| (1) | From cube to sphere |
| (2) | From torus to tube |
| |
| (W / Mouse wheel) | Zoom in |
| (S / Mouse wheel) | Zoom out |
| (SPACE) | Stop/Play |
| (RIGHT) | Step forward |
| (LEFT) | Step backward |
| (UP) | Faster |
| (DOWN) | Slower |
The term homeomorphism describes the topological transformation between two spaces as a function. In the context of
computergraphics and animation, those spaces are two or three dimensional objects and the function is a continuous
deformation of one object into another. This transformation may contain stretching and bending, but not cutting
or drilling holes - the topology may not be changed. It is also not alowed to change the dimension of an object
(e.g. from sphere to circle).
If one object can be transformed into another by a homeomorphism, those objects are called homeomorphic.
Homeomorphic can have very different looking shapes but are from a topological standpoint the same.
For example, a coffe mug is homeomorphic to a donut (torus). One just need to pull up the ground of the mug to
form a cylinder and squeeze it into the handle.