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Re: Mirror Point Across A Given Plane
Posted:
Aug 4, 2014 6:53 PM


"Connor Pyles" <connor.owen.pyles@gmail.com> wrote in message <lrof52$4og$1@newscl01ah.mathworks.com>... > Say I have a plane given by a matrix M containing 3 points, and a fourth point like this: > > M = [P1x P1y P1z ; > P2x P2y P2z ; > P3x P3y P3z ]; > > P4 = [P4x P4y P4z]; > > What is the easiest way to mirror the fourth point across the plane? > > Thanks, > Connor
A plