Presented in this thesis are improved $VC^1$ conditions between rectangular patchs and two methods of interpolating over unevenly spaced point data with rectangular arrangement.
Ferguson composite surface method and FMILL In APT-III, which are commonly used in CAGD, have a critical drawback that distortion may occur in the fitted surface when input point data are unevenly spaced. This results from neglecting the effect of chord lengths of unevenly spaced point data when determning the length of tangent vectors of mesh curves. This problem is overcomed in this thesis by considering chord lengths and by improving the existing $VC^1$ conditions.
Applying each of the improved $VC^1$ conditions which provide enough degree of freedom to make $VC^1$ correction when mesh curves are fixed, two different approachs of fitting composite surfaces are proposed. First, cubic Bezier $VC^1$ composite surface method; second, quintic Bezier $VC^1$ composite surface method. Both of the procedures consist of three steps: 1) Construct mesh curves applying chord length spline fitting, 2) Estimate inner control points (construct initial patchs), 3) Make $VC^1$ corrections by applying coresponding $VC^1$ condion.
