Winter Quarter 2003

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Project 3: Animator

Assigned: February 12, 2003
Due: February 25, 2003
Artifacts Due: February 28, 2003

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Project Description

This project consists of three parts: (1) use a simple OpenGL modeling tool to create and animate the hierarchical models of your own design (2) compose them into a scene and implement a keyframe animation system and (3) implement a particle system and integrate it with the animation system.  We have provided a nifty user interface to help you draw curves and animate your model.  When finished with the coding part of the project, you will use your system to create a animation artifact. 

Table of Contents

• Hierarchical Modeling
• Keyframe Animation with Curves
• Particle System Simulation
• User Interface
• Animation Artficat
• Bells and Whistles

Hierarchical Modeling

A hierarchical model is a way of grouping together shapes and attributes to form a complex object. Parts of the object are defined in relationship to each other as opposed to their position in some absolute coordinate system. Think of each object as a tree, with nodes decreasing in complexity as you move from root to leaf. Each node can be treated as a single object, so that when you modify a node you end up modifying all its children together. Hierarchical modeling is a very common way to structure 3D scenes and objects, and is found in many other contexts. We provide a simple framework such that you can experiment your hierarchical model.

Requirements for Hierarchical Modeling

First of all, you must come up with a character. This character can be composed solely of primitive shapes (box, generalized cylinder, sphere, and triangle).  It should use at least ten primitives and at least four levels of hierarchy. You must also use at least one each of the glTranslate(), glRotate() and glScale() calls to position these primitives in space (and you will probably use many of all of them!) You must also use glPushMatrix() and glPopMatrix() to nest your matrix transformations. The modeler skeleton provides functions for creating sliders and hooking them to different features of your model. You must add at least one of these as a control knob (slider, actually) for some joint/component of your model - have your character do some simple action as you scrub a slider back and forth. In addition, at least one of your controls must be tied to more than one joint/component; this knob will change the input to some function that determines how several parts of your model can move. For example, in a model of a human, you might have a slider that straightens a leg by extending both the knee and hip joints.

Keyframe Animation with Curves

Keyframe animation is one of the most common methods for controlling a hierarchical model.  The idea is to pose the model at select moments in time and then smoothly interpolate between the poses (sometimes called "in-betweening").  The pose is determined by the control parameters (degrees of freedom) of the model, such as joint angles, and each parameter has a separate curve describing how it changes over time.  In practice, you do not need to pose the whole model at each keyframe; you can adjust each curve independently, adding keyframes for that curve as needed.  For this component of the project, you will implement a set of curve types for keyframe interpolation.

Requirements for Animation Curves

You will need to implement each of the following curve types:

• Bézier (splined together with C⁰ continuity)
• Catmull-Rom
• B-spline

For each curve, you will also have to implement support for "wrapping," so that when the animation starts over, the curves return smoothly to the initial conditions. 

Skeleton Code for Curves

The GraphWidget object owns a bunch of Curve objects. The Curve class is used to represent the time-varying splines associated with your model parameters.  You don't need to worry about most of the existing code, which is used to handle the spiffy user interface.  The one important thing to understand is the curve evaluation model.  Each curve is represented by a vector of control points, and a vector of evaluated points. 

mutable std::vector m_ptvCtrlPts;
mutable std::vector m_ptvEvaluatedCurvePts;

Control points define a curve; they are the ones that you can see and manipulate in the graph interface.  The evaluated points are a sampled representation of the curve itself (i.e. the solid line that runs through or near the control points).  At any given time t, the value of the curve is defined as the interpolated value between the two closest evaluated points (i.e. the two evaluated points on either side of t).  

Since the user only specifies control points in the graph widget, the program must determine the actual shape of the curve.  In other words, given a set of control points, the system figures out what the evaluated points are.  This conversion process is handled by the CurveEvaluator member variable of each curve. 

const CurveEvaluator* m_pceEvaluator;

In the skeleton, we've only implemented the LinearEvaluator.  You should use this as a model to implement the other types of curve evaluators required: Bézier, B-Spline, and Catmull-Rom.  The following section describes in greater detail what you need to do to add a curve.

Adding Curve Types

For each curve type, you must write a new class derived from CurveEvaluator. Inside the class, you should implement the evaluateCurve function. This function takes the following parameters: ptvCtrlPts--a collection of control points that you specify in the curve editor, ptvEvaluatedCurvePts--a collection of evaluated curve points that you return from the function calculated using the curve type's formulas, fAniLength (the maximum time that a curve is defined), and bWrap - a flag indicating whether or not the curve should be wrapped. To add a new curve type, you should look in the GraphWidget constructor and change the following lines to use your new set of evaluator classes.

m_ppceCurveEvaluators[CURVE_TYPE_BSPLINE] = new LinearCurveEvaluator();
m_ppceCurveEvaluators[CURVE_TYPE_BEZIER] = new LinearCurveEvaluator();
m_ppceCurveEvaluators[CURVE_TYPE_CATMULLROM] = new LinearCurveEvaluator();

For Bézier curves (and the splines based on them), it is sufficient to sample the curve at fixed intervals of time. The adaptive de Casteljau subdivision algorithm presented in class may be implemented for an extra bell.

