## Project 4: Final Project

Assigned: Tuesday, 29 February, 2000

Due: Tuesday, 14 March, 2000

Artifacts Due: Friday, 17 March, 2000 (by 12:00PM)

## Project Description

The topic of the final project is open to you. You get to define your own final project. It should be ambitious enough to demonstrate a significant result, but not so hard that you aren't confident about shipping a reasonably complete product. The project ideas below are for your reference.

## Some Project Ideas

(Note that some of the pictures don't correspond to the

algorithmsuggested, though they all depict theideadescribed.)## NPR and Image Processing

MorphingMorphing is a useful technique for generating smooth transitions between two objects. Implement the morphing algorithm introduced in Thaddeus Beier and Shawn Neely's SIGGRAPH 92 paper on Feature-Based Image Metamorphosis.Non-photorealistic lighting model

Technical illustration has some important characteristics which makes it very different from realistic rendering. Therefore, the popular shading model like Phong shading is not appropriate for technical illustrations. Gooch et al. introduced a shading model for technical illustrations in their Siggraph'98 paper.## Rendering

Distribution ray tracing. Implement semi-diffuse reflections and refractions by distributing the secondary rays emanating from each surface according to a bidirectional reflectance distribution function (BRDF) of your own choosing. Allow slider control over one or more parameters of the BRDF. Stop ray recursion if the weight for a ray's color drops below a slider-selectable threshold. You can refer Ward's paper as an example of BRDF representation. You can also implement distribution ray tracing for area light sources to simulate penumbrae, for a finite aperture to simulate depth of field, and for a finite shutter interval to simulate motion blur.Texture/Bump mapping and ray tracing differential. Add texture mapping to your ray-tracer spheres, triangle meshes, and planar quadrilaterals. Textures may be 2D or 3D, and may be procedurally generated or optically scanned. To map a texture onto a surface, you must compute texture indices at each ray-surface intersection. Methods for spheres, quadrilaterals, and triangles are described by Eric Haines in sections 2.5 and 3.3 of chapter 2 in Glassner. For a triangle mesh, you can convert from publically available meshes (3D Cafe has many).For antialiasing, you can refer Homan Igehy's SIGGRAPH'99 paper about ray tracing differential.

Use your texture to modulate something besides just reflectance (i.e. color). Experiment with transparency, specularity, or orientation (i.e. bump mapping). Alternatively, try modulating an interpolation between two other textures or between two entirely different shading models. See Cook's Siggraph '84 paper on shade trees and Perlin's Siggraph '85 paper on texture synthesis (FvDFH, p. 1047) for ideas.

Ray-tracing geometric primitives.Implement a class of more complicated primitives (e.g., from Hanrahan's chapter in Glassner's book). Choose wisely. Quadrics are too easy; deformed surfaces are too hard. Recommended are general swept surfaces, bicubic patches, CSG models, or fractals. Fractals are relatively easy to implement and fun to use. For extra fun, map textures onto your patches or fractals. Other primitives that can be used for terrific visual effect are particle systems (e.g., for fire and water) and L-systems (great for modeling plants).

Ray tracing volume. Start by implementing spatially inhomogeneous atmospheric attenuation. Divide each ray into intervals. For each interval, interpolate between the ray's color and some constant fog color based on a procedurally computed opacity for that location in space. Experiment with opacity functions. Once you get this working, try defining a solid texture (probably procedurally) that gives color and opacity for each interval. See Perlin and Hoffert's and Lewis's Siggraph '89 papers on solid texture synthesis and Kajiya and Kay's teddy bear paper (also Siggraph '89) for ideas. For smoke and clouds, you should also cast a ray to the light source to capture (one bounce of) the scattering. If you want to make your volume renderer fast, use hierarchical spatial subdivision (e.g. an octree).

Hierarchical radiosity. This is actually not as hard as it sounds. To implement the Hanrahan hierarchical solver , the main ingredients are a simple polygonal scene, a routine to break a triangle or rectangle into a few smaller pieces, a patch to patch visibility solver (your ray tracer already does this), and a simple mechanism for traversing a hierarchy of polygons. The simplest way to visualize your results would be to write out a file in the obj format accepted by your subdivision editor extended with an rgb triple for each point in addition to the xyz values, and extend your subdivision modeler to read and render the vertex color. Alternatively, you can do a "final gather" ray-tracing pass to achieve smooth shading. For best results, combine the radiosity solution with a ray-tracing pass that incorporates specular highlights and textures.## Geometric modeling

Subdivision surface. Subdivision surfaces gain more and more attention from industry and have been widely used in animation production, like "Geri's Game" and "Toy Story II". As a final project, you are required to implement both non-interpolating (Loop) and interpolating (Butterfly) subdivision. Use the evaluation mask to calculate final vertex positions if necessary, and the tangent masks to calculate vertex normals. You also need to have support for feature edges and vertices. Your subdivision editor should have an interface for selecting a vertex or an edge and then marking (or unmarking) it as a feature. You can start from last year's subdivision surface skeleton code (in MFC only).Sketch interface for modeling. Teddy is a sensational system introduced in Siggraph'99 and presents a new paradigm for modeling. In Teddy, users scrabble on the panel and the system automatically infers the underline 3D model reasonablly. As a final project, you can design your own interface for modeling or follow Teddy's design (you are not required to implement all operations introduced in the paper).C2, interpolating, local control curves for animation. Design and implement a curve that is C2 continuous, interpolates the control points and has local control. Prove that all of the properties hold. Construct a fast algorithm for rendering, value, first and second derivative evaluation. Note that this curve cannot be a cubic. Devise a quick rendering, value, first and second derivative computation methods.Subdivision curves for keyframing. Create a multiresolution keyframing system which can edit the motion curves at different levels of detal. The curves should be able to interpolate the keyframe constraints by changing the coefficients at a specific level of detail. Devise a scheme which can interpolate at non-integer levels of detail.## Animation

Cartoon physics simulation.Design a simulation environment that would model various aspects of cartoon physics. Augment the traditional simulation of Newtonian physics with additional constraints, damping parameters and other modifications which would produce an exaggerated cartoon-like behavior.Inverse kinematics.Implement inverse kinematics for character modeling and animation. Given a sequence of trajectories for a few end-effectors on the character's body construct the character's joint angle which would interpolate the end-effector trajectories while ensuring that the character moves "naturally". See lecture on inverse kinematics for details.Cloth Simulator.Design a cloth simulation model. Design a methodology and determine the parameters of the cloth model which will mimic the behavior of wool, cotton, silk.Rigid body simulation.Incorporate rigid body simulation with the keyframe animator. The keyframed character should be able to interact in realistic ways with the simulated objects in the scene.Motion Warping.Implement a technique for editing already existing animations, by warping the motion curves to meet the new constraints.Explosions.Develop a particle system approach to modeling and rendering realistic explosions (fire, dust plumes, etc.)

## Demos

You should prepare in advance for the demo, since you'll be the expert, not us. If you choose a rendering project you should have precomputed some images. If you project is interactive you may not need precomputed images, but you'll want to have inputs ready that effectively demonstrate your work. In any case, please generate an artifact to show off your project. It can be a rendering or a model or a visualization of your results.