Abstract
To avoid collisions of two objects such as a workpiece and a tool, computation of collision domain in which the tip of the tool cannot locate is crucial. Collision domain can well be computed by Inverted Template Method using envelope operation. In this paper, a high-speed algorithm is proposed for three dimensional envelope operation by means of convolution operation. From two input domains α and β, an envelope domain γ is quickly computed by three dimensional Fast Fourier Transform (3D-FFT). Because it needs a huge memory capacity to convolute a whole cubic space precisely at one time, octree model is adopted to represent each of whole domains α, β and γ and Double-stage FFT method is established. First, the upper parts of input octree α and β are convoluted to get the rough sketch of the envelope domain γ. Second, pairs of lower subcubes of α and β are convoluted to compute precise 3D bitmaps. Among all the pairs, only the corresponding to boundary leaf cells of the upper γ octree are extracted. Each set of bitmaps for a leaf cell is converted into a suboctree through OR operation and added under the upper tree. Comparison of computing time with a precedent algorithm shows the superiority of Double-stage FFT method.
