Reconstructing Triangular Mesh Surface Model With Vertex Curvature Continuously Patch

With the rapid development of science and technology, and also the substantial increase of the equipment’s precision, models acquired by 3D scanner is more and more sophisticated, and have more and more information, but it also leads to increase its storage capacity and speed of network real-time transmission is less than the model precision lifting speed, so that the model transmission efficiency becomes low and its interactive display capability decreased significantly. Therefore, in order to eliminate many problems caused by enhancing the precision of the model, it will be used to store or transport the lightweight model. After simplifying the model, when you need to use the model again, we need to reconstruct the lightweight model, and quickly retur ned to the original fine model which will have the same or similar effect as the previous.In order to improve the efficiency and accuracy of surface reconstruction, we will adopt the principle of surface subdivision. When the broken surface interpolated to the specified surface, then blend surfaces. In order to get fully smooth surface, not only require patches to meet the G~1 geometric continuity along the boundary curves, but the normal curvature at the apex of the triangle have the only value. Therefore, in order to optimize the normal curvature at the vertex, and eliminate dark spots on the model problem, this article will be based on G~1 geometric continuity interpolating subdivision surface mesh into quartic Gregory surface, and then will have curvature value locally and global optimization at the apex.This paper discusses the quartic Gregory smooth surface modeling problem which meet G~1 continuous. As compared to Bezier surfaces, Gregory surfaces are just different from the internal control points, the same as its boundary property, so interpolating the boundary curve into a cubic Bezier curve and then increase its order to quartic, so we can get the quartic Gregory boundary curve in the end. The internal control points of the surface are estimated based on a tangent ribbon, and finally modified internal control points according to G~1 continuously constraints, so we get all control points of the surface, and can calculate surface based on surface parameters expression.After interpolating the G~1 geometry continuity Gregory surface, normal curvature of vertex needs to be optimized. Two optimizations are included: local optimization and global optimization.In the local optimization algorithm, assuming the vertex coordinates have a certain amount of change along the vertex normal direction, and then solving the change based on the constraint equations, and updating the vertex coordinates according the change, at last the vertex curvature has a certain improvement.In the global optimization algorithm, assuming that all vertices have a certain amount of change in its normal vector direction, and then solving the changes according to the G~1 continuously constraint equations, after that we need to amend all points coordinates and correct normal curvatures, so that each patch connected to the same vertices have the same normal curvature, and the normal curvature is equal to the original vertex curvature or the smallest difference. After optimization, the surface smoothness has been a good upgrade.