Metamorphosis of a Cube
The clip showed the folding and unfolding animation of the cube. This was performed by cutting along the edges of the cube. One of the unfolding was described as the star unfolding. Another unfolding was described as the Latin unfolding. Several interesting shapes were formed by gluing the edges of this unfolding.
In the end, open questions raised by the folding and unfolding of the cube were put forward. One of them is folding a polygon to form a convex polyhedron. The problem is partly answered by Aleksandrov's theorem. Another is: Can you unfold one and fold it to form the other? And another was: Can a cube be unfolded to a polygon that can then be folded to form a regular tetrahedron?
Deals with the possiblity of obtaining smooth surfaces. There were different models shown, for example the engine-piston model. The problems of interference between two or more geometeric models in dynamic and static environment were brought to the fore-front.
For collision detection, the models were represented as numerous unstructured polygons with no topological information. The models were brought in close proximity of each other, and the determination of the accurate points of contact was emphasised. All these points were stressed by bringing the piston into close proximity of the engine block.
The research team stressed on acquiring efficient and real-time algorithms.
Mesh Collapse Compression
The video clip presented an algorithm for encoding the topoloy (eg the connectivity) of triangle meshes was shown. The mesh were collapsed into a single vertex by a series of edge contractions. With every edge contraction an integer was stored and the sequence of the integers thus obtained was called the mc coding of the mesh. The coding was 1221.
"Bunny ears" were demonstrated as examples. They were split to obtain two mesh components, each bounded by a loop. The loops were compressed and in the end bunny ears were obtained.
Real-time Rendering of Massive Models
Real-time is defined as 20 fps, and a massive model is defined to have more than 500,000 pieces. The problem is the time consumed to render them for applications involving virtual world and other immersive technologies.
The solution described was: polygonizing the sculptured models and rendering them using the current graphic systems. The rendering of those parts was emphasised which were noticeable. The rendering was done by decomposing the surfaces into Bezier surfaces, and then tessellating them. The tessellation was based on the sizes of the triangles.
Other important methods such as radiosity for improving the image quality was also mentioned. The radiosity method simulates the actual behavior of light, and thus is very useful.
Interactive Boundary Computation of Boolean Combinations of Sculptured Solids
Boundary representation of solid models is important for the collision detection during object placement and simulation studies. The algorithms and systems for interactive and accurate boundary computation of Boolean combinations of sculptures solids were demonstrated. The algorithm was implemented on a Bradley fighting vehicle on an SGI. The system has been integrated with an immersive design and manipulation environment. The resulting system then evaluate boundaries of the models, display them for model validation nd place them at appropiate position using collision detection algorithms.
A curve is said to be geodesic at a point if it vanishes there, and is called a geodesic if it is geodesic everywhere. That is, a surface curve is a geodesic if its acceleration is restricted to the up direction at every point. Segments of great area taken by airplane and ship can be considered as geodesic curves. Just as the lines provide the shortest path between two points on a plane, geodesics provide the shortest path between two points on the surface.
Correspondence between 3D Polyhedra for Metamorphosis
In this video clip, the realization algorithm on a cube and polyhedra was described. This algorithm removes triangles from the face of a polyhedra and then adds them back with the help of a vertex.
Last modified: Fri Feb 4 21:52:13 EST 2000