CS 284: CAGD 
Project Planning and General Schedule

Project Scope

• Ideally, each project consists of three parts:
• some programming to implement some new capability,
• an interface to the SLIDE environment to make this capability usable by others in a larger context,
• some demonstration of this new capability with some neat final result.
• Keep the projects small and well focussed!
There are only about 5 weeks left after the formal project proposal; so this does not allow to construct large and elaborate systems. Some of the ideas below may be too ambitious for a complete implementation; but you can do an essential part for any one of them, and demonstrate that you have mastered the basic concept.
• Projects can be done alone or in pairs.
  
Obviously, I expect more from a team of two -- about 50% more than from a single person
(not twice as much, -- since there is certain amount of overhead from communication, sharing code, etc.).
• Ideally projects should concern: 1-, 2-, or 3-dimensional spline manifolds or subdivision structures,
  smooth implicit surfaces or point clouds. It could coprise tools to design, edit, optimize, or decorate such surfaces.
  
It could be some converter between two different shape representations. I would like to see some demonstrable program
that shows that you got something to work based on what you learned during this course.

General Schedule

Project Proposal Presentation
A 5-minute formal presentation in class of your chosen (and approved) project.
- - due in week 10; (counts for 8% of course grade).

Project Presentation and Demonstration
A 15-20-minute formal presentation in class of your project implementation and results.
- - due in week 15; (counts for 20% of course grade).

Project Report
A written documentation of your project and final results obtained.
- - due in week 16; (counts for 8% of course grade).

Special Project Suggestions for 2006

• Subdivision with Texture Mapping. (1 pers.)
  Implement a simple subdivision scheme and add texture coordiante information to the vertices, which gets subdivided just like the parameter domain.
  However, a vertex may have to carry multiple texture coordinates for different faces so that you can create Escher tilings on surfaces of arbitrary genus.
  
  
• Fly-over on Smooth Surfaces of Arbitrary Genus (1 pers.)
  Create a moving viewpoint that moves along a geodesic line with a fixed offset above a smooth subdivision surface (Loop or CC).
  A simple 2-key or mouse based interface alows the user to deviate slightly from the geodesic and curve it gently to the right or to the left.
  
  
• Combination of the above two projects (2 pers.)
  This will give the capability to skim over the surface of a planet with an interesting texture with a moderately high genus.
  
  
• Interactive Escher Tiler on the Torus. (1 pers.)
  Inspired by the Escher-Sphere Generator, build an equivalent too that allows to define one repetivitve tile on a torus, edit it, see the changes at once on the whole torus.
  In the end extract the prototype geometry for one tile, so that it can be realized on a rapid-prototyping machine.
  
  
• Circle-Spline Editor on the Sphere (1 pers.)
  Implement the circle-spline algorithm for a sphere and couple it with an interactive user interface that allows to place and move a few control points which then are interpolated by the circle-spline curve. Output a  finely segmented polyline path in SLIDE format.
  
  
• Surface Modeling Based on a Point Cloud (1 pers.)
  In the neighborhood of each point define a best fitting quadric patch function. Form a surface with high continuity by overlapping and blending these patches for all the points. Demonstrate smoothness of the generated surface by coloring the surface according to local curvature or by performing raytracing on a highly reflecting surface mirroring an environment of straight lines (like the linear lights in car design shops).
  
  
• Surface Optimization Based on a Point Cloud (2 pers.)
  Add an optimization module to the above project that will incrementally move the points in the cloud so as to minimize some global energy functional.
  
  
• Surface Modeling with Implicit Functions (1 pers.)
  Implement an efficient way to extract a smooth representation from a sum of implicit functions. Create a simple editor to construct and modify such surfaces in an interactive way.
  
  
• Surface Optimization Based on Implicit Functions (2 pers.)
  Add an optimization module to the above project that will incrementally change the parameters in the implicit function so as to minimize some global energy functional.
  
  
• 
  

Other Possible Projects Concerning Curves

• Geodesic Lines on a Given Surface (1 pers.)
  
A geodesic line on a surface is one for which its normal vector at every point is in line with the normal vector of the surface; i.e., the curve bends only as necessary to follow the surface, but does not bend unnecessarily within the surface. Given an initial starting point and a starting direction, draw a geodesic line onto surfaces composed of triangle meshes or spline patches by calculating incrementally the positions of subsequent Frenet frames. Use the calculated Frenet frames and the sweep mechanism to draw a semicircular ridge of small diameter onto the surface.


• De Casteljau on the Sphere (1 pers.)
  
Implement the de Casteljau algorithm on the sphere, using great circle arcs instead of straight line segments. Then use these spline curves to make a tool to interactively draw smooth splines on a sphere surface, and sweep some cross-sectional profile along it.


• Global 3D Curve Optimization (1 pers.)
  
Find a good heuristic approximation to move the control points of a curve in such a way as to minimize some functional over the arclength of the curve, e.g., curvature squared, square of curvature derivative, torsion squared, or combinations of such terms. Then change some of the constraints, e.g., move the endpoints or some intermediate points to be interpolated, and watch the curve adjust to the new conditions within seconds.

Other Possible Projects Concerning Surfaces

• Interpolating Triangle-based Subdivision Surface (2 pers.)
  
Try to find a way to make a smooth subdivision surface by carrying only enhanced triangle information from one generation to the next. Add suitable parameters to each triangle vertex, e.g., averaged normal vectors and some other values indicating the velocity distribution in the tangent plane. It should then be possible to construct the next generation of triangles from this information associated with the three vertices alone.


• Enhancement to Point-shop 3D (1 or 2 pers.)
  
Make some enhancement to this down-loadable software, perhaps to do visualization of intrinsic surface parameters, or carry out surface optimization, or link to rapid prototyping or manufacturing.


• Global Surface Optimization (1 pers.)
  
Use Brakke's Surface Evolver to make some minimal surfaces such as Costa Surfaces or some other Minimal Energy Surfaces.


• Boy's Surface (1 pers.)
  
Make a nice, G2-smooth, 3-fold symmetric representation, including a nice "regular" texture of Boy's surface.


• Topological Surface Morph (1 pers.)
  
Deform a rectangular array of B-Spline patches so as to form one third of a Boy surface (and from 3 such pieces make the whole surface) similar to the deformation of one rectangle into a Klein bottle. Generate a sequence of still images or a 10 second MPEG movie to dynamically demonstrate the necessary defomation.


• Moebius Strip + Moebius Strip = Klein Bottle (1 pers.)
  
Make a series of shapes appropriately rendered that demonstrates that a Klein bottle can be made from two Moebius bands.


• Moebius Strip sewn together properly = Klein Bottle (1 pers.)
  
Make a demonstration sequence that shows that a suitable cut on a Klein Bottle can result in a single Moebius strip.

Other Possible Projects with Emphasis on Interaction

• Global Curve Optimization (1 or 2 pers.)
  
Build a wavelet-based curve editor that allows global optimization of 2D or perhaps 3D curves at interactive speeds.


• Teaching Demo for Rational Splines (1 or 2 pers.)
  
Extend the kind of tool that you have played with in the first few programming assignments to include the domain of rational curves; provide a user interface that also allows to conveniently explore the effect of changing weights.


• Teaching Demo for Surface Patches (1 or 2 pers.)
  
Create a tool similar to that which you have played with in the first few programming assignments about curves to provide a teaching and demonstration environment for B-Spline and/or Bezier patches, including a suitable user interface and sliders for setting the various parameters.

Other Possible Projects Leading to Part-Fabrication

• From Implicit or Point-Cloud Representation to SFF (1 or 2 pers.)
  
Build a converter from an implicit or point-cloud representation of a surface to the slice description needed for rapid prototyping with layered manufacturing, e.g., based on marching squares in each slicing plane.


• Model for a Minimal Surface (1 or 2 pers.)
  
Make an SFF model of the minimal surface that results when an interesting knot (say a figure-8 knot or a torus knot) is dipped into a soap solution. Use the surface evolver or write your own surface "tightener."