On a relationship between the moving line and moving conic coefficient matrices Original Research Article

The method of moving curves and moving surfaces is a new, effective tool for implicitizing rational curves and surfaces. Here we investigate a relationship between the moving line coefficient matrix and the moving conic coefficient matrix for rational curves. Based on this relationship, we present a new proof that the method of moving conics always produces the implicit equation of a rational curve when there are no low degree moving lines that follow the curve.