Discussion:
Project/Map a triangle into plane at origin
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canjiang ren
2012-08-29 08:20:04 UTC
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Hello, i was wondering given a triangle face in 3D space, defined by three corners, for example:
v0(x0, y0, z0), v1(x1, y1, z1), v2(x2, y2, z2).

Find a triangle at plane z = 0, the first corner is (0, 0, 0), have the same shape (same edge length and corner angles) with the triangle in 3D space, how to do that ?

Thank you.
g***@hs-emden-leer.de
2012-08-29 16:48:19 UTC
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Post by canjiang ren
v0(x0, y0, z0), v1(x1, y1, z1), v2(x2, y2, z2).
Find a triangle at plane z = 0, the first corner is (0, 0, 0), have the same shape (same edge length and corner angles) with the triangle in 3D space, how to do that ?
Thank you.
There is one degree of freedom left. You may align edge 0-1 with the
x-axis, for instance. Then apply the Gram-Schmidt orthogonalization:
http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process

More information on request.

Best regards --Gernot Hoffmann

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