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| code logs -> 2021 -> Thu, 08 Jul 2021 | < code.20210707.log - code.20210709.log > |
| --- Log opened Thu Jul 08 00:00:24 2021 |
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| 18:13 | | * Vornicus pokes vaguely at excel |
| 18:17 | <~Vornicus> | Okay so: I'm doing discrete differential geometry; one of the things I need is something called the discrete wedge product, of which there are several forms, and I'm working on making excel calculate some of them. |
| 18:22 | <~Vornicus> | The first one that's bugging me is the 1,0 form, where we take data on each edge and multiply it by the average of (a different kind of) data on the vertices at the ends of that edge. So if I have f(AB) = 3, g(A) = 2, g(B) = 10, I have (f wedge_0,0 g)(A) = 3 * (2+10)/2 = 3 * 6 = 18. |
| 18:27 | <~Vornicus> | so: I have an incidence matrix, which tells me what vertices are associated with an edge, and the values for f on the edges and g on the vertices, how do I calculate f wedge_1,0 g |
| 18:27 | <~Vornicus> | --correction on the formula in the second message, (f wedge_1,0 g)(AB) = ... |
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| 18:44 | <~Vornicus> | okay it's mmult(vertex_edges, g) * f / 2, looks like |
| 18:48 | <~Vornicus> | 2,0 is the same deal but it's face vs vertices, just divide by 3 since this is a triangle mesh |
| 19:08 | <~Vornicus> | finally, 1,1 which is properly complicated: for each face, pair up sequential edges A, B, add h(A)*i(B) - i(A)*h(B) |
| 19:10 | <@celticminstrel> | Why the heck is Object.values turning a function into a string…? |
| 19:25 | <~Vornicus> | --this is a 3-dimensional thing, really - edges and face together, so I can't quite fit it into a matrix trick |
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| 21:37 | <~Vornicus> | well... I got there |
| 21:37 | <~Vornicus> | sort of |
| 21:39 | <~Vornicus> | made the mmult(h, transpose(i)), made a list of edge indices for each face, used offset six times to pick out the correct cells |
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| --- Log closed Fri Jul 09 00:00:26 2021 |
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| code logs -> 2021 -> Thu, 08 Jul 2021 | < code.20210707.log - code.20210709.log > |
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