3D model spherical surface area-preserving parameterization method and system based on mirror reflection

Abstract

The invention provides a 3D model spherical surface area-preserving parameterization method and system based on mirror reflection, and the method comprises the steps: carrying out the deduplication of points on an original triangular mesh, and increasing the disturbance through a random number; randomly selecting from the scrambled point set to form an initial convex geometry; traversing other points except the four points on the original convex geometry in sequence, if the point is in the current convex geometry, ignoring the point, and otherwise, finding and deleting all surfaces which can be observed by the point; connecting all points of the shadow boundary with the current traversal points to form a triangle adding surface set which is used as a surface set of the convex geometry corresponding to the original triangular mesh; performing mirror reflection on points in the convex geometry in the original grid relative to the obtained convex geometry, so that new positions of the points are obtained; and continuously iterating until the error of the convex geometry relative to the minimum surrounding sphere is smaller than a threshold value, and outputting an area-preserving parameterization result of the spherical surface. Strong preconditions are not needed, area preservation is efficiently achieved, and the method can be widely applied to digital geometric processing.

Description

Technical field [0001] The present invention relates to the field of digital 3D geometric models, and more particularly to a technical solution for a 3D model spherical protection area based on mirror reflection. Background technique [0002] With the development of the 3D geometric model, the parametricization of the network surface has become one of the research hotspots in graphics in recent years, which is the basic core of digital geometric treatment research. The triangular network surface has a simple, flexible and flexible support for a variety of graphics hardware, so the parametricization of the triangular mesh surface has been widely used in the fields of entertainment, manufacturing, medicine and science. [0003] The parametricization of the triangular mesh model is a research foundation for the division of consistent mesh division, heavy gridization, texture mapping and other work. The heavy mesh is converted into a rule grid with a subdivided endotroph, and further...

AI Technical Summary

Problems solved by technology

[0007] The first two types of methods are not robust spherical parameterization methods, both require strong assumptions, and do not theoretically consider the problem of parametric deformation

Although the third type of method extends the plane Laplace operator to the Laplace-Beltrami operator, and then solves the nonlinear equation system to obtain the spherical parameterization and proves the reliability of the method theoretically, it needs to solve the highly complex The non-linear equations therefore bring various problems such as time overhead to the solution results. The root of this non-linearity is that spherical equations can only be expressed by non-linear equations in the Cartesian coordinate system

However, the traditional method has the disadvantages of requiring strong assumptions, no theoretical support, or the need to solve complex nonlinear equations, so there is an urgent need for new methods that do not have the above problems

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