Signed Distance Calculation Of Point To Polyhedra Represented As Triangle Meshes

Computing the signed distance of an arbitrary point to polyhedron has been used in many area,such as Virtual Reality,Robotics Path Planning and Collision Detection.It was used to avoid colliding and intersection during movement.so computing the minimum signed distance is the key of this problem.Considering the relationship of objects represented with triangle mesh,we compute the signed distance of a point to 3D objects using the Angle weighted pseudonormal .and discuss the algorithm of computing the distance between two objects.Firstly for objects with closed, smooth, and orientable surfaces,the surface normal is an important tool for determining whether a given point is inside or not. However,an object represented as triangle mesh is not a smooth surface and, hence, does not have normals defined everywhere on the surface (i.e., the surface is discontinuous at edges and vertices).In this paper , we prove that the angle weighted pseudonormal has the important property that it allows us to discriminate between points that are inside and points that outside a mesh. The algorithm uses dynamic sphere searching technology which takes the given point as sphere center. A potential facet set can be found quickly and accurately and this set is compact enough to accelerate the distance calculation greatly. Compared with the hierarchical presentation approach, this algorithm avoids frequently calculating the distance between the point and hierarchical structure.We also discuss the algorithm of computing the distance between two objects.And introduces a family of bounding volumes called swept sphere volumes ,furthermore, we build hybrid hierarchies using those volumes. And the efficiency can be further improved by accepting a relative error in the returned result. We limit the error between the reported distance and the exact distance to be a user specified fraction of the exact distance; By using a relative error, exact distance computation and collision detection become two extremes of the same problem.When the user specifies zero relative error, we compute the exact distance.Conversely, when the acceptable relative error approaches one hundred percent, the objects intersect.