Coon's Patch Examples

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Coon's Patch Examples

Posted: Hakan Tiftikci 87 Product: Maple 13

December 16 2010

Coon's patch defines a patch from 4 curves forming a chain. 4-examples to Coon's patch are given following worksheet. Boundary curves in the examples are constructed by parametric cubic curves (in Bezier and Hermite form). First example is in 3D and comparable to parametric bicubic surface. Rest of examples are in 2D (abstract surface) which can be described shortly as:

2D Example#1: 4 circular-arc like curves are combined by Coon's patch to form a circular-like region
2D Example#2: vertices of a square are assigned to rotating tangents
2D Example#3: boundaries corresponding to nozzle like geometry

Introduction

Coon's patch defines a surface by 4 curve segments that are connected in end-to-end to form curve chain. For left, right, bottom, top boundary curves denoted by convex sum (blending) defines two lofting surfaces from to and to .

First patch interpolates and second patch interpolates Adding two patches

and evaluating at boundaries yields

this shows that left boundary curve of , which is sought to be has extra term that can be modelled by Expanding yields

from symmetry, there is no need to perform same procedure for other direction (~ bottom,right). The final form of patch to interpolate all four curves is