Intersection between Bi-cubic Bezier Curved Surface and Plane

Abstract

The paper presents a solution to calculate intersection between a plane and bi-cubic Bezier curved surface. The paper first constructs bounding box based on the control grid by the characteristics of the Bezier surface, and then makes use of the plane half-space properties to convert the problem that calculates the intersection line between the plane and the parameter curved surface into calculating a series of intersection points by using the method that apply the bi-linear interpolation algorithm to the curved surface in representation of parameter area. The intersection line between the plane and the surface can be calculated by connecting the intersection points. This method can solve the surface intersection line well whether the line is discontinuous or form a closed cycle. The algorithm is relatively simple, and has good adaptability for calculating the intersection line between the plane and the curved surface. urround��dr����I�o-page-border-surround-footer:no;} @page Section1 {size:612.0pt 792.0pt; margin:72.0pt 90.0pt 72.0pt 90.0pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> Multiresolution technique is one of the most efficient approaches to improve the rendering performance, but its design and implementation for massive meshes are still very difficult. This paper researches and realizes constructing and rendering of multiresolution representation for massive meshes base on surface partition, which could provide vertex-grained local refinement and generate the optimal rendering quality. Our approach adopts dual hierarchy to represent the mesh. One is cluster hierarchy of progressive meshes for coarse-grained selective refinement. The other is vertex hierarchy built with progressive mesh in the cluster node to provide fine-grained local refinement. In order to promote the speed of local refinement, we introduce some data structures and dependency rules to realize parallel view-dependent refinement for vertex hierarchy by using GPU, which greatly reduces the load of CPU and enables it to prefetch data to hide I/O latency effectively. In addition, we propose a new mesh layout algorithm which reorders triangles contained by cluster node to reduce the average cache miss ratio and further improve the rendering speed.