D2 Shape Distribution

Robert Osada, Thomas Funkhouser, Bernard Chazelle, and David Dobkin released a paper in 2002 detailing a method for measuring the similarity between 3D shapes.

The paper proposes creating probability distributions from shapes which might be easily compared with metrics like Earth Mover’s Distance. Such probability distributions promise to capture a shape’s signature. Figures like a square

• The D2 shape function generates a distribution of distances between randomly sampled points from a 3D model (or 2D model!).
• The D3 function generates a distribution of the square root of the area of sampled triangles
• The D4 function similarly operates on the cube root of volumes of sampled tetrahedrons.

Some basic characteristics of objects like straight lines, squares, and crosses can be studied for simple line drawings.