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This paper presents a general method for transformations of an object between 2D and 3D which can be used efficiently in computer‐aided garment design. A uniform triangular spring–mass‐based deformable model is employed. Both 2D‐to‐3D and 3D‐to‐2D transformations can be implemented in the same model. An efficient collision detection method is also discussed. © 1998 John Wiley & Sons, Ltd.

For some assembly structures, parallel disassembly of components is necessary in order to reach a particular internal component. Due to the large number of possible combinations, the parallel disassembly problem is not easily solved in a general form. In order to reduce the time complexity of finding a disassembly sequence, this paper introduces a simplified mating graph and develops a data structure to facilitate an efficient parallel disassembly algorithm. This algorithm takes Max {O(N3 ), O(E)} time to find an efficient sequence to reach a particular component, where N is the number of components and E is the number of mating faces. Separability testing is incorporated to determine whether the query component can be disassembled and moved to infinity without obstruction.

For some assembly structures, parallel disassembly of components is necessary in order to reach a particular internal component. Due to the large number of possible combinations, the parallel disassembly problem is not easily solved in a general form. This paper addresses parallel disassembly via geometrical reasoning and presents an algorithm for finding a sequence to disassemble a structure by an onion peeling procedure, from outside to inside. This algorithm takes Max{O(N3), O(E)} time to find an efficient sequence to reach a particular component, where N is the number of components and E is the number of mating faces. In this algorithm, the disassemblability of various combinations of components are determined by traversing the mating graph of the structure and testing the monotonicity of paths in the graph. Separability testing is incorporated to determine whether the query components can be disassembled and moved to infinity without obstruction.