Author: KermMartian
Posted: 09 Apr 2013 11:16:14 pm (GMT -5)
Tri is a matrix of row vectors defining a triangle. [x, y, z] are cartesian coordinates missing one of the coordinates. The desired output is [l1, l2, l3, x, y, z], where x, y, and z are all filled, and l1, l2, and l3 are the barycentric lambda coordinates.
Sample success matrix:
Code:
Sample failure matrix:
Code:
Notice that [0,0] = [2,0] and [0,1] = [2,1] (and because the z-axis span is the smallest, z will be the missing coordinate). This will make (tri[1,b]-tri[2,b])*(tri[0,a]-tri[2,a]) + (tri[2,a]-tri[1,a])*(tri[0,b]-tri[2,b]) of course be zero. And that will be true even if the triangle points get shuffled. What to do.
Edit: Unless I shuffle rows 1 and 2 in this case, I believe... That would give:
Code:
For which we get the det = (nonzero)*(nonzero) + (nonzero)*(nonzero). And I guess I can then just reshuffle the lambdas at the end.
Edit #2: Nope, although that makes the terms nonzero, it also makes the sum cancel out to zero. I should have expected it wasn't that easy.
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Posted: 09 Apr 2013 11:16:14 pm (GMT -5)
Tri is a matrix of row vectors defining a triangle. [x, y, z] are cartesian coordinates missing one of the coordinates. The desired output is [l1, l2, l3, x, y, z], where x, y, and z are all filled, and l1, l2, and l3 are the barycentric lambda coordinates.
Sample success matrix:
Code:
[[ 84.68746953 59.83120068 155.70715938]
[ 82.88576245 60.64850894 152.60306357]
[ 83.41658276 58.7063019 152.60306357]]Sample failure matrix:
Code:
[[ 49.42879067 88.10337266 56.30088594]
[ 57.97150024 83.39647856 56.89353193]
[ 49.42879067 88.10337266 56.89353193]]Notice that [0,0] = [2,0] and [0,1] = [2,1] (and because the z-axis span is the smallest, z will be the missing coordinate). This will make (tri[1,b]-tri[2,b])*(tri[0,a]-tri[2,a]) + (tri[2,a]-tri[1,a])*(tri[0,b]-tri[2,b]) of course be zero. And that will be true even if the triangle points get shuffled. What to do.
Edit: Unless I shuffle rows 1 and 2 in this case, I believe... That would give:
Code:
[[ 49.42879067 88.10337266 56.30088594]
[ 49.42879067 88.10337266 56.89353193]
[ 57.97150024 83.39647856 56.89353193]
]Edit #2: Nope, although that makes the terms nonzero, it also makes the sum cancel out to zero. I should have expected it wasn't that easy.
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