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May 21st, 2015, 08:51 PM   #1
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How can I find Orthogonal Projection of a non-linear surface?

Suppose I want to find the orthogonal projection of (x1,x2,y1,y2) such that x1=x2, y1=y2. I have to calculate the A matrix whose columns are the basis vectors of given subspace. I choose A=[v1;v2] as basis vector combination, where v1=[1 0 1 0] and v2=[0 1 0 1]. Then I calculated the Projection matrix as P=A*inverse(transpose(A)*A)transpose(A).

Now if I want to find the Projection matrix of (x1,x2,x3,y1,y2,y3,z1,z2,z3) such that

(x2−x1)^2+(y2−y1)^2+(z2−z1)^2=64

(x2−x3)^2+(y2−y3)^2+(z2−z3)^2=36

(x3−x1)^2+(y3−y2)^2+(z3−z1)^2=100

Do I have to find the basis vector for calculating Projection matrix? If yes, how?

Is there any other way to find its Projection matrix (P)?

Last edited by Tehseen; May 21st, 2015 at 08:57 PM.
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