You do not have to sort the control points or the evaluated curve points. This has been done for you. Note, however, that for an interpolating curve (Catmull-Rom), the fact that the control points are given to you sorted by x does not ensure that the curve itself will also monotonically increase in x. You should recognize and handle this case appropriately.  One solution is to return only the evaluated points that are increasing monotonically in x.

Wrapping

The linear curve code provided in the skeleton can be "wrapped," which means that the curve has C⁰ continuity between the end of the animation and the beginning.  As a result, looping the animation does not result in abrupt jumps.  You are required to support wrapping for each curve type; for information on Bézier curve wrapping, please click here.

Particle System Simulation

The skeleton code has a very high-level framework in place for running particle simulations that is based on Witkin's Particle System Dynamics paper in the course reader.  In this model, there are three major components:

1. Particle objects (which have physical properties such as mass, position and velocity)
2. Forces
3. An engine for simulating the effect of the forces acting on the particles that solves for the position and velocity of each particle at every time step

You are responsible for coming up with a representation for particles and forces.  

Requirements for Particle System 

Here are the specific requirements for the particle system:

1. Implement the simulation solver using Euler's method
2. Create a particle system with at least two types of forces acting on it.  One force should be gravity, and the other should be something that is tied to a feature of your model.  For example, you can have a steam particle system that shoots particles up from the chimney of a moving train.  The initial velocity of these particles should reflect the velocity of the train at the moment they're created.
3. Using robotarm.cpp as an example, hook your particle system up to the application.   

Once you've completed these tasks, you should be able to run your particle system simulation by playing your animation with the "Simulate" button turned on.  As you simulate, the position of the particles at each time step are baked so that you can replay your animation without re-simulating.  When you disable simulation, normal animation continues.  The gray region in the white indicator window above the time slider indicates the time for which the simulation has been "baked."   

Skeleton Code for Particle System

The skeleton provides a very basic outline of a simulation engine, encapsulated by the ParticleSystem class.  Currently, the header file (ParticleSystem.h) specifies an interface that must be supported in order for your particle system to interact correctly with the animator UI.  Alternately, you can try to figure out how the UI works yourself by searching within the project files for all calls to the particle system's functions, and then re-organizing the code.  This second option may provide you with more flexibility in doing some very ambitious particle systems with extra UI support.  However, the framework seems general enough to support a wide range of particle systems.  There is detailed documentation in the header file itself that indicates what each function you are required to write should do.  Note that the ParticleSystem declaration is by no means complete.  As mentioned above, you will have to figure out how you want to store and organize particles and forces, and as a result, you will need to add member variables and functions.

One of the functions you are required to implement is called computeForcesAndUpdateParticles:

virtual void computeForcesAndUpdateParticles(float t);

This function represents the meat of the simulation solver.  Here you will compute the forces acting on each particle and update their positions and velocities based on these forces using Euler's method.  As mentioned above, you are responsible for modeling particles and forces in some way that allows you to perform this update step at each frame.  

Baking Particles

Since particle simulation is often an expensive and slow process, many systems allow you to cache the results of a simulation. This is called "baking."  After simulating once, the cached simulation can then be played back without having to recompute the particle positions at each time step.  You are required to add this functionality to the ParticleSystem class.  Included in the header file are a number of baking-related functions that you are required to implement.  For your convenience, we've also left what we feel are relevant baking variables in the class:

/** Baking properties **/
float bake_fps; // frame rate at which simulation was baked
float bake_start_time; // time at which baking started
float bake_end_time; // time at which baking ended
bool baked; // flag for baked particles

The one significant baking variable that is NOT included in this list is a data structure that stores a collection of particle configurations that can be indexed by time.  When simulation mode is enabled, you should call bakeParticles at each time step from within computeForcesAndParticles to save the positions of all particles into this data structure.  Then, when we play back, we can simply look up into this data structure with the current time to see if a configuration has been saved.  If so, you should just draw the particles according to this configuration without re-simulating them.  For example, this is a possible structuring of the code:

virtual void computeForcesAndUpdateParticles(float t)
{
    ...
    if (simulate) {
        ... 
bakeParticles(t);
        ...
    }
    ...
}

virtual void bakeParticles(float t)
{
    // save particles in data structure
}

virtual void drawParticles(float t)
{
    // if we need to draw particles, check 
    // if there's an entry in your baked data structure
    // for time t.  if there is, use the saved
    // configuration to draw.
}

