccessful dive in which the extension action is executed too early. 37 38 39 5.4 Freestyle Aerial Ski Jumping For skiing, we unite the lower leg, foot and ski into one rigid body segment for the simulation model. Similar to platform diving, aerial ski jumps have 6 executed stages: in-run, crouch, takeoff, aerial positions, stretch for landing and finish posi-tion. The purpose of the "finish" position is to improve the visual effect by making the character straighten and raise the arms upon a successful landing. Table B.2 describes the definition of the vir tual buttons we use to control the acrobatic ski actions and Figure 5.7 shows the feasible transitions between them. For the in-run action, one of the button parameters provides control over the start position on the in-run, and hence the speed accumulated upon take-off. Big Crouch Kicker Arms Up Small Crouch Kicker Arms Down Takeoff Figure 5.7: States of Ski Jumping. The kicker jumps and ski-hil l in our system have been designed to match freestyle skiing competition specifications [25]. Figure 5.8 shows the specification of ski-hil l , while Figure 5.9 and Table 5.1 illustrates the dimensions of kicker jumps. In reality, the snow friction coefficients are different between the forward sliding Cf and the sideway sliding Cs. We use 0.001 for Cf and 0.1 for Cs to ensure the realistic interaction of the skis and the snow. 40 Figure 5.9: Dimensions of kicker jumps. kicker A B C D(lm) E ( 2 m ) F ( 2 m ) G ( 2 m ) small 6.70 3.25 5.95 50° 30° 13° 5° big 8.10 3.65 6.70 55° 33° 14° 6° Table 5.1: Dimensions of kicker jumps. The creation of successful aerial ski jumps is more difficult than diving be-cause of the difficulty of maintaining balance upon landing. It is important to find the best time for extension in order to decrease the rotation and twist speed before landing. We decrease the stiffness of knees and hips for landing position in order to 41 cushion the kinetic energy of the character when landing on the ground. This also makes the landing action look more natural. A series of 12 aerial ski jumps were created using our interface: b F F , b L , b L L T , b L T L , b P P , b T T , fF, £L, fPP, fT, f T T , and f T T T , where T and 'b' indicate front and back flips respectively, ' F ' indicates a flip wi th a full twist, and ' L ' , ' P ' , and ' T ' indicate layout, pike, and tuck positions, respectively. Figures 5.10, 5.11 and 5.12 show three of them and Figure 5.13 illustrates a bad landing for a back-full-full jump. We have also experimented wi th simulating landings in water, as is typical of summer training. 42 Figure 5.10: Ski jump: double twisting double back flip. IS! Pi \ / Figure 5.11: Ski jump: front pike single. 43 1 Figure 5.12: Ski jump: back layout-tuck-layout. .1: Figure 5.13: Ski jump: bad landing for a back-full-full. 44 5.5 Half-pipe Snowboarding Half-pipe snowboarding was the most difficult motion to produce using our system, the principal reason being the difficulty of maintaining balance at a variety of points in the half-pipe. Landing diagonally on the transition between the wall and ground was found to be much harder to control than on the landing h i l l of ski jumps. Also, the snowboarder needs to be well balanced upon approaching the wall of the half-pipe in the lead up to the jump in order to successfully initiate a jump. The terrain anticipation of a real snowboarder during the rapid transition from the horizontal to the near-vertical edge of the half-pipe is not implemented in our system, making this challenging to properly execute. Face Left Takeoff Face Right C r o u c h A" Front Landing r>—! Back G r a b Figure 5.14: States of Half-pipe Snowboarding. From our experience with platform dives and ski jumps, motions wi th twists were generally found to be more difficult to reconstruct than motions without twists. Most half-pipe