Three-dimensional geometric body surface smooth vector field calculating method under guidance of typical line

Abstract

The invention brings forward a three-dimensional geometric body surface smooth vector field calculating method under the guidance of a typical line. The method comprises the following steps: S100, calculating three-dimensional vectors at the grid summits of a three-dimensional geometric body, a set of the three-dimensional vectors constituting a harmonic vector field of the three-dimensional geometric body; S200, introducing the typical line as a boundary condition, by taking all summit tangential vectors which the typical line passes through as updating values, adding the updating values into a penalty diagonal matrix, and employing a supernode algorithm to obtain a harmonic vector field after the boundary condition is updated; and S300, utilizing a greedy algorithm to calculate a vector field by taking the current typical line as a boundary condition, and obtaining a smooth vector field under the guidance of the typical line. The method provided by the invention has the following advantages: in the prior art, only a surface smooth vector field can be calculated, and a vector field under the guidance of a typical line cannot be calculated, however, the method provided by the invention realizes rapid calculation of typical line orientation by use of a dynamically updated harmonic vector field.

Description

【Technical field】 [0001] The invention relates to computer graphics, in particular to a method for calculating a smooth surface vector field guided by three-dimensional geometry feature lines. 【Background technique】 [0002] The calculation of vector field on the surface of three-dimensional geometry is an important problem in computer graphics. The vector field on the surface of a 3D geometry is mainly used for surface texture synthesis, surface meshing, and non-realistic, stylized rendering effects for 3D geometry. [0003] The calculation of the surface vector field of the existing 3D model mainly adopts the discrete outer differential method and the parallel movement method. The discrete external differential method mainly uses the discrete differential geometry method to calculate the surface differential forms (differential forms) to define the smoothness of the surface vector field. This method was proposed by Caltech Matthew Fisher et al. at the SIGGRAPH2007 confere...

AI Technical Summary

Problems solved by technology

The advantage of these two methods is that a very smooth surface vector field can be obtained, but due to the high computational complexity, the update speed of the vector field is slow after the boundary conditions change, so it is not suitable for the vector field calculation guided by the characteristic line

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