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Bilinear interpolation: Difference between revisions
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Let n mean shape function, C mean constants, i mean interpolant, and the three digits meaning dimensionality, number of corners, and (in base 36) the number of nodes we construct various linear and quadratic interpolants in 1, 2, and 3 dimensions as
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Note 'Some elemental information'
Node order
1D:
0 2 1
2D:
2 7 3
5 8 6 Node 8 at origin, Node 3 at (1,1)
0 4 1
Names for shape functions and constants:
n249: n means shape function, 2 dimensions, 4 corners (quadrilateral), 9 nodes
C244: C constants for 2 dimensions, 4 corners (quadrilateral), 4 nodes
3D
At z = _1 z = 1 z = 0
2 b 3 6 j 7 e o f
9 k a h p i m q n
0 8 1 4 g 5 c l d
)
mp =: ($: |:) : (+/ .*) NB. A Atranspose : matrix product A B
identity =: =@:i. NB. generate identity matrix
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