Hooking Up Your Particle System

In the sample robotarm.cpp file, there is a comment in the main function that indicates where you should create your particle system and hook it up into the animator interface.  After creating your ParticleSystem object, you should do the following:

ParticleSystem *ps = new ParticleSystem();
...
// do some more particle system setup
...
ModelerApplication::Instance()->SetParticleSystem(ps);

User Interface

The interface for this project consists of two components: a slider control interface and an animation curve interface.  The slider control interface allows you to control each degree of freedom of your hierachical model with a slider.  The animation curve interface allows you to specify how each degree of freedom behaves as a function of time.  In addition, you can manipulate the viewpoint by interacting directly with the view of the 3D model.

Fluid

In the skeleton code distribution, we've included the fluid file for the ModelerUIWindows class (modeleruiwindows.fl). In addition, we've included the binary for fluid so that you can (if you want) make additions to the UI. We will talk a bit more about FLUID during the help sessions.

Animation Curve Interface

After selecting a series of model parameters in the browser window, their corresponding animation curves are displayed in the graph. Each spline is evaluated as a simple piece-wise linear curve that linearly interpolates between control points. You can manipulate the curves as follows:

Command	Action
LEFT MOUSE	Clicking anywhere in the graph creates a control point for the selected curve. Ctrl points can be moved by clicking on them and dragging.
CTRL LEFT MOUSE	Selects the curve
SHIFT LEFT MOUSE	Removes a control point
ALT LEFT MOUSE	Rubber-band selection of control points
RIGHT MOUSE	Zooms in X and Y dimensions
CTRL RIGHT MOUSE	Zooms into the rubber-banded space region
SHIFT RIGHT MOUSE	Pans the viewed region

Note that each of the displayed curves has a different scale. Based on the maximum and minimum values for each parameter that you specified in your model file, the curve is drawn to "fit" into the graph. You'll also notice that the other curve types in the drop-down menu are not working. One part of your requirements (outlined below) is to implement these other curves.

At the bottom of the window is a simple set of VCR-style controls and a time slider that let you view your animation. "Loop" will make the animation start over when it reaches the end.  The "Simulate" button relates to the particle system which is discussed below.  You can use the Camera keyframing controls to define some simple camera animations. When you hit "Set", the current camera position and orientation (pose) is saved as a keyframe. By moving the time slider and specifying different pose keyframes, the camera will linearly interpolate between these poses to figure out where it should be at any given time.  You can snap to a keyframe by clicking on the blue indicator lines, and if you hit "Remove", the selected keyframe will be deleted. "Remove All" removes all keyframes.   

Animation Artifact

You will eventually use the curve editor and the particle system simulator to produce an animated artifact for this project. Under the File menu of the program, there is a Save Movie As option, that will let you specify a base filename for a set of movie frames.  Each frame is saved as a bitmap.  IMPORTANT: To get your movie to save correctly, you must add a call to endDraw at the very end of the draw function in your model:

void RobotArm::draw()
{
    ...
    // draw your model
    ...
    ...
endDraw();
}

Each group should turn in their own artifact. We may give extra credit to those that are exceptionally clever or aesthetically pleasing. Try to use the ideas discussed in the John Lasseter article in your CoursePak. These include anticipation, follow-through, squash and stretch, and secondary motion. 

Finally, please try to limit your animation to 30 seconds or less.  This may seem like a short amount of time, but it really isn't.  Frequently, animations that are longer than this time seem to be running in slow motion.  Actions should be quick and to the point.

Bells and Whistles

Render your particle system as something other than white points!

Enhance the required spline options. Some of these will require alterations to the user interface, which is somewhat complicated to understand.  If you want to access mouse events in the graph window, look at the handle function in the GraphWidget class.  Also, look at the Curve class to see what control point manipulation functions are already provided.  These could be helpful, and will likely give you a better understanding of how to modify or extend your program's behavior.  A maximum of 3 whistles will be given out in this category.

• Let the user control the tension of the Catmull-Rom spline
• Implement higher degree polynomial splines (ones that are C³ or C⁴ continuous)
• Implement one of the standard subdivision curves (e.g., Lane-Riesenfeld or Dyn-Levin-Gregory).
• Allow the user to specify the derivatives at the two endpoints of your C² interpolating curves (see bell on this below).
• Add options to the user interface to enforce C⁰ or C¹ continuity between adjacent Bézier curve segments automatically. (It should also be possible to override this feature in cases where you don't want this type of continuity.)
• Add the ability to add a new control point to any curve type without changing the curve at all.

