Perimeter-maintaining curve subdivision method and system

Abstract

The invention discloses a perimeter-maintaining curve subdivision method and system. The method comprises the following steps: obtaining information of an un-subdivided curve; carrying out four-point triple subdivision processing of fusion approach and interpolation on the un-subdivided curve, and obtaining a curve subdivision mode; modifying parameters of the curve subdivision mode and enabling second derivatives of the curve in the curve subdivision mode to be continuous; adjusting the parameters within a parameter range with continuous second derivatives of the curve, and determining an perimeter error of the curve before and after a subdivision to be within a threshold range; and outputting a perimeter-maintaining subdivided curve of fusion approach and interpolation. According to the perimeter-maintaining curve subdivision method and system, the invariable perimeter before and after the subdivision can be achieved by a fusion approach and interpolation subdivision method; the smoothness of the curve can be improved; and the use experience of a user is improved.

Description

technical field [0001] The invention relates to the technical field of image processing, in particular to a perimeter-preserving curve subdivision method and system. Background technique [0002] In the field of CAGD (Computer Aided Geometric Design), subdivision is an efficient method for generating smooth curves and surfaces because it can handle arbitrary topologies. The subdivision method actually defines the control polygon or the curve of a surface from an initial arbitrary given control grid, according to the refined rules of specific design, so that the restricted curve or surface can achieve a certain degree of smoothness and continuity; The subdivision method only needs to store discrete point columns (from discrete control vertices to discrete display points), which can greatly improve the speed of calculation, generation and display of curves or surfaces in computers; therefore, it has been widely valued in computer animation, scientific computing There are appl...

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Problems solved by technology

[0003] In each subdivision rule, the new vertex position can be derived from the row vector of the previous vertex action subdivision matrix, so its position can be seen as the sum of the specific weights of the previous old vertices; in practice, Subdivision schemes can be divided into two categories: one is interpolation subdivision, the other is approximation subdivision, both have their own advantages; for interpolation subdivision schemes, because they have to pass through all initially given control points , with many constraints, this type of subdivision is suitable for specific industrial applications; the approximation subdivision scheme can be conveniently used for intersection operations, and produces a restricted curve with high smoothness and continuity; therefore, two schemes are disclosed a close relationship between them, mixing them may combine the advantages of possible approximation and interpolation subdivision schemes, and yield a hybrid approach with broader application prospects if it is computationally simple enough; however, it is still a lack of integration and An Efficient and Simple Way to Approximate Interpolation Subdivision Schemes

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