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Lumalalelo

Matrix base-transformation

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Lumalalelo    134
hi everyone ! ok, to be honest this isn't something i need for a game, it's an important thing i need to understand for my upcoming linear algebra exam ^^; However i wasn't able to get the hang to it via my script or google. -------------------------------------------------------------------------------- the problem is i have a plane in the "point-direction"-form like: r = t1 * vector + t2 * vector2 r = (2 -1 1) + t1*(1 0 1) + t2* (1 1 1) I should make a matrix S via base-transformation so that i can reflect on this plane. (there is an excercise-part b) where i get 3 points that i should reflect with the help of the matrix S) but my question is only how i can construct this matrix S ? -------------------------------------------------------------------------------- i assume that the matrix is: 2 1 1 -1 0 1 1 1 1 but then i have a plane whose span-vectors aren't orthogonal... so how can i find the right base for this matrix ? thank you very much for your time ! Chris

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LilBudyWizer    491
You orthogonalize and normalize the matrix. All points in a plane can be referanced by a point in the plane and two vectors in the plane that are not parallel. P+a*X+b*Y, P is the point and (a,b) is the coordinates of the point given the basis X, Y. So M*V = v1*C1 + v2*C2 + v3*C3 = a*X + b*Y + 1*P. Three non-linear points in a plane gives a point and two vectors in the plane.

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