论文标题
测量曲率的近似和球形几何细分方案的应用
Approximation of the geodesic curvature and applications for spherical geometric subdivision schemes
论文作者
论文摘要
几何建模和计算机图形的许多应用必要的精确曲率估计平面或歧管上的曲线。在本文中，我们定义了平滑表面上测量多边形的离散地球曲率的概念。我们表明，当测量多边形P紧密刻在$ c^2 $常规曲线上时，P的离散的地球曲率估计了C。C的测量曲率C。该结果使我们能够评估表面离散曲线的地质曲率。特别是，我们将这种结果应用于平面和球形4点角度细分方案。我们表明，此类方案不能在一般$ g^2 $连续曲线中生成。我们还提供了一个仅使用点和离散的地质曲率的单位球体上的$ G^2 $连续细分方案的新颖示例，称为基于曲率的6点球形方案。
Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a smooth surface. We show that, when a geodesic polygon P is closely inscribed on a $C^2$-regular curve, the discrete geodesic curvature of P estimates the geodesic curvature of C. This result allows us to evaluate the geodesic curvature of discrete curves on surfaces. In particular, we apply such result to planar and spherical 4-point angle-based subdivision schemes. We show that such schemes cannot generate in general $G^2$-continuous curves. We also give a novel example of $G^2$-continuous subdivision scheme on the unit sphere using only points and discrete geodesic curvature called curvature-based 6-point spherical scheme.
