Directional newton methods and restricted domains

Abstract

Let F : D ⊂ ℝn → ℝ be a differentiable function. In computer graphics, we often need to compute and display the intersection C = A ⋂ B of two surfaces A and B in ℝ3 [5], [6]. If the two surfaces are explicitly given by A = {(u, v, w)T : w = F1(u, v)} and B = {(u, v, w)T : w = F2(u, v)}, then the solution x = (u, v, w)T ∈ C must satisfy the nonlinear equation F1(u, v) = F2(u, v) and w = F1(u, v).