Timeline for Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
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| Sep 26 at 17:21 | comment | added | Romogi | @ybeltukov If you are okay, I would like to name it the tree-trunk surface when I refer to it unless if you want to give it a different name or name it after yourself. | |
| Sep 26 at 13:38 | comment | added | ybeltukov | @TegLouis I don't think so. For circular boundary loops it becomes a catenoid. | |
| Sep 23 at 2:46 | comment | added | Romogi | @ybeltukov What is the name of the surface in the second image? Does it have a common name? | |
| Dec 3, 2023 at 22:08 | comment | added | Ulrich Neumann | I am aware that I am a few years behind finding this interesting answer. I don't understand the syntax of the minimization FindArgMin[.., {vars, vc[[pts]]}, ...] . From documentation I would expect FindArgMin[..,Transpose[ {vars, vc[[pts]]}], ...] with paired variables and starting values! Any idea or explanation? Thanks! | |
| Oct 23, 2017 at 1:52 | comment | added | Greg Hurst | This is great! Instead of manually computing vertex normals with your function normals[], you could use the "SmoothShading" plot theme: MeshRegion[v, cells, MeshCellStyle -> {2 -> FaceForm[Red, Blue]}, PlotTheme -> "SmoothShading"] | |
| Nov 19, 2015 at 2:13 | history | edited | ybeltukov | CC BY-SA 3.0 | added 150 characters in body |
| May 26, 2015 at 23:32 | comment | added | J. M.'s missing motivation | I know, that's why I linked you to it; it seems Max's weighted average normal might help here. | |
| May 26, 2015 at 20:02 | comment | added | ybeltukov | @Guesswhoitis. Thank you for the reference. I wrote my normals function as simple as possible by averaging vector areas of neighbour triangles. However it produces visible defects on the Costa's surface. | |
| May 26, 2015 at 1:35 | comment | added | J. M.'s missing motivation | With respect to generating normals: have you already seen this? | |
| Jan 23, 2015 at 17:16 | comment | added | ybeltukov | @halirutan I added a link to one of the articles on topic. Googling "minimal surface method" gives a lot of references. | |
| Jan 23, 2015 at 17:10 | history | edited | ybeltukov | CC BY-SA 3.0 | added 245 characters in body |
| Jan 23, 2015 at 17:06 | comment | added | ybeltukov | @Rahul I update my post and include the visualization with VertexNormal and an example with another topology. | |
| Jan 23, 2015 at 17:03 | history | edited | ybeltukov | CC BY-SA 3.0 | added 3290 characters in body |
| Jan 23, 2015 at 9:10 | vote | accept | CommunityBot | moved from User.Id=484 by developer User.Id=27403 | |
| May 19, 2018 at 11:45 | |||||
| Jan 23, 2015 at 1:11 | comment | added | halirutan | @Narasimham This was really only an example. I'm interested what one could do in the general case with not too evil initial curves. If you can share knowledge about this, I would be happy to hear it. | |
| Jan 23, 2015 at 0:58 | comment | added | Narasimham | @halirutan: This surface is like the monkey saddle where there are now four humps/falls instead of three.The surface is Re or Im part of (x + I y)^4. | |
| Jan 22, 2015 at 8:07 | history | edited | user484 | CC BY-SA 3.0 | fixed some errors |
| Jan 22, 2015 at 4:53 | comment | added | user484 | Fantastic! I for one am perfectly happy to provide an initial surface. @halirutan: For your curve one could simply form a "cone" by connecting all the points to the origin. I think that works for arbitrary curves, but I don't know if self-intersections will cause the result to get stuck in local minima. | |
| Jan 22, 2015 at 2:54 | comment | added | halirutan | In your answer you have an initial guess for the surface which is the parametric plot. When I understand the question correctly, then the starting point is only a curve. Do you know a solution when we have for instance this curve, let's assume not even analytically but as coordinate list. Do you have an idea for this? Additionally, it would be awesome if you could provide some links to algorithms/literature. | |
| Jan 22, 2015 at 2:15 | history | answered | ybeltukov | CC BY-SA 3.0 |