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Oct
8
accepted Volume of a triangular prism with non parallel bases
Aug
21
awarded  Tumbleweed
Aug
14
asked Constrained optimization using a cutting plane on a tetrahedron
Jul
2
awarded  Curious
Jun
12
accepted Quaternion exponential map, rotations and interpolation
Jun
12
comment Quaternion exponential map, rotations and interpolation
Thanks for the info.. I still have some difficulties picturing how these computations relate to the equations on the question. Is the $\mathfrak{q}_{rotationInduction}$ stored in the tangent plane? It doesn't make sense to do it like that too much..
May
13
awarded  Teacher
Oct
28
answered Volume of a triangular prism with non parallel bases
Oct
28
comment Volume of a triangular prism with non parallel bases
$\lambda_i$ are not necessarily equal for $i=\overline{1,3}$ - I guess that might not work as desired.
Oct
28
asked Volume of a triangular prism with non parallel bases
Oct
25
revised Surface integral for a scalar function defined on a discrete surface
corrected surface integral to double integral expression
Oct
23
awarded  Promoter
Oct
19
revised Surface integral for a scalar function defined on a discrete surface
added 1694 characters in body
Oct
18
comment Surface integral for a scalar function defined on a discrete surface
@Evgeny, I agree with your observation, my bad for not clarifying. the scenario. you should consider each point to have a convex combination of the energies stored. at the vertices of the triangle it lies in.
Oct
18
revised Surface integral for a scalar function defined on a discrete surface
added 354 characters in body
Oct
18
comment Surface integral for a scalar function defined on a discrete surface
I'll edit the question to reflect the need of adapting a continuous concept to a discrete context
Oct
18
comment Surface integral for a scalar function defined on a discrete surface
@Evgeny, if you compute the surface integral of a function over something that lacks the dimension of a surface element, I guess common sense (not only measure theory) tells us that the integral is zero.. but this is discrete differential geometry, and the issue is adapting a continuous concept as faithfully to the discrete context. I'm not looking for abstract caveats coming from Measure Theory because, well, I will have to use a computer to perform practical calculations and measurements. I can't just "measure" abstract sets using digital tools :(..
Oct
18
comment Surface integral for a scalar function defined on a discrete surface
@studiosus: for an edge, you could always LERP the $k_1^2+k_2^2$ values of its endpoints. The same goes for a point on a triangular face: interpolate its value from the vertices.
Oct
18
comment Surface integral for a scalar function defined on a discrete surface
You can associate them to any point on the polyhedral surface, but if you want to qualitatively asses the importance of a vertex, then you must see what happens in the vicinity of that vertex, i.e. all neighbouring 1-ring incident triangles to it.
Oct
18
comment Surface integral for a scalar function defined on a discrete surface
Actually, any kind of approximation would be good for starters as precision isn't the biggest problem. I wonder if I could consider each triangle to lie in the XOY plane and define a function $f$ over this triangle. $f$ should interpolate the curvature values at the triangle's vertices. Then computing the area under the triangle $(x,y, f(x,y))$ could be the answer, but I have a feeling this is alchemy.