Near-stability of a quasi-minimal surface indicated through a tested curvature algorithm

作者：Ahmad Daud^*; Masud Bilal

来源：Computers & Mathematics with Applications, 2015, 69(10): 1242-1262.

DOI：10.1016/j.camwa.2015.03.015

• Curvature algorithm
• Bilinear interpolation
• Variational improvement
• Minimal surfaces

We decrease the rms mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately chosen non-minimal surface, we achieve up to 65 percent of the total possible decrease in area. When we apply our algorithm to a bilinear interpolant bounded by four non-coplanar straight lines, the area decrease by the same algorithm is only 0.116179 percent of the original value. This relative stability suggests that the bilinear interpolant is already a quasi-minimal surface.

• 出版日期2015-5