VARIABLE-RADIUS BLENDING BY CONSTRAINED SPINE GENERATION

Radius blends, very important in geometric and solid modeling, can be seen as the trimmed envelope of a rolling sphere or a sweeping circle with a constant or variable radius that centers on a spine curve and t ouches the surfaces to be blended along the linkage curves. Usually, i n variable-radius blending, the radius is difficult to specify, and th e spine curve is hard to trace. We propose several geometric constrain ts to specify the variable radius, which we then translate to a nonlin ear system to represent the spine curve exactly. This is finally trace d numerically in a high-dimensional space. We also propose a paradigm that implements the constraints while tracing along the spine curve in 3D space. We represent the result in parametric form.