Abstract: A novel tangent detection and calculation algorithm is presented for parametric surfaces based on discrete surfels. The two surfaces are initially uniformly sampled into surfels. Surfels of each surface are then organized into a space octree with surfels’ normal bounding cones being built at each octree node. By checking the consistency of the normal bounding cones together with the enclosing box test, the algorithm can detect the potential tangent area between the two surfaces robustly. The candidate surfels are resampled at high resolution to ensure the accuracy of the result and then tangent operation is carried out at last. Experiments show that the algorithm is effective and easy to implement by analyzing possible tangent area to find tangent points within the error range.

Key words: tangent detection for surfaces, normal bounding cones, adaptive sample of surfels, intersection calculations