Math problem with linear transformations

[SpaceDude]

I have a math problem to do with linear transformations.

Suppose I have a plane defined by a point, P, which lies on the plane and the plane's normal, N.

And I have a linear transformation defined by a 3x3 matrix. The question is, how can I apply this linear transformation to the plane? I can apply the linear transformation to the point P simply by multiplication but I can't do the same with the Normal because it won't give me what I want.

One solution I thought of is to pick 3 points lying on the plane, apply linear transformations to these 3 points and calculate the new plane normal by cross product. But there must be a more direct way, I just can't figure it out . Any help would be greatly appreciated.

[Mikachu]

I think the best would be to only apply the rotational part of your linear transformation to the plane's normal. Translations and scaling shouldn't affect a normal.

[SpaceDude]

I think the best would be to only apply the rotational part of your linear transformation to the plane's normal. Translations and scaling shouldn't affect a normal.

Yes but how? I've used polar decomposition in the past but it's very complicated and I'm not sure it would work in this case anyway.

[Kojack]

Try applying the matrix to the point on the plane, and the transpose of the inverse of the matrix to the normal. Like in this article: http://www.unknownroad.com/rtfm/graphic ... rmals.html
I haven't tried it, but looks like what you'd want (the article was for 4x4, but should still work).

[SpaceDude]

Try applying the matrix to the point on the plane, and the transpose of the inverse of the matrix to the normal. Like in this article: http://www.unknownroad.com/rtfm/graphic ... rmals.html
I haven't tried it, but looks like what you'd want (the article was for 4x4, but should still work).

Great thanks! just what I need with a good explanation. I owe you one.