以多条离散曲线为测地线构造离散曲面

Constructing Discrete Surface Through Given Discrete Geodesics

为了解决CAD中逆向主动设计问题,提出以任意多条空间离散曲线为测地线构造离散曲面的算法.首先通过密切圆思想离散化曲线相关几何变量;其次利用局部插值思想和测地线蕴涵特征,推导出满足约束条件的离散曲面公式;最后给出以B样条为度量函数的离散曲面构造公式.逆向主动设计实例表明,该算法是可行的并有较强的交互性,可以通过调整B样条度量函数的节点向量或控制顶点来调节曲面形状,设计出满足各种不同需求的曲面,在服装、鞋帽、义齿设计等领域有很好的应用前景.

To solve the reverse active design problem in computer aided design, an algorithm for constructing discrete surface with arbitrary multiple spatial discrete curves as geodesics is proposed. Firstly, the geometrical variables of the curve are discretized by using the idea of osculating circle, and then the formula of discrete surface which satisfies the constraint conditions is derived by means of local interpolation and the characteristics of geodesics. Finally, the formula for constructing the discrete surface with B-spline as the measurement function is given. The reverse active design test results show that this algorithm is feasible and has strong interactivity, the shape of surface can be adjusted by modifying the knot vector of the B-spline measurement function or the control points, therefore this algorithm has bright application prospect in garment, shoes and hats, false tooth design industry.