过两端点分段三次 B 样条方法应用研究*

摘要

通过引入约束点 P0和常量 r，构建过两端点分段三次B样条曲线并推出衔接点光滑衔接条件。应用过两端点分段三次B样条方法可以构建直线、三角形、四边形及蛋形画法，并通过消齿光顺得到理想效果。实现图形的平移、缩放和旋转，通过逆时针、顺时针旋转计算消除偏差，保形效果理想。按顺时针方向生成闭曲线并记录轨迹点位置数据，方便平面上闭曲线对象间关系的计算，并得到布尔运算结果。应用该方法可以构建空间图形，实现颜色渐变效果理想。%By introducing the constraint point P0 and constant r ,two endpoints piecewise cubic B spline curve is built and some smooth cohesion terms are introduced .Application of two endpoints piecewise cubic B spline method can build straight lines ,triangles ,quadrilateral and egg painting .Through the elimination of tooth smoothing ,ideal effect is got . Translation ,scaling and rotation of graphics are achieved and eliminated by counterclockwise ,clockwise calculation devia‐tion ,conformal effect is ideal .Clockwise to generate closed curve trajectory point location and record data ,convenient plane closed curve calculation of relations between objects ,Boolean calculation results are obtained .The method can build space graphics ,make color gradient effect ideal .