Perpustakaan Digital ITB

In A Generative Theory of Shape Michael Leyton presents an extremely rich and compelling theory with foundations in and applications to art and architecture, music, math, physics, psychology, computer science, mechanical design and manufacturing, and CAD. As is standard, shapes are viewed as originating from primitive shapes (e.g., circles, squares, cubes, cylinders, etc.), primitives themselves are ultimately defined from the fundamental building blocks (point, line, plane, etc.), and shapes are mathematically specified using group theory. What is different about Leyton’s theory is that the information necessary to generate a given shape is recoverable from the mathematical definition of the shape. This generative approach is in contrast to the standard Klein geometry, where a shape is defined as an invariant under specified group transformations. Leyton describes this standard approach as memoryless, since the shape’s generation is ignored rather than stored for later recovery. By contrast, his theory works by capturing the evolution of the shape from the building blocks, rather than merely specifying the end result. Leyton’s approach has the additional benefit of allowing for the complete mathematical specification of quite complex shapes.