Fig. 3

Vertex-face test: To perform a vertex-face test between a deforming triangle (defined by a₀, b₀, and c₀ at t = 0, and a₁, b₁, and c₁ at t = 1) and a moving vertex (defined by p₀ at t = 0 and p₁ at t = 1), coplanarity between the vertex and the triangle by finding a t (t ∈ [0, 1]) when the projected distance along the normal vector of the triangle is equal to zero, that is, (p_t − a_t) · n_t = 0 is checked. a: Deforming triangle T and deforming vertex p; b: Projected distance between p_t and T_t