Timeline for How to make a Spherical Cow?
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 31, 2016 at 0:58 | comment | added | andre314 | @Clément Yes, surjective, sorry. A bijective mapping is surely harder to implement. | |
| Aug 31, 2016 at 0:36 | comment | added | Clément | In any case, I think you spotted the issue that I tried to express: namely, that the mapping isn't bijective. | |
| Aug 31, 2016 at 0:35 | comment | added | Clément | @andre: Thanks. Did you mean surjective in your last comment? | |
| Aug 30, 2016 at 23:05 | comment | added | andre314 | @Clément It is nevertheless true that there is a folding effect, ie the mapping of the cow towards the final sphere is injective, not bijective. | |
| Aug 30, 2016 at 22:57 | comment | added | andre314 | @Clément : I have added 3 images with a constant plot range. It show clearly that all the parts of the cow are in expansion. One see also the the volume get largely bigger. | |
| Aug 30, 2016 at 22:54 | history | edited | andre314 | CC BY-SA 3.0 | added 179 characters in body |
| Aug 30, 2016 at 22:44 | comment | added | andre314 | @Clément In fact, the head and the legs expand. What is happening is that Mathematica is in a automatic plot-range mode : during the spreading, the range increase with constant image size, so the scale is reduced. If you have Mathematica, just fix the plot range and it will be clear. | |
| Aug 30, 2016 at 22:30 | comment | added | Clément | This looks wrong; the example on Wikipedia shows that the cow and the sphere have essentially the same topology, but your transformation doesn't do this: the head and the legs should expand, not contract. Essentially, your transformation just folds the legs and the head onto the body. Isn't there a way to create an "inflating" effect. in which you get a sphere as the limit of smoothing the surface? | |
| Aug 30, 2016 at 15:20 | comment | added | Arek' Fu | I joined mathematica.SE just to be able to upvote this question and this answer. | |
| Aug 30, 2016 at 13:39 | comment | added | Sumit | you can do it by integrating over the region. Integrate[1, {x, y, z} ∈ ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]]. I added it in my question as an edit. | |
| Aug 29, 2016 at 16:25 | comment | added | andre314 | @user3490 It is clear that these transformations don't conserve the volume. The final sphere is always the unity sphere. It would be hard to conserve the volume because it is hard to estimate the volume of the cow (which is specified as a surface, not a volume). I would be very interested by a way to estimate the volume enclosed in a surface. | |
| Aug 29, 2016 at 15:51 | comment | added | user3490 | What would this look like if you wanted to conserve volume? I get the impression that the final sphere is a bit bigger than the original cow. | |
| Aug 29, 2016 at 15:14 | comment | added | Tim S. | This is math and physics as their best. :) | |
| Aug 29, 2016 at 14:03 | vote | accept | Sumit | ||
| Aug 29, 2016 at 14:03 | comment | added | Sumit | Neat and simple mapping to a sphere - I like it :) | |
| Aug 29, 2016 at 13:59 | history | edited | andre314 | CC BY-SA 3.0 | deleted 17 characters in body |
| Aug 29, 2016 at 13:47 | history | answered | andre314 | CC BY-SA 3.0 |