Folks,
would this topic be suitable for some corner of Sage ?
It would need applets / at least wireframe pictures to liven it up
but I'd need examples / handholding for that. Please let me know.
Thanks,
cheers
4-triangle roof for interpolation and least squares
Abstract:
Interpolation or blending in triangles, and triangular meshes,
are both well-known in math for graphics.
This note introduces these topics at an elementary level,
using this split of one triangle into 4:
C
/ \
/ \ xA + yB + cZ, x+y+z = 1
.-----. 1 0 0 is A,
/ \ / \ x >= 1/2 is the lower left triangle,
/ \ / \ x y z all <= 1/2 is the middle triangle
A-----.-----B
Fold the outer small triangles along the 3 seams, to make a 4-triangle
"roof";
this can fit a round surface better than a single plane.
Keywords: interpolation, piecewise-linear, triangle, mesh, Python
Contents:
1. blending in a triangle
2. splitting a triangle / a cube into 4 pieces
3. interpolation with 4 triangles
4. roof4 least squares
... 3-page note w snippets of Python
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