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18
revised The distribution of barycentric coordinates
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revised The distribution of barycentric coordinates
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Jul
27
comment uniform random point in triangle
But the generalization of your approach itself is here math.stackexchange.com/questions/563129/… .
Jul
27
comment uniform random point in triangle
One way to get random point inside of simplex $P = \{\mathbf{p}_i\}_{i = 1}^{d + 1}$ is to pick $\mathbf{c} = (c_1, c_2, ..., c_d, c_{d + 1}), c_i \sim U[0;1]$, then $\mathbf{c} \leftarrow -\log(\mathbf{c})$, then $c \leftarrow \displaystyle \frac{\mathbf{c}}{\sum \limits_{i = 1}^{d + 1} c_i}$, then random point is: $\displaystyle \sum \limits_{i = 1}^{d + 1}c_i \cdot \mathbf{p}_i$ (based on Dirichlet distribution and properties of affine transformations).
Jul
27
comment uniform random point in triangle
merico, I think it is wrong. We need spatial uniform distribution.
Jul
25
revised The distribution of barycentric coordinates
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Jul
25
revised The distribution of barycentric coordinates
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Jul
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revised The distribution of barycentric coordinates
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Jul
19
revised The distribution of barycentric coordinates
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Jul
19
revised The distribution of barycentric coordinates
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Jul
19
revised Random points inside a convex polytope
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Jul
18
revised The distribution of barycentric coordinates
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Jul
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revised The distribution of barycentric coordinates
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Jul
18
answered The distribution of barycentric coordinates
Jul
18
comment uniform random point in triangle
How to generalize it onto higher dimensions? What to do with arbitrary $n$-simplex?
Jul
18
comment Random points inside a convex polytope
OK, triangulation is obvious step. But what to do with individual simplixes? I think, that mapping of standard unit simplex to arbitrary simplex is the task close to normal transformations problem (every volume element suffers defformation, and inverse function of its spatial distribution is what I need, if I understand right).
Jul
18
revised Random points inside a convex polytope
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Jul
18
asked Random points inside a convex polytope
Jul
5
comment Number of integer solutions of $x^2 + y^2 = k$
Here is the right solution: press Help button
Jun
30
answered What are algorithms or approaches to find a convex hull on higher dimensions?