Multi-level optimized grid curved surface discrete spline curve design method

Abstract

The invention discloses a multi-level optimized grid curved surface discrete spline curve design method. According to the method, the constraint that a curve is strictly located on a curved surface isrelaxed, only discrete sampling points of the curve are located on a grid curved surface, the thought of an interior point method is adopted, and numerical solution is conducted through a global optimization method based on a block coordinate descent method. In order to more accurately estimate a discrete differential operator, improve the solving precision, reduce the calculated amount of movingsampling points and improve the solving efficiency, a coarse-to-fine multi-scale hierarchical solving strategy is adopted, that is, the density of curve sampling points is gradually increased for iterative solving until the algorithm converges. And finally, mapping the curve segments to the grid curved surface by means of local parameterization. A convergence analysis experiment shows that the multi-level optimization method can achieve rapid convergence, and a smoother result is obtained under a multi-scale strategy. Compared with an existing projection method and an existing fairing method,the method is higher in efficiency and has certain advantages in controllability, universality and robustness.

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 multi-level optimized grid surface discrete spline curve design method to realize the design of smooth discrete curves on discrete grids. Background technique [0002] Curve design is an important subject with a long research history in computer graphics and computer-aided geometric design. At present, the curve design method for Euclidean space has become mature; with the wide application of digital geometry and the increasing demand for CAD / CAM, the curve design on discrete mesh surfaces has gradually attracted people's attention, and has been widely used in computational geometry, digital Geometry processing, virtual surgery, shoe design, and numerical control machining have been widely used. [0003] Curves on mesh surfaces are usually defined as piecewise linear discrete curves. Similar to Euclidean space, there ...

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Problems solved by technology

This type of method has good robustness, and the designed curve usually has good smoothness, but the strict manifold constraints reduce its efficiency, and at the same time, due to the inherent limitations of the smoothing method used, its scope of application is affected to a certain extent

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