The `Linz' method is characterized by the simultaneous approximation of:
The method produces an approximate implicit representation of the form f(x, y,z) = ∑ (Ci Bi(x, y, z)) with basis Bi(x, y, z) and a certain coefficients Ci. This method is fully general, i.e., it can be applied to any space of functions. For practical applications, however, fast evaluation of basis functions is important. For this reason we implemented the algorithm for using only polynomial function, namely, Tetrahedral Bèzier polynomial, Tensor product Bèzier polynomial, and Tensor product B-splines piecewise polynomials. We implemented a prototype which is used as a stand alone version for experimental purposes. It can be run from a Linux shell using the parameters:
<file> Offset OffsetDistance Basis Degree Cellsize [nonstop] [debug]
The parameters have the following meaning: <file> the input file including the full patchOffset an integer switch whether to approximate an offset surface, set to be 0 (no offset) 1 (offset one side), 2 (offset double sides) OffsetDistance the offset distance in the case of offset surface.Basis an integer set to be 1 (Tensor product B-splines) , 2 (Tensor product Bèzier) or 3 (Tetrahedral Bèzier)Degree the degree of the basis[nonstop] an integer switch the user input from the keyboard during the running.[debug] an integer control the debug message: 0 no, 1 part, 2 full.
Published June 24, 2005