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Apr
10
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Jan
3
comment Distance between a point and a m-dimensional space in n-dimensional space ($m<n$)
What do you mean by $x_1,\dots,x_n$ in the last formula?
Jan
2
comment Distance between a point and a m-dimensional space in n-dimensional space ($m<n$)
Last LHS should be the $G(v_1,\ldots,v_k)$ not $G(x_1,\ldots,x_k)$, isn't it?
Dec
20
comment Determinant: Alternative Definitions
@Freeze_S maybe). I am not sure what I want to say.
Dec
19
comment Determinant: Alternative Definitions
There is axiomatic definition, but it is not constructive.
Dec
13
comment Distance between a point and a m-dimensional space in n-dimensional space ($m<n$)
What to do if subspace is translated? Say, (m - 1)-dimensional subspace is defined by a set $S:|S| = m \leq n$ of its points?
Aug
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
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 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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revised The distribution of barycentric coordinates
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Jul
18
answered The distribution of barycentric coordinates