274b-ab

Spring 2000

CSC 274 Computational Geometry

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1. The Walkthrough Project/Real Time Rendering of Massive Models

The problem is to render massive models in real time. Massive models being ones with 500,000 or more separate pieces. Real time allows only 2 frames / second. And it is not possible to expect a hardware to make this possible in the future since the hardware improvement is a lot less than the speed of improvement in model size. There are a number of solutions to this problem, and they are as follows:

-Simplification Envelopes - getting rid of details in each envelope, eventually ending up with triangles.

-Hierarchial structures - usin unstructed polygons

-Hierarchial backface culling - sppeds up the procedure 50%, takes 5% of total drawing time of each frame

-Fast display of complex CSG - viewframe representations/less patches

-Dynamic texture based simplification - geometry vs. texture - 20 min o drawing can be done in 17 secs.

-Radiosity as textures(RAT) - subdivision of polygons, texture mapping

2. OBB Trees

Again the problem is rendering in real time. The data structures used in this is called the OBB Trees. A whole animation is divided into separate pieces. and each piece the rejection set of engine and the rejection set of the piston (or the moving piece of engine) is computed. This also allows the fast computation of collusion query.

3. Interactive Boundary Computation of Boolean Combintaions of Sculptured Solids

The goal is model visualization again. Bradley fighting vehicle is taken into consideration. Both the exterior and the interior is used. Object placement and avoiding collusions is important. They showed an interactive boundary computatin of a drive wheel of the vehicle. They use BSP Trees(which Ihave read about for my previous hw- it was really exciting to see it in use! :)) ) and ray shooting. By the use of CHIMP all images are generated in real time. The boundary representations are exceptionally important in detection of object collusions.

15th Annual ACM Symposium

4. Metamorphosis of the Cube

There are two problems:

-Unfold a convex polyhedron into a simple polygon -- This has been solved by using "star unfolding" -Folding a simple polygon into convex polyhedron -- Alla examples for this were done by hand.

5.Geodesics and Curves

A Geodesic is a straight line showing the smallest distance between two points. Finding the geodesic lines and the curves on different objects were visualized. Especially the two-hole donut example was really beautiful. Discrete geodesics in polygonal surfaces were explored. And most of the time the discrete guess curvature of a vertex were used to compute the geodesics.

6. Correspondance between 3D Polyhedra for metamorphosis.

Ralization of an epcot is the first problem that comes up. To do this there are two steps:

-Simplification - removal of some verteces and edges and forming the new triangulation

-Reattachment - forming new vertices and edges that can be removed in the following simplification process.

There ware the realization of a deformed cube but I cannot say that I understood enough. They made a transformation between two deformed cubes to find correspondance. And I guess they found an algorthm to do this.

7.Correspondance computation

The goal was to compute correspondance between two distinct objects.They used shortest path algorithms for this.Some of the examples were donut-morph ->cup, human heads morph and the most interesting one was that animal morphing into a human body.

8. Silouhuettes of Geometric Models

The authors of this paper thought that a silouhette of an object might be easier and can be done faster than rendering of that object. They had to compute the shadow generation and the collusion detection. They did this by using the following duality:

ax+by+cz+d = 0 ------> P(a/d, b/d, c/d)

9.Mesh Collapse Compression

Really interesting video with beautiful graphics. In a graph you take an mc-vertex and the one closest to it on the left side(?) gets to be the mc-edge. and then you start collapsing the verteces one by one. Especially the collapsing of the mesh with two handles was beautiful.It was really interesting how the algorithm allowed the route of compression to divide in two and then converge to become one again.

10. C++ Library

The Authors of this paper created a c++ library using the advantages of CGAL. CGAL provides correctness, flexibility, efficiency and robostness in code. This library has all these advantages providing an interactive debugging of geometric code.

Altough we watched a few more video clips from this symposium, I guess I lost concentration since my notes are not readable at all, after this point. But overall I really enjoyed the graphics in all videos. They were amazing! I think I want to specialize in computer graphics in the future :))