【摘要】 给定曲线/曲面的参数方程求其隐式方程,称为曲线/曲面的隐式化.隐式化是经典代数几何消元理论中的研究问题,同时在现代计算数学与计算机应用的交叉学科分支——计算机辅助几何设计中有重要应用.本文在回顾曲线与曲面隐式化的经典方法的基础上,重点介绍近十几年发展起来的基于动曲线/曲面与μ基理论的隐式化方法的相关进展.更多还原

【Abstract】 The procedure of converting the parametric equation of a curve or a surface into the implicit equation is called implicitization.Implicitization is a classic elimination problem in algebraic geometry and has found important applications in computer aided geometric design — an inter-discipline in computer science and scientific computing.The classic methods for implicitization were reviewed first,and then the state of the art techniques in curve and surface implicitization were surveryed,especially the recent advances of the moving curves/surfaces method andμbasis method developed in the last decade.更多还原