New Geometric Continuity Solution of Parametric Surfaces
Vaclav Skala
TL;DR
This paper introduces a new mathematical approach for computing geometric continuity in parametric bi-cubic patches, simplifying the process and accommodating various corner valencies, applicable to Hermite, Bézier, and B-Spline patches.
Contribution
It provides a novel reformulation method for geometric continuity that simplifies calculations and is versatile across different patch types and corner valencies.
Findings
Simplifies geometric continuity computation for bi-cubic patches.
Applicable to Hermite, Bézier, and B-Spline patches.
Handles cases with varying corner valencies.
Abstract
This paper presents a new approach to computation of geometric continuity for parametric bi-cubic patches, based on a simple mathematical reformulation which leads to simple additional conditions to be applied in the patching computation. The paper presents an Hermite formulation of a bicubic parametric patch, but reformulations can be made also for B\'ezier and B-Spline patches as well. The presented approach is convenient for the cases when valencies of corners are different from the value 4, in general.
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