基于五次Catmull-Rom样条的日用陶瓷产品造型设计  

Modeling Design of Daily Ceramic Products Based on the QuinticCatmull-Rom Spline

作　　者：李军成 LI Juncheng(College of Mathematics and Finance,Hunan University of Humanities,Science and Technology,Loudi 417000,Hunan,China)

机构地区：[1]湖南人文科技学院数学与金融学院,湖南娄底417000

出　　处：《中国陶瓷工业》2025年第1期61-66,共6页China Ceramic Industry

基　　金：湖南省自然科学基金项目(2024JJ7254)。

摘　　要：由于大多数日用陶瓷产品形体从几何上可视为由其轮廓曲线旋转一周生成的旋转体,故可将这类陶瓷产品的造型设计重点放在其轮廓曲线的描述上。提出了利用可直接插值于数据点的C^(2)连续五次Catmull-Rom样条描述陶瓷产品轮廓曲线的方法,通过修改样条所含的形状因子可获得不同形状的轮廓曲线,能满足陶瓷产品形体设计的实用性与个性化需求。进一步给出了利用应变能极小与曲率变化能极小确定五次Catmull-Rom样条所含形状因子的最优取值方法,该方法可构造出尽可能光顺的陶瓷产品轮廓曲线,能满足陶瓷产品形体设计的优美性需求。Due to the fact that most daily ceramic products can be geometrically viewed as rotating bodies generated by one revo-lution of their profile curves,the modeling design focus of these ceramic products can be on the description of the profile curves.A method for describing the profile curves of ceramic products using the quintic Catmull-Rom spline that satisfies C^(2) continuity and directly interpolates the data points is proposed.By modifying the value of the shape factor in the spline,different shapes of the profile curves can be obtained,which can meet the practicality and personality requirements of ceramic product form design.Furthermore,the optimal methods for determining the shape factor in the quintic Catmull-Rom spline using strain energy mini-mization and curvature variation energy minimization are proposed.The methods can obtain the fairing profile curves of ceramic products,which can meet the aesthetics requirements of ceramic product form design.

关 键 词：五次Catmull-Rom样条 形状因子 日用陶瓷产品 形体设计 轮廓曲线 光顺 

分 类 号：TQ174.73[化学工程—陶瓷工业]