A basis for the implicit representation of planar rational cubic Bzier curves ?
We construct a basis for the implicit representation of planar rational cubic Bzier curves. We present an explicit formulation of the implicit polynomial coefficients. Barycentric formulas for the double point of the cubic curve are derived. A simple test for when unwanted branches occur is formulated. Conditions for the degeneration of cubics to conics are presented.
implicit representation bzier curves double point rational cubic curves conic sections singularity