Implement adaptive Bézier curve generation; i.e., use a recursive, divide-and-conquer, de Casteljau algorithm to produce Bézier curves, rather than just sampling them at some arbitrary interval. You are required to provide some way to change these variables, with a keystroke or mouse click.  In addition, you should have some way of showing (a printf statement is fine) the number of points generated for a curve to demonstrate your adaptive algorithm at work.  If you provide visual controls to toggle the feature, modify the flatness parameter (with a slider for e.g.) and show the number of points generated for each curve, you will get an extra whistle.

Extend the particle system to handle springs. For example, a pony tail can be simulated with a simple spring system where one spring endpoint is attached to the character's head, while the others are floating in space.  In the case of springs, the force acting on the particle is calculated at every step, and it depends on the distance between the two endpoints.  For an extra bell, implement spring-based cloth.

Euler's method is a very simple technique for solving the system of differential equations that defines particle motion.  However, more powerful methods can be used to get better, more accurate results.  Implement your simulation engine using the Runge-Kutta technique.

Allow for particles to bounce off each other by detecting collisions when updating their positions and velocities.  Although it is difficult to make this very robust, your system should behave reasonably.

Implement a "general" subdivision curve, so the user can specify an arbitrary averaging mask  You will receive still more credit if you can generate, display, and apply the evaluation masks as well.  There's a site at Caltech with a few interesting applets that may be useful.

If you find something you don't like about the interface, or something you think you could do better, change it! Any really good changes will be incorporated into Animator 2.0.  Credit varies with the quality of the improvement.

Implement a C²-Interpolating curve.  There is already an entry for it in the drop-down menu.

Use some sort of procedural modeling (such as an L-system) to generate all or part of your character. Have parameters of the procedural modeler controllable by the user via control widgets.

Add the ability to edit Catmull-Rom curves using the two "inner" Bézier control points as "handles" on the interpolated "outer" Catmull-Rom control points. After the user tugs on handles, the curve may no longer be Catmull-Rom.  In other words, the user is really drawing a C¹ continuous curve that starts off with the Catmull-Rom choice for the inner Bézier points, but can then be edited by selecting and editing the handles.  The user should be allowed to drag the interpolated point in a manner that causes the inner Bézier points to be dragged along.  See PowerPoint and Illustrator pencil-drawn curves for an example.

Implement picking of a part in the model hierarchy.  In other words, make it so that you can click on a part of your model to select its animation curve.  To recognize which body part you're picking, you need to first render all body parts into a hidden buffer using only an emissive color that corresponds to an object ID.  After modifying the mouse-ing UI to know about your new picking mode, you'll figure out which body part the user has picked by reading out the ID from your object ID buffer at the location where the mouse clicked.  This should then trigger the GraphWidget to select the appropriate curve for editing.  If you're thinking of doing either of the six-bell inverse kinematics (IK) extensions below, this kind of interface would be required.

If you implemented a "twist" degree of freedom for some part of your model, applying the rotational degrees of freedom can give some unexpected results.  For example, twist your the degree of freedom by 90 degrees.  Now try to do rotations as normal.  This effect is called gimbal lock.  Implement Quaternions as a method for avoiding the gimbal lock.

An alternative way to do animations is to transform an already existing animation by way of motion warping (see example animations). Extend the animator to support this type of motion editing.

Incorporate rigid-body simulation functionality into your program, so that you can correctly simulate collisions and response between rigid objects in your scene.  You should be able to specify a set of objects in your model to be included in the simulation, and the user should have the ability to enable and disable the simulation either using the existing "Simulate" button, or with a new button.

Extend your system to support subdivision surfaces.   Provide a simple interface for the user to edit a surface.  The user should also be able to specify surface features that stay constant so that sharp creases can be formed.  Tie your surface to the animation curves to demonstrate a dynamic scene.  Look here for a collection of links.  As mentioned above in the blurb for the subdivision curve bell, Caltech has a few nice applets here.

You might notice after trying to come up with a good animation that it's difficult to have very "goal-oriented" motion. Given a model of a human, for instance, if the goal is to move the hand to a certain coordinate, we might have to animate the shoulder angle, elbow angle -- maybe even the angle of the knees if the feet are constrained to one position. Implement a method, given a set of position constraints like:

left foot is at (1,0,2)
right foot is at (3,0,4)
left hand is at (7,8,2)

that computes the intermediate angles necessary such that all constrains are satisfied (or, if the constraints can not be satisfied, the square of the distance violations is minimized). For an additional 4 bells, make sure that all angle constraints are satisfied as well. In your model, for instance, you might specify that the elbow angle should stay between 30 and 180 degrees.  If you're planning on doing this bell, you should talk to the TA and/or the instructor.  In addition, you can look here for some related material.