The normalform of a space curve and its application to surface design
The normalform of a space curve is introduced analogously to the normalform of a plane curve and a surface, i.e. an implicit representation h (x) = 0 with \ \ delh \ \ = 1. The normalform function h is (unlike the latter cases) not differentiable at curve points. Despite of this disadvantage the normalform is a suitable tool for designing surfaces which can be treated as common implicit surfaces. Many examples (bisector surfaces, constant distance sum/product surfaces, metamorphoses, blending surfaces, smooth approximation surfaces) demonstrate applications of the normalform to surface design.
normalform bisectors constant distance sum/product surfaces pipe surfaces intersection curves intersection points g(n)-blending isophotes