Graphics Library ‘4DGL’ for Projection of 4D Shapes into a 3D Space

The fourth axis in the 4D space can be associated with time, weight, or something other than length. It is known that a 4D shapes can be transformed into a 3D shapes by 4D to 3D projection. This transformation is purely mathematical, and it is possible to make a model of 3D shape which is corresponding to projection of 4D shapes by hand based on the calculated results. If 3D shape projected from 4D shape is expressed using CG, it becomes possible to create more dynamic expressions, such as the animation of rotating 4D shapes on the plane that includes the fourth axis. However, the 4D to 3D projection necessary to express 4D shapes is realized only by computer program developed by each researcher. And 4D to 3D projection is still far from the case of expressing 3D shapes on a 2D plane using a 3D graphics library. The objective of this research is to develop a generic 4D graphics library, 4DGL, and spread the use of 4D graphics in the design field. This library is implemented on POV-Ray, a free 3D computer graphics tool, and can describe 4D shapes themselves and manipulation of the 4D shapes using similar description method. When projecting a 4D shape into 3D space, orthographic, oblique, and perspective projections can be selected.