加权可调的广义三角形中点细分

摘要

To select proper weight value in modeling of subdivision surface,the quantitative relationship of limit points and weighting coefficient a was proved with equivalent subdivision mask,and the smoothness of the resulting subdivision surface C1 when weighting coefficient was negative had also been analyzed.A new weighting coefficient γ which had obvious geometric meaning was proposed.The geometric meaning of weighting coefficient γ was that the limit point of a specific original control point pulled towards the original control point itself on a line as weighting coefficient γ varies from O.25 to 1.Meanwhile,the limit subdivision surface had lied closer to the control mesh with C1 continuity when γ gradually became larger.Some typical examples were illustrated to verify the validity of the conclusion at length.%为了能在细分曲面造型时选取合适的权因子值,使用等价细分模板证明了权因子α与极限点之间的定量关系,并分析了权因子α为负数时细分曲面的C1连续性.给出了一个具有明确几何意义的新权因子γ,即当权因子γ从0.25逐渐增加到1时,广义三角形中点细分的控制顶点所对应的极限点将在不断地接近该控制顶点的过程中扫掠出一条直线.广义三角形中点细分的极限曲面在保持C1连续的前提下逐渐逼近原始控制网格.通过实例验证了该结论的合理性.