Transformation of 4D Geometries in Display

Tutorial on usage of cameras to transform geometries registered in a display. This applet shows a 4d cube in the 3-sphere. The cube is projected either parallel by removing the fourth coordinate, or by stereographic projection from the projection center (1,0,0,0).

Inside the camera menu enable transformation of the currently selected geometry. Depending on the chosen space form the geometry is transformed in its own coordinate system. E.g. translation in S3 moves the geometry along a great arc in S3. As an exception, also in R3 and R4 the geometry is transformed individually but with respect to the global coordinate system of the camera. This keeps the space ball like transformation of geometries as in camera mode.

In a scene with different models, the currently selected model is transformed.

View source code:
PaTransform.java of applet,
PjTransform.java of project,
PjTransform_IP.java of project panel.