Detecting self collision
- Handled as moving point in collision with moving triangle
- - Triangle \(P_1(t) P_2(t) P_3(t)\) , a point \(P(t)\)
- - Each position \(P_k(t)=P_k(0)+t\,v_{P_k}\)
- Necessary condition
- - Find \(t_i\in[0,h]\) such that \(P(t_i)\) is in triangle plane
-
- \( (P(t_i)-P_1(t_i))\times n(t_i) = 0\)
- \(n(t_i)\): normal of the triangle at time \(t_i\)
- Sufficient condition
- - Check \(P(t_i)\) is inside the triangle
-
- \(P(t_i)=\alpha P_1(t_i)+\beta P_2(t_i)+ \gamma P_3(t_i)\)
- \((\alpha,\beta,\gamma)\in[0,1]^3\), \(\alpha + \beta + \gamma = 1\)