stunts involve a twist and this thus makes the snowboarding motions more challenging to control. We have thus far created 4 types of half-pipe snow-boarding stunts, including a back 360, back 360 with grab, a front grab, and a back grab. Figure 5.16, 5.17, 5.18 and 5.19 illustrate some successful or unsuccessful mo-45 tions we have made. Figures 5.14 and Table B.3 explains the vir tual buttons for this stunt. The specification of the half-pipe comes from [9]. Figure 5.15 illustrates the section view of the half-pipe, which has an inclination wi th respect to the horizontal of 15° in the dimension going into the page. Figure 5.15: Section view of half-pipe. 5.6 User Experiences Our system has been used by several users who have little knowledge of control mechanisms. After 10 minutes tutorial, all of them can create relatively simple diving motions in 5 minutes, such as forward 1^ somersaults in pike position, and backward l\ somersaults in tuck position. For the dives which involve more som-ersaults, these users need some basic knowledge of platform diving and about half an hour guided practise before they can produce such motions wi th in 10 minutes. For the creation of ski jumps, these users usually spend most of time on finding the appropriate time of takeoff and the proper pose for landing. This makes the time of creating successful ski jumps three times as much as that of creating successful platform dives. As we expected, the most difficult part is the creation of half-pipe snowboarding or motions which involve a twist. Mak ing these motions may take several hours to fine-tune the inputs. 46 5.7 Summary Our animation system provides a method for interactively controlling 3D simulated characters. It allows for dynamic aerial motions to be produced in a short time by a novice user. A variety of motions and variations can be created as demonstrated in this chapter. Since we expose the key parameters of each action in a readily accessi-ble fashion, this interface can work in different environments wi th no modification. For example, the vir tual buttons for 5m platform diving can also be used to produce 10m platform diving without any changes to the animation palette. The main weakness of this system lies in the balance controllers, especially for motions wi th twist and landing actions. More robust and adaptive control strategies are required to make the interface more tractable for creating successful examples of these types of motions. 47 HI • Figure 5.18: Half-pipe snowboarding: back 360. / m Figure 5.19: Half-pipe snowboarding: crash landing for back-grab. 49 C h a p t e r 6 Conclusions and Future Work We have presented an interface for prototyping dynamic aerial motions. This tech-nique demonstrates the future feasibility of designing sports games based upon fully dynamic character simulations. It allows a user to exploit his knowledge and in-tuition to design a variety of motions. Our interface can also help the user to understand and learn these acrobatic stunts. There are several directions which require further research to make the in-terface easier to use and the resulting motions more realistic. 6.1 Improved Dynamic Controller Actions We plan to investigate how controllers specific to the execution of twists and landing actions can be constructed. Addi t ional work on "automatic landing" controllers and user control is required in order to make the required user skil l more manageable for use in a game scenario. Our current automatic optimization tool uses a simple metric and optimization technique. We wish to explore the use of other metrics that allow for more abstract specifications of a desired motion, as well as an analysis of 50 the t iming requirements of the various stages of the motion. 6.2 Natural Motion We wish to seek feedback from coaches and athletes wi th regard to using this type of tool. In order to become an accurate prototyping tool, better strength models wi l l likely be required. It would also be interesting to use this system in conjunction wi th a vision-based motion tracking system. This would support the asking of "what if" questions in the context of exploring changes to a recently executed motion. 6.3 GamePad Interface Another possible direction for future work is toward the using of gamepad as the input device. One of the potential applications of our research is sports genre video games. These are most commonly played on video game consoles, which are equipped wi th a gamepad rather than a mouse. Although a gamepad has a large number of inputs, namely dual thumb sticks and about ten buttons, it is difficult to map our parameterized action button interface onto such a device. We need to find other methods to map the gamepad inputs to the control parameters. 51 Bibliography [1] Nick Alexander. Endorphin, ht tp: / /www.naturalmotion.com/. [2] Lynne Shapiro Brotman and A r u n N . Netravali. Mot ion interpolation by op-t imal control. In SIGGRAPH 88, Computer Graphics Proceedings, pages 309-315. A C M Press, 1988. [3] K y l e Clark. 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Eurographics Association, 2003. 55 Appendix A Dynamic Model Details Below are the details of three dynamic models shown in Figure 5.1: diver, skier and snowboarder. For each model, the C O M of hip is placed at the origin, wi th the character facing the positive z-axis. We present only the information of left arm, hand, leg and foot; the properties of corresponding right parts are symmetrical. For some joints, the strength constants depend on whether the character is in stance, takeoff, flight or landing state. In these tables we use's ' , 't', ' f and '1' to represent them. link mass (kg) center of mass (x,y,z m) moment of inertia (x,y,z kgm2) hip 16.61 0.000 0.000 0.000 0.1147 0.1147 0.1445 thigh 8.35 0.086 -0.237 0.025 0.1654 0.0176 0.1662 shin 4.16 0.086 -0.663 0.025 0.0522 0.0069 0.0522 foot 1.34 0.086 -0.887 0.075 0.0076 0.0084 0.0020 chest 29.27 0.000 0.335 0.025 0.5282 0.1645 0.5829 neck 1.00 0.000 0.611 0.025 0.0021 0.0021 0.0021 head 5.89 0.000 0.792 0.025 0.0457 0.0261 0.0417 upper arm 2.79 0.300 0.498 0.025 0.0047 0.0229 0.0229 lower arm 1.21 0.568 0.498 0.025 0.0009 0.0061 0.0062 hand 0.55 0.732 0.498 0.025 0.0004 0.0018 0.0015 Table A . l : Physical parameters of diver model. 56 name location (x,y,z m) axis k p k d hip 0.086 0.000 0.025 X 1275 60 y 200 10 z 1275 60 knee 0.086 -0.475 0.025; X 1275 60 ankle 0.086 -0.850 0.025 z 80 5 x (s) 1275 60 X (t, f) 120 12 waist 0.000 0.114 0.025 X 1275 60 z 1275 120 y 800 40 neck 0.000 0.555 0.025 z 100 10 y 20 2 X 200 10 shoulder 0.152 0.498 0.025 y 100 5 z 100 10 elbow 0.449 0.498 0.025 X 20 1 y 100 5 Table A .2 : Joint strength of diver model. link mass (kg) center of mass (x,y,z m) moment of inertia (x,y,z kgm?) hip 16.61 0.000 0.000 0.000 0.1034 0.1034 0.1445 thigh 8.35 0.086 -0.237 0.025 0.1654 0.0176 0.1662 shin 4.16 0.086 -0.663 0.025 0.0522 0.0069 0.0522 foot 2.34 0.086 -0.891 0.083 0.0141 0.0147 0.0044 ski 1.80 0.086 -0.952 0.094 0.33.76 0.3394 0.0020 chest 29.27 0.000 0.335 0.025 0.5282 0.1645 0.5829 neck 1.00 0.000 0.611 0.025 0.0021 0.0021 0.0021 head 5.89 0.000 0.792 0.025 0.0457 0.0261 0.0417 upper arm 2.79 0.300 0.498 0.025 0.0047 0.0229 0.0229 lower arm 1.21 0.568 0.498 0.025 0.0009 0.0061 0.0062 hand 0.55 0.732 0.498 0.025 0.0004 0.0018 0.0015 Table A . 3 : Physical parameters of skier model. 57 name location (x,y,z m) axis k p k d hip 0.086 0.000 0.025 z 900 30 y 1275 60 x (s) 4000 60 X (t, f) 1275 60 x(l) 400 60 knee 0.086 -0.475 0.025 x (s) 4000 60 X (t, f) 1275 60 x(l) 400 60 waist 0.000 0.114 0.025 X 2000 100 z 2000 100 y (s, f, l) 2000 100 y ( t ) 3000 100 neck 0.000 0.555 0.025 z 100 10 y 20 2 X 200 20 shoulder 0.152 0.498 0.025 y 100 5 z 100 10 elbow 0.449 0.498 0.025 X 20 1 y 100 5 Table A.4 : Joint strength of skier model. link mass (kg) center of mass (x,y,z m) moment of inertia (x,y,z kgm2) hip 16.61 0.000 0.000 0.000 0.1147 0.1147 0.1445 thigh 8.35 0.127 -0.234 0.025 0.1654 0.0176 0.1662 shin 4.16 0.201 -0.652 0.025 0.0522 0.0069 0.0522 foot 2.34 0.233 -0.887 0.075 0.0141 0.0147 0.0044 snowboard 3.80 0.000 -0.950 0.075 0.0390 0.6595 0.6209 chest 29.27 0.000 0.335 0.025 0.5282 0.1645 0.5829 neck 1.00 0.000 0.611 0.025 0.0021 0.0021 0.0021 head 5.89 0.000 0.792 0.025 0.0457 0.0261 0.0417 upper arm 2.79 0.300 0.498 0.025 0.0047 0.0229 0.0229 lower arm 1.21 0.568 0.498 0.025 0.0009 0.0061 0.0062 hand 0.55 0.732 0.498 0.025 0.0004 0.0018 0.0015 Table A . 5 : Physical parameters of snowboarder model. 58 name location (x,y,z m) axis k p k d hip 0.086 0.000 0.025 x (s, f) 1275 60 X (t) 200 60 x(\) 400 60 z(s) 4000 60 z (t, f, 1) 900 30 knee 0.168 -0.468 0.025 x (s, f) 1275 60 X (t) 200 60 x ( l ) 400 60 ankle 0.233 -0.837 0.025 X 170 17 y 50 5 z 80 8 waist 0.000 0.114 0.025 z 2000 100 X 2000 100 y (s, f, 1) 2000 100 y(t) 4000 100 neck 0.000 0.555 0.025 X 200 20 z 100 10 y 20 2 shoulder 0.152 0.498 0.025 y 100 5 z 100 10 elbow 0.449 0.498 0.025 X 20 1 y 100 5 Table A .6 : Joint strength of snowboarder model. 59 Appendix B Description of Virtual Buttons n a m e a x i s d e f i n i t i o n n o t e stand forward X target c.o.m. position stand facing water y arm position stand backward X target c.o.m. position stand back to water y arm position crouch arms-up X target c.o.m. position crouch, raise arms for forward takeoff y height of crouch crouch arms-down X target c.o.m. position crouch, lower arms for backward takeoff y height of crouch takeoff forward X waist bend extend hips, knees and ankles for jump y jump height takeoff backward X waist bend extend hips and ankles swing arms back y jump height pike y time to reach pose open pike X target pike angle y time to reach pose tuck y time to reach pose twist X twist of waist right hand to head, left hand to chest y time to reach pose lateral extend X waist bend bring arms laterally to over head y time to reach pose straight extend waist bend bring arms straight over head y time to reach pose Table B . l : Description of diving buttons. 60 name axis definition note start big X start position start for the big kicker y angle of arm raise start small X start position start for the small kicker y angle of arm raise crouch arms-up X hip bend bring arms to front for forward takeoff y knee bend crouch arms-down X hip bend swing arms down for backward takeoff y knee bend takeoff forward X waist bend extend hips, knees and ankles for jump y strength of jump takeoff backward X waist bend extend hips and ankles for jump, swing arms back y strength of jump takeoff twist fwd X waist twist extend hips, knees, and ankles while twisting waist y strength of jump takeoff twist bwd X waist twist as above/but swing arms back and apply less knee extension y strength of jump pike y time to reach pose tuck y time to reach pose layout X waist bend extend arms y time to reach pose twist y time to reach pose bring arms to body landing X hip bend alter stiffness of hips and knees for landing -y knee bend finish X arm position stand up and raise arms y time to reach pose Table B.2 : Description of buttons for aerial ski jump control. name axis definition note crouch left X waist twist crouch down facing left y front/back balance crouch right X waist twist crouch down facing right y front/back balance grab front y. time to reach pose grab front side of snowboard grab back y time to reach pose grab back side of snowboard takeoff X waist bend y time to reach pose landing X waist bend y lateral balance position Table B.3: Description of buttons for snowboard control. 61 

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