## Moving objects

We now consider dynamic environments.

To efficiently update the radiosity computed, we must only consider form factors affected by the moving objects.

For example, when the lower triangle moves, the form factor between the two upper triangle does not have to be recomputed.

Animation (56 Ko)

When a point is moved in the scene, its dual line moves too.

If an object moves in a scene, its associated dual lines will be modified.

First, even if the complex is not topologically modified, some form factors must be numerically recomputed.

Animation (95 Ko)

And when three points becom aligned, there is a change in the topology of the complex. A face is created or removed, and the corresponding form factor must be created or deleted.

Here we can see the dual lines of the points of the scene.

 scene dual space

 scene dual space

 scene dual space

Here we see the two vertices of the complex we will consider.

 scene dual space

Consider a direction. We show the corresponding section of the complex.

the left segment is in front of the complex on the green face.

 scene dual space

and the right one is behind on the red face.

 scene dual space

Now we move the object and its associated dual line.

Animation (176 Ko) or better version (575 Ko)

a new face is created while two edges of polygons become mutually visible.

The incremental update of the complex is not yet implemented, but we show here a simulation of a dynamic scene where the complex is recomputed from scratch for each frame.

The white square is a light, and the red rectangle will move.

the 2D scene will be shown in a pseudo-3D with illumination shown on walls.

We can see the complex associated with the scene. But all the faces are not represented.

The faces corresponding to the big square are transparent.

We can see the dual lines associated to the objects.

The faces in red correspond to form factor between the red rectangle and another object, and the yellow ones are those where the red rectangle hides objects.

Animation (262 Ko)

Let's zoom in.

We can see a face corresponding to the form factor between the red rectangle and the light source.

It is going to disappear while the rectangle is moving to the umbra.

Animation (300 Ko)

Here the rectangle stops to cause umbra on the back wall. The face is no longer considered.

Animation (900 Ko)