Function approximation using a centered cubic packing with tetragonal disphenoid extraction

摘要

The invention provides approximation of the value of a function of three variables. The invention embraces three processes: function domain packing, polyhedron extraction, and volumetric interpolation. The processes are applied to a mathematical function to calculate an approximation for the function range output value at a point which has been arbitrarily selected from the input domain of the function. Function domain packing utilizes two interlocked domain subdivisions. A first subdivision and a second subdivision each divide the domain space into rectangular solids. Each subdivision is accomplished by means of a plurality of planes of constant value corresponding to each of the input dimensions. After a function domain has been so subdivided, a tetrahedral volume is extracted from the fraction domain space. This tetrahedral volume is defined by two points from the first subdivision and two points from the second subdivision. The third process of the invention is a function approximation method using volumetric interpolation. If the fraction domain is subdivided according to the present invention, a continuous approximation of function range output values will result. The volumetric interpolation process commences by subdividing the extracted tetrahedron into four sub-tetrahedra. The subdivision is implemented by drawing lines from each of the vertices of the extracted tetrahedron to the target evaluation point to form four sub-tetrahedra.