A shape is a closed and simply connected subset of ''RR^n''.
A shape ''S'' is called convex, if it holds that
''A, B in S => forall t in [0, 1]: A + t(B - A) in S''.
A shape that is not convex is called concave. Shapes overlap if their intersection is non-empty.
Pastel implements various shapes, of which most are convex. The reason for this is that overlap testing between convex shapes is easier than between concave shapes.
All shapes overload the operators +=, +, -=, and - to translate by a vector and the operators =, , /=, and / to scale by a real number. The scaling is always defined for a given shape so that it commutes with translation.
Geometric Tools for Computer Graphics, Philip J. Schneider, David Eberly, 2003.
| Axis-aligned box | Plane |
| Axis-aligned plane | Polygon |
| Capsule | Ray |
| Ellipsoid | Simplex |
| Flat | Sphere |
| Line | Sphere shape |
| Line segment | Triangle |
| Oriented box | |