Topology of the Intersection of Two Parameterized Surfaces, Using Computations in 4D Space

Stéphane Chau (1, 2) , André Galligo (1, 2)

1 GALAAD2 - Géométrie , Algèbre, Algorithmes
2 LJAD - Laboratoire Jean Alexandre Dieudonné

The intersection curve of two parameterized surfaces is characterized by 3 equations $F_i(s,t) = G_i(u,v)$, $i = 1, 2, 3$ of 4 variables. So, it is the image of a curve in four dimensional space. We provide a method to draw such curve with a guaranteed topology.

Domaines: Géométrie différentielle [math.DG]; Calcul formel [cs.SC]

Stéphane Chau, André Galligo. Topology of the Intersection of Two Parameterized Surfaces, Using Computations in 4D Space . Tor Dokken Georg Muntingh. SAGA – Advances in ShApes, Geometry, and Algebra, 10, Springer, pp.123-145, 2014, Geometry and computing, ⟨10.1007/978-3-319-08635-4_7⟩. ⟨hal-01292835⟩