Generating Simplified Bounding Shell Of Triangular Mesh With User-Controllable Global Error

In computer graphics,there are many algorithms which deal with complex meshes.Us-ing some approximation will significantly reduce the cost of the algorithms.Among these ap-proximations,simplified bounding shells are widely used in applications like collision detection.However,it is hard to acquire both simplicity and similarity to the original mesh in prevalent simplified bounding shell generation algorithms.In many cases,people need to control error of the simplification,especially global error.Among previous error control techniques,one important category is tolerance-volume-based approaches.These approaches control global error by restricting the simplification process in a tolerance volume.In these approaches,people do not need to calculate global error during the simplification,and by contructing tolerance volumes flexibly,they may reach effects such as pre-serving sharp features.It is of great importance about how to construct tolerance volumes in these approaches.In this thesis,we present a method to generate bounding shells with precisely controllable error.Applying the potential theory,we treat the mesh as a conductor with charge distribution,use a method based on Green's function to solve a Laplacian with boundary condition applied on the mesh surface to get the potential field.We then sample the original mesh surface,trace the samples along the gradient line of the potential field to a distance equals the maximum allowed error,thus producing a tolerance volume.Finally we use the algorithm presented by Manish Mandad et.al in 2015 to produce the simplified bounding shell within the tolerance volume.Our experiment result shows that our algorithm is robust and can produce thick tolerance volumes.Combined with mandad et.al's algorithm,our method is able to generate simplified bounding shell with user-controllable global error well.