Abstract: A data compression method for processing topological structures of various geometric models. A topological transformation is performed for a three-dimensional (3D) geometric model that is to be compressed, and a triangle mesh is generated. A conventional triangle mesh compression method is employed. Associated data required for the performance of a reverse operation for the topological transformation are prepared. As a result, topological data for the 3D geometric model is compressed. As needed, the data for the compressed triangle mesh and associated operation data are output. Furthermore, a necessary process (e.g., a compression process) is also performed for geometric data for the 3D geometric model, and the resultant data are either stored or output. For the decompression of compressed data, the compressed triangle mesh is decompressed using the method employed for compression, and a triangle mesh is generated.

Abstract: Information is embedded in a three-dimensional geometric model in a visible or invisible state by changing geometric parameters of a three-dimensional geometric model. The three-dimensional geometric model comprises polyhedrons, lines, a set of points, or curved surfaces which are primitives (components) of the model. Each primitive is defined by a geometric parameter. The geometric shape of a three-dimensional geometric model is defined by a set of many geometric parameters. The information is embedded by changing the geometric parameters of a plurality of primitives constituting a three-dimensional geometric model.

Abstract: The present invention is directed to a real-time controllable reflection mapping function which covers all stereoscopic directions of space. More specifically, the surface of a mirrored object is segmented into a plurality of polygonal elements (for example, triangles). Then, a polyhedron, which includes a predetermined point (for example, the center of the mirrored object) in a three-dimensional space (for example, a cube) in the interior thereof, is generated and a rendering process is performed for each surface of the polyhedron with the predetermined point as a view point. The rendered image is stored. Thereafter, a reflection vector is calculated between each vertex of the polygonal elements and a view point used when the entire three-dimensional space is rendered. Next, the surface of the polyhedron, in which an intersecting point between the reflection vector with the predetermined point as a start point and the polyhedron exists, is obtained.

Abstract: In order to render a three-dimensional space which has a spotlight source with a cone angle .theta. at high speed and with better quality, an object's surface in the three-dimensional space is first meshed into a plurality of elements. Then, a radiosity from the spotlight source is calculated for each element which is included inside of the cone angle .theta. when viewed from the spotlight source. Thereafter, an intensity-value at each vertex of each element is calculated from the radiosity calculated for each element. Next, Gouraud shading is performed by using the intensity-value at each vertex of each element, and the result is displayed on a display.