HCR - Bounding Box

NOT_SURE_ABOUT_THIS Old notes taken really fast

Bounding Box

Let’s define the shape of our triangles with equations: (Triangles equations are planes equations) #NOT_SURE_ABOUT_THIS Nel disegno ho rappresentato due linee, è sbagliato, in quanto $ax+by+cz+d$ in uno spazio 3D rappresenta un piano e non una linea, per ottenere una linea in uno spazio 3D è necessario intersecare due piani.

We can define being in an object if we are inside the bounding box, then we can say that we are “touching” that object.

→ We are in the bounding box if our current position $<x,y,z>$ respects all the inequalities:

$$a_{i}x+b_{i}y+c_{i}z+d\le 0\forall i$$

(this is not entirely true, for just touch it should be $=0$, and for penetration $<0$ but having it exactly equal to 0 is impossible).

The touching simulation and prevision is really good if the mesh has a lot of points (better approximation), but more points also mean more delay.