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 |
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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<lang J> |
<lang J> |
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Note 'Some elemental information' |
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Node order |
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1D: |
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0 2 1 |
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2D: |
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2 7 3 |
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5 8 6 Node 8 at origin, Node 3 at (1,1) |
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0 4 1 |
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Names for shape functions and constants: |
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n249: n means shape function, 2 dimensions, 4 corners (quadrilateral), 9 nodes |
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C244: C constants for 2 dimensions, 4 corners (quadrilateral), 4 nodes |
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3D |
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At z = _1 z = 1 z = 0 |
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2 b 3 6 j 7 e o f |
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9 k a h p i m q n |
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0 8 1 4 g 5 c l d |
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) |
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mp =: ($: |:) : (+/ .*) NB. A Atranspose : matrix product A B |
mp =: ($: |:) : (+/ .*) NB. A Atranspose : matrix product A B |
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identity =: =@:i. NB. generate identity matrix |
identity =: =@:i. NB. generate identity matrix |
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