Axial moving planes and singularities of rational space curves
Xiahong Jia, Rice

The concepts of moving curves and moving surfaces were introduced by Sederberg,Cox and Chen. The concept of mu-basis was then developed, which can be used to implicitize as well as to find singularities of rational planar curves. We now provide a method of detecting the singularities of rational space curves by deriving an one-to-one correspondence between the singular points of rational space curves and the axial moving planes that follow these space curves.