A new type of free-form curve given by an integral form

K. Miura, Teruhisa Nakaseko, T. Ikedo
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引用次数: 4

Abstract

The paper proposes a new type of free-form curve for fairness. A unit quaternion curve is used to specify the tangent of the curve in order to more directly manipulate its curvature and variation of curvature than is possible for the traditional parametric representations like Bezier and NURBS curves. Since the new curve is represented by can integral form of a unit quaternion curve, it is named unit quaternion integral curve or QI curve for brevity. It is a generalization and an extension of the clothoid into three dimensional space and the norm of its tangent is always equal to 1. Its curvature and variation of curvature are given by rather simple expressions.
一种由积分形式给出的新型自由曲线
本文提出了一种新型的公平自由曲线。单位四元数曲线用于指定曲线的切线,以便比传统的参数表示(如Bezier曲线和NURBS曲线)更直接地操纵其曲率和曲率变化。由于新曲线采用单位四元数曲线的积分形式表示,为简洁起见,将其命名为单位四元数积分曲线或QI曲线。它是仿线在三维空间中的推广和扩展,其切线的范数总是等于1。它的曲率和曲率的变化是由相当简单的表达式给出的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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