A mesh surface curve design method based on distance constraint

Abstract

The invention discloses a mesh surface curve design method based on distance constraint. The designed curve passes through a given interpolation point and is smooth (in the sense of discreteness) andstrictly located on the mesh surface. The method transforms the complex manifold constraints into distance constraints and describes them as optimization problems together with smooth constraints andinterpolation constraints. The local surface is approximated by the tangent plane, and the distance constraint is relaxed to the distance from the point to the tangent plane. Because the points on thecurve used to calculate the distance are interdependent with their corresponding tangent points, a global-local iterative strategy is adopted and Gauss- Newton idea method is used to control its convergence behavior: in the whole stage, it is relaxed into a convex optimization problem by distance approximation to solve the iterative step size; In the local phase, a robust and efficient projectionmethod is used to map the optimized curves to the surface to update the tangent points. Finally, all the relaxed polygons are mapped to the mesh surface by using the cutting plane method. Compared with the existing methods, this method has many advantages in efficiency, robustness and application range.

Description

technical field [0001] The invention relates to the fields of computer graphics, geometric processing, computer-aided design and the like, in particular to a method for designing curves on grid surfaces based on distance constraints, so as to design smooth discrete curves on discrete grids. Background technique [0002] Curve design on the mesh surface is an important part of geometry processing and editing, and has a wide range of application backgrounds, such as part segmentation in mesh processing, simulated cutting in virtual surgery, pattern design in manufacturing, Computational geometry on manifolds, and CAD systems, etc. There are many ways to design this kind of curve, among which there are two common ones: interpolation and smoothing: the user inputs several control points or an initial curve on the grid surface, and the system generates a smooth curve attached to the surface, making it pass through These input points (interpolation). In other words, designing cu...

AI Technical Summary

Problems solved by technology

This method is often robust, efficient and flexible, but it is limited to local areas, making it difficult to design large-scale curves

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