关于三次B样条曲线重构中射影变换及控制点反求的一点思考

Some Thoughts on the Projective Transformation and the Inverse of Control Point in the Reconstruction of Three B-spline Curve

证明了三次B样条曲线经过射影变换后仍然是三次B样条曲线;提出了像平面中三次B样条曲线是空间中三次B样条曲线的射影;给出了像平面中三次B样条曲线控制点与空间中三次B样条曲线控制点的射影关系;提出了B样条曲线控制点的反求方法。

It is proved that the cubic B- spline curve is still cubic B- spline curve after projective transformation. It is proposed that cubic B- spline curves in the image plane are the projective of cubic B-spline curves in space. The projective relations between the control points of the cubic B- spline curves in the image plane and the cubic B- spline curves in space are given. A method of solving B- spline curve control points is proposed.