Generalized Coons Surface

The generalized Coons surface (shown in the middle) is defined by four rectangular surface patches. By changing the shape of the constituents, the shape of the resulting surface will change as well, even if the boundary lines are fixed. This case can be illustrated by changing the bump on the patch in the front.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The classical Coons surface is generated by its four boundary curves. Instead of four curves, four surface patches are the input data of this generalized Coons surface. The four patches are defined on the same parameter domain, and one boundary curve of each forms a side of a curvilinear rectangle. The resulting surface interpolates these boundary curves, and its shape is influenced also by the shapes of the constituent parts. This surface can be applied for filling holes in a composite surface, where not only the hole but also the surrounding surfaces are considered. The construction presented ensures only a continuous connection of the generated surface to the constituent parts along their common boundary curves.
M. Szilvasi-Nagy, P. T. Vendel, and H. Stachel, Filling of Gaps by Convex Combination of Surfaces under Boundary Constraints," KoG, Information Journal of Croatian Society of Constructive Geometry and Computer Graphics, 6, 2002 pp. 41–48.
M. Szilvasi-Nagy and I. Szabó, "Generalization of Coons' Construction," Computers & Graphics, 30, 2006 pp. 588–597.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+