pyle@lll-lcc.UUCP (03/08/87)
Some questions please: 1.) Does anyone know how to determine a bounding ellipsoid for an arbitrary object? Kajiya stated in one of his papers that one could be created via a "principal axis transformation on the covariance of the points." Can someone tell me what this involves? 2.) Has anyone ever implemented a cluster sphere hierarchy for a ray-tracer? Can the hierarchy be constructed automatically, given a set of local bounding spheres? 3.) Given a unit object (see Roth's paper, 1982, in Computer Graphics and Image Processing), like a unit cube, can one determine its bounding sphere in world coordinates, just given the local-to-world transform? If the scaling factor was even in X, Y and Z, I concluded that it was possible. I was wondering if it was still obtainable, given that the cube is transformed into, for example, a retangular box. Thanks a bunch, Ernie Pyle P.S. Responses via E-Mail would be just great.
shirley@uiucdcsm.UUCP (03/11/87)
Semi-answer to 3): If the bounding sphere is to be used as an extent for the unit primitive, a bounding ellipsoid can be substituted. This ellipsoid will correspond to the bounding sphere in primitive space. This will give you a tighter fit, but the ray will have to be transformed into primative space. If the extent is hit, the ray will NOT have to be transformed again (the primitive space is the same for the unit prim and the bounding sphere). A question about CSG ray tracing: How do you handle the interface between two transparent objects, such as water and glass? If they touch the basic union operation will ignore the interface. If they don't touch the water-air-glass will have a higher reflection than is desired, so simply separating the objects slightly doesn't cut it. I currently treat very small separations as a special case and ignore the air in the calculation the reflectance and the refracted ray, but this is terribly inelegant (as well as making object specification ugly). Is there a nice way to handle this? Thanks Peter Shirley U of Illinois at U/C