给定精度条件下的Catmull-Clark细分曲面求交研究

细分曲面由于没有整体解析表达式,与参数、隐式曲面相比求交更加困难。针对基于平面四边形网格的Catmull-Clark细分曲面,在给定精度条件下,把对细分曲面的求交转化为对一定细分层次控制网格的求交:首先构造两张控制网格上相交四边形网格带及其1-邻域网格带,然后不断细分相交四边形网格带及其1-邻域网格带,提高求交精度,其次求解出相交四边形网格的交点,并根据拓扑关系将其顺序连接起来既得到两细分曲面之间的相交曲线,实现了细分曲面的求交。

On Catmull-Clark Subdivision Surface Intersection with a Given Precision

Because of no global analytic representation for a subdivion surface,intersection of subdivision surfaces is more difficult than that of the parameter surfaces and implicit surfaces.For a Catmull-Clark subdivision surface which is based on a plane quadrangle,on the condition of a given precision,a method which converts the calculation of subdivision surface intersection into that of control mesh intersection is put forward in this paper.First,the 1-neighborhood zone of intersecting quadrangle mesh on the control mesh is constructed.Then the 1-neighborhood zone is subdivided continuously to improve the precision of intersection.Finally,the intersection points between the intersection quadrangles are calculated;they are linked according to their topology relation,so that intersection line between the two Catmull-Clark subdivision surfaces which satisfies the given precision is calculated.