Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a ...Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry driven because we utilize the old points and their tangent vectors whereas most other iterative schemes rely only on the old points. Some numerical examples are presented to show the advantageous properties of the new scheme.展开更多
基金Supported partially by the National Natural Science Foundation of China (Grant Nos. 60673032, 60773179)the National Basic Research Program of China (Grant No. 2004CB318000)the Scientific Starting Foundation of Hangzhou Dianzi University
文摘Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry driven because we utilize the old points and their tangent vectors whereas most other iterative schemes rely only on the old points. Some numerical examples are presented to show the advantageous properties of the new scheme.
