Page 16 - Geometric Modeling and Algebraic Geometry

10 T. Dokken

Fig. 1.1. Transversal intersection between two sculptured surfaces

Fig. 1.2. Tangential intersection between two surfaces

p(t)= P 0 + tT 0 ,t ∈ IR,

with P 0 a point on the line and T 0 the tangent direction of the line.
• A straight line represented as an implicit equation

q(x, y)=((x, y) − P 1 ) · N 1 =0, (x, y) ∈ IR ,
2
with P 1 a point on the line, and N 1 the normal of the line.