Method for transforming CAD model using general function composition mechanism

A method for transforming the geometry of a solid model with an arbitrary transformation function, comprising the steps of:

• providing a procedural solid modeler which supports using procedural surfaces and curves to allow the use of composition of arbitrary functions to define surface and curve geometry functions, said modeler comprising a transformation component adapted to permit the definition of arbitrary transformation functions and to create composed surface and curve geometry functions by composing surface and curve geometry functions with said arbitrary transformation functions;
• obtaining a solid model having a topology and a geometry corresponding to said topology, said topology comprising one or more faces, edges and/or vertices, said geometry comprising one or more surfaces, curves, and/or positions, where each surface in the geometry corresponds to a face in the topology, each curve in the geometry corresponds to an edge in the topology, and each position in the geometry corresponds to a vertex in the topology, and each surface or curve is defined by a parametric function mapping from a domain space to 3-dimensional space;
• defining a transformation function;
• operating said transformation component to transform the geometry of the solid model by creating new surfaces, curves and/or positions defined by composing each surface and curve function of the geometry with said transformation function and by transforming each position of the geometry by said transformation function;
• and
• resetting the geometry of said solid model to create a procedural solid model by replacing the underlying geometry of each face, edge and/or vertex with surface, curve and/or position geometry, respectively, defined in the case of surface and curve geometry by the new, transformed functions corresponding to the original representing functions and in the case of position geometry by the new, transformed positions.