Improved shape for multi-surface blends

For many design applications, where multiple primary surface pieces meet, the distribution of curvature is more important than formally achieving exact curvature continuity. For parametric spline surfaces, when constructing a multi-sided surface cap, we demonstrate a strong link between the uniform variation of the re-parameterization between (boundary) data of the joining pieces and a desirable distribution of curvature. We illustrate this interdependence between parameterization quality and surface quality by developing a G bi-quintic surface cap consisting of n pieces that smoothly fills holes in a piecewise bi-cubic tensor-product spline complex. These bi-5 surface caps have arguably better shape than higher-degree, formally curvature continuous alternatives.