Abstract: A three-dimensional geometry processing system generates an intersection curve between two surfaces, an intersection point between a surface and a curve, an intersection point between three surfaces, and a parameter of a surface at a given point. In this system, candidate points for endpoints of an intersection curve between surfaces are generated and stored in a table, a judgment is made whether or not a tracing of intersection from one of the candidate points in the table can be performed, and, if it is judged that the tracing can be performed, a direction in which the tracing is performed is determined. Convergence calculations are performed so that a leading point of a tracing vector lies on both the two surfaces.

Abstract: A three-dimensional geometry processing system generates an intersection curve between two surfaces, an intersection point between a surface and a curve, an intersection point between three surfaces, and a parameter of a surface at a given point. In this system, candidate points for endpoints of an intersection curve between surfaces are generated and stored in a table, a judgment is made whether or not a tracing of intersection from one of the candidate points in the table can be performed, and, if it is judged that the tracing can be performed, a direction in which the tracing is performed is determined. Convergence calculations are performed so that a leading point of a tracing vector lies on both the two surfaces.

Abstract: An apparatus for converting a three dimensional data inputted in one system to a data for another system so that the converted data is used for displaying graphical models representing a real object includes a unit for separating a three dimensional data into a Gregory patch data and a non-Gregory patch data, a unit for converting the Gregory patch data to a general patch data and a unit coupled to both the separating unit and to the converting unit for transforming the general patch data and the non-Gregory Patch data to a data used for another system. Furthermore, the converting unit is used for receiving information on control points of the Gregory patch, and for transforming the information into another information on control points and weights of the general patch data, and the general patch data is a rational Bezier patch. The converting unit is further used for transforming the information into another information on a non-uniform rational B-Spline patch.

Abstract: A solid modeling method for modeling solids which include free-form surfaces calculates intersecting portions of two solids and storing calculated results as first data, stores free-form shapes of the two solids as second data, approximates free-form surface portions of the two solids by polyhedrons so as to describe the two solids in a form of polyhedrons, obtains a union, a difference or an intersection of the two solids by carrying out set operations on the polyhedrons, and returns the polyhedrons obtained by the set operations into solids including free-form surfaces based on the stored first and second data.