中文摘要：

几何形体间最近距离在机器人、游戏动画及装配仿真等领域有着广泛应用。现有的研究大部分需要将形体分解离散成若干个凸多面体的集合,用于近似原模型。对于具有曲面的形体,利用这些方法通常不能找到它们间最近距离的准确解。引入了一种几何形体R-函数表示法。通过该方法并结合形体的几何信息及Constructive Solid Geometry（CSG）信息,将它用单个形如g（x）≤0的隐式不等式表示;根据形体的隐式不等式,给出形体间最近距离的非线性约束优化模型;利用已有的SQP算法,求解该优化模型而得到形体间的最近距离。为了验证本文所提出的方法,开发了形体间最近距离的求解系统R-MinDist,实例计算结果表明该方法准确有效。

英文摘要：

The calculation of the minimum distance between geometric objects has wide applications in robotics,video games and assembly simulation. For non-convex objects with smooth curved surfaces,most of the previous studies in this area have to decompose or discretize them into sets of polyhedra as approximations of original objects.The minimum distance obtained is approximate,being not precise. To address these issues,we propose a method of geometric object representation with R-functions; with the method,a geometric object can be defined with the implicit inequality g（ x） ≤ 0 based on the object’ s geometrical information and its constructive solid geometry.Then,according to their implicit equality,we derive certain non-linear constrained optimization models to calculate the minimum distance between the objects. Finally,the optimization models are solved with the exiting SQP algorithm,and the minimum distance is obtained. To verify the method proposed in the paper,a system named R-MinDistis developed. The verification results show the correctness and effectiveness of the calculation results.