First, I quote the description of Wikipedia:
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary, a problem raised by Joseph-Louis Lagrange in 1760. However, it is named after Joseph Plateau who experimented with soap films. The problem is considered part of the calculus of variations. The existence and regularity problems are part of geometric measure theory.
In 1931, Jesse Douglas published an article "Solution of the problem of Plateau".
Douglas, Jesse (1931). "Solution of the problem of Plateau". Trans. Amer. Math. Soc. 33 (1): 263–321. doi:10.2307/1989472. JSTOR 1989472.
Referring to his paper, I realize his ideas by using C++ to find the minimal surface.
For the minimal surface, there is an analytical solution for a type of problems, which is the catenoid. https://en.wikipedia.org/wiki/Catenoid
So it's a good choice to valite my codes by a catenoid.
For more information, please read my report.
Catenoid:
Test1:
Before optimisation:
After optimisation:
Test1 area change:
Test2:
Before optimisation:
After optimisation:
Test2 area change:
