隐曲面变换中纹理映射的研究

ON TEXTURE MAPPING IN IMPLICIT SURFACES TRANSFORMATION

曲面映射有多种应用,纹理映射、多通道变形和曲面分析。给定一个4维的隐函数,在两个隐曲面之间定义一个变形,提出一种在形变中产生纹理迁移的映射算法,通过在4维上的四面体超曲面求解两个偏微分方程来得到这种算法。求解第一个PDE产生一个矢量场,指出如何从源曲面上指向目标曲面。求解第二个PDE,生成沿着矢量场的位置标签,这样目标曲面就由源曲面上的唯一的位置所标记。

Surface mapping has a variety of uses,including texture mapping,multi-way morphing and surface analysis.Given a 4D implicit function that defines a morph between two implicit surfaces,this article presents a mapping algorithm of texture transform during morphing.We create such an algorithm by solving two PDEs over a tetrahedralized hypersurface that connects the two surfaces in 4D.Solving the first PDE yields a vector field that indicates the flow of how source surface pointing on target surface.Solving the second PDE propagates position labels along this vector field so that the target surface is tagged with a unique position on the source surface.