Hodographs and normals of rational curves and surfaces Original Research Article

Derivatives and normals of rational Bézier curves and surface patches are discussed. A non-uniformly scaled hodograph of a degree m × n tensor-product rational surface, which provides correct derivative direction but not magnitude, can be written as a degree (2m − 2) × 2n or 2m × (2n − 2) vector function in polynomial Bézier form. Likewise, the scaled normal direction is degree (3m − 2) × (3n − 2). Efficient methods are developed for bounding these directions and the derivative magnitude.