陶瓷产品几何造型的美化技术

The surface fairing of the ceramics is not only a measure of the aesthetics of ceramic products, but also have a major impact on product quality and physical properties. In geometric modeling, the curvature distribution of the curve and surface directly affect the degree of the surface fairing. Thus, in order to improve the quality of ceramic products, this project study the optimal design of curves and surfaces based on the curvature variation.By analysis of characteristics of the discrete ceramic surface, the surface curvature and third-order differential invariants are given, and then feature curves, such as ridge and valley lines, are extracted by use of the differential invariants.Also the smoothing algorithm about ceramic sketch curves is explored by the spiral arc,and the smooth reconstruction problem of the ceramic surface based on the contours is discussed by the use of third-order energy.In short, by the use of knowledge in Computer Aided Geometric Design, high quality,convenient and reliable tools and algorithm theories were provided for ceramic design system.

陶瓷器型表面光顺程度不仅是衡量陶瓷产品美观度的重要标志, 而且对产品的质量和物理性能都将产生重要影响.在几何造型中, 曲线曲面的曲率分布直接影响了物体表面的光顺度. 因而,为了提升陶瓷产品的质量,本课题研究了以曲率变化为约束的曲线曲面的优化设计问题. 基于分析陶瓷类网格曲面的特征, 研究了网格曲面上曲率和三阶微分不变量的计算公式，并利用这些微分不变量，提取了如脊线和谷线等特征曲线;同时也探讨了利用螺线弧的陶瓷草图曲线的光顺算法；并利用三阶能量，讨论了基于轮廓线的陶瓷曲面的光滑重构问题.总之,利用计算机辅助几何设计中的知识，为陶瓷设计系统提供高质、方便、可靠的工具及算法理论.

表面光顺度不仅是衡量产品美观度的重要标志, 而且对产品的质量和物理性能都将产生重要影响.在几何造型中, 曲线曲面的曲率分布直接影响了物体表面的光顺度. 本课题研究了以曲率变化为约束的曲线曲面的优化设计问题. 由于螺线，是曲率恒正或恒负，且曲率单调变化的平面曲线，因此，本项目设计了一类螺线弧，探讨了利用螺线弧构造直线和圆弧之间缓和曲线的算法，从而设计出曲率单调的拟合曲线; 在曲线的含端点约束的多项式逼近方面，探讨了多项式对偶函数的一般理论，给出圆弧等曲线的多项式逼近表示; 利用计算机辅助几何设计中的知识，探讨了陶瓷器皿造型中线、几何面及体的数字化建模及造型美化算法。

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