图学学报
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摘要: :曲面上的测地线是曲面上一类重要的曲线。测地线在计算机可视化、图像处理、 服装设计等领域均有广泛应用。该文利用一条曲线为所在曲面的测地线当且仅当它的从切面与 该曲面在这条曲线上的切平面重合这一论断,做了以下工作:对给定的三次Bézier曲线,构造 双三次Bézier曲面,使该曲面以给定的曲线为其边界测地线;讨论了具有给定测地线的组合双 三次Bézier曲面的连续性拼接问题;为了说明所给方法的有效性,给出了几个数值实例。
关键词: 三次Bé, zier曲线, 双三次Bé, zier曲面, 测地线, 控制点, 曲面构造
Abstract: Geodesic curve on a surface is a kind of important one and has its applications in computer vision and image processing, such as in garment design. A curve is a geodesic if and only if its rectifying plane coincides with the tangent plane to the surfaces. This fact is used to construct bicubic Bézier pathes through geodesics, and the continuity of composite Bézier patches through pairs of geodesics discussed. Finally, some examples are provided to demonstrate the effectiveness of the proposed method.
Key words: cubic Bézier curve, bicubic Bézier surface, geodesic curve, control point, surface construction
郭清伟, 胡 梅. 以给定的三次Bézier曲线为边界测地线的双三次Bézier曲面构造[J]. 图学学报.
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http://www.txxb.com.cn/CN/Y2014/V35/I4/523