Research on the describing method of 3D product shape based on Fourier operator

The 3D product shape innovation design has possessed a very important ability to develop more pleasurable products, in which Shape Descriptor is one of key technologies. The describing method of 3D product shape based on Fourier operator is presented, which includes the following four steps. The first is data preparation, which can obtain the geometry and topological relations of 3D product shape. The second is spherical parameterization, which creates a continuous and uniform mapping from the object surface to the surface of a unit sphere. The third is to compute spherical harmonics, which expands the 3D surface data into a complete set of spherical harmonic basis functions, so the 3D product shape is expressed by the Fourier operators (harmonics). The fourth is to find an ideal number of harmonics, which represents the main shape feature of product shape and eliminates the noise. The mouse shape is chosen to do experimental study. The result appears that a few first harmonics are suitable for representing 3D product shape and shows that the describing method is robust, compact and simple, which is promising to apply in the product shape innovation design and the 3D shape retrieval.