Fair curve and surface design system using tangent control

N. Sakiyama, K. Miura, T. Takahashi, T. Kaneko, T. Kubo
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引用次数: 2

Abstract

The paper proposes a generation system of unit quarternion curves and surfaces to design fair curves and surfaces. Curvature and variation of curvature are the primary factors that determine the quality of fair curves and surfaces; however not so many methods have been explored to directly manipulate them, especially in three dimensional space. We use unit quaternion curves in integral forms to specify the tangent of a curve and the first derivative of a surface in one parameter direction. This enables us to control their curvature and variation of curvature more than is possible with traditional parametric representations like Bezier and NURBS curves and surfaces. Using unit quaternion curves balances the efficiency of the design process and the fairness of the designed curves and surfaces. Our system can generate fair curves and surfaces within a short time and their quality is acceptable for industrial applications as well as CG animation.
公平曲线和曲面设计系统采用切线控制
提出了一种单位四分位数曲线曲面生成系统,用于设计美观的曲线曲面。曲率和曲率的变化是决定美观曲线和曲面质量的主要因素;然而,目前还没有很多方法可以直接操纵它们,特别是在三维空间中。我们用积分形式的单位四元数曲线来表示曲线的正切和曲面在一个参数方向上的一阶导数。这使我们能够控制它们的曲率和曲率的变化,而不是像Bezier和NURBS曲线和曲面这样的传统参数表示。使用单位四元数曲线兼顾了设计过程的效率和设计曲线曲面的公平性。我们的系统可以在短时间内生成公平的曲线和表面,其质量可以接受工业应用以及CG动画。
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