Hodographs and normals of rational curves and surfaces

Abstract Derivatives and normals of rational Bezier 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 (2 m − 2) × 2 n or 2 m × (2 n − 2) vector function in polynomial Bezier form. Likewise, the scaled normal direction is degree (3 m − 2) × (3 n − 2). Efficient methods are developed for bounding these directions and the derivative magnitude.