Described in this thesis is a procedure of sculptured surface interpolation based on the triangular surface method proposed by Farin. The main motivation was to investigate the possibility of applying the triangular surface method(TSM) in sculptured surface machining. Original TSMs have been developed in order to obtain smooth response surfaces by interpolating "scattered data" from engineering experiments.
The overall procedure consists of triangulation of input data, estimation of surface normal vectors, interpolation of the data points by using triangular Bezier patches, and generation of CL-data to machine the surface.
The original triangulation method is modified so that optimization is done in local 3-D space. Also a special triangulation method is deviced to handle "regular data" sets where data points are measured along measuring paths. In estimating interior normal vectors, weighting factors inversely propotional to the square of edge distance are found to be satisfactory. A new method of estimating normal vectors at boundary points is developed.
In the interpolation step, a local 3-D domain method is proposed to overcome the shortcomings of the non-parametric method. $VC^1$-condition is maintained by employing subdivision and degree elevation. Initial interpolants are quadratic Bezier patches. CL-data are generated by a contouring method based on subdivision.
The interpolation scheme found to need improvement to be used in sculptured surface machining. Some undulations and curvature variations were observed on the test surface of sphere.The program is written in Fortran77.
