Implicit modeling of swept volumes and swept surfaces

Abstract

A method of determining surfaces of swept volumes, which defines a region reserved for the removal of an object, or the motion of an object, is determined employing implicit modeling. A definition of an object and the trajectory in which it is to be moved are provided to the swept surface display device. An implicit model is created by determining shortest distance from each voxel of a object volume to a surface point of the object. A workspace volume has voxels each initialized with distances which are much larger than any distance envisioned. The implicit model space voxels are transformed relative to the workspace voxels according to the trajectory at a time t. Workspace voxels are updated with corresponding implicit model space voxels when the value of the implicit model space voxel is lower than the workspace voxel value. The implicit model space voxels are transformed relative to the workspace voxels for another time t and the number of workspace voxels are again updated. This process is repeated for a number of times, t, to result in workspace voxel values which reflect the closest each voxel would be to the surface of the object as it is swept through the trajectory. All workspace voxels having a predefined distance value are identified and a surface is constructed. This is the surface of the swept volume having a clearance defined by the predefined distance.