Self-intersecting (ConceptAttribute, 4)

From Hi.gher. Space

If a shape is self-intersecting, it has the property that not every point in it is uniquely representable by its Cartesian coordinates relative to the shape's bounding space. There are several problems with self-intersecting shapes. A self-intersecting shape can however be made concave and appear the same to a hypothetical observer, while remedying these problems.

Problems with self-intersecting shapes

Self-intersecting shapes do not technically have an "inside" and an "outside". There are two main effects of this:

  • Computer programs will not correctly render a self-intersecting shape, unless they have been specifically programmed to correct such shapes. Most programs are however programmed to recognise and correct these shapes, so the following effects are not often seen.
    • In a 3D render, some parts of the shape will not appear, as the normals will point away from the camera.
    • A test for whether a point lies inside or outside the shape will return very erroneous results, and any attempt to shade the "inside" of the shape will look strange.
  • The hypervolume calculated from a self-intersecting shape will usually, but not always, be incorrect, often zero or negative.