How to scale rotated matrix in a new coordinate?
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Hello All: I have rotated foil data (each point has x,y coordinate) and I want to scale the foil after the rotation. In other words, I want to apply the scaling factor in different coordinate ( say the new coordinate is rotated 15 deg).
Appreciate your suggestions
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Jan
2017년 12월 18일
The question is not clear. You can rotate, translate, sheer and scale the coordinate systems. Scaling means to multiply the coordinates, so this seems to be trivial. Maybe it would help if you show us an example of the inputs and wanted outputs.
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Jan
2017년 12월 18일
Your question is still vague, so I can post a vague answer only:
If you have a set of points, and want to scale the values "along a direction", rotate the points such, that the direction vector point to the x axis. Then divide the x component of the coordinates and rotate the point back. You can express this as 3 matrices:
T = Rot(alpha) * Scale * Rot(-alpha) =
= [cos(alpha) -sin(alpha); sin(alpha) cos(alpha)] * ...
[0.5, 0; 0, 1] * ...
[cos(alpha) sin(alpha); -sin(alpha) cos(alpha)]
You can multiply this to get the matrix, which scales the points in the direction vector, which includes the signed angle alpha with the x axis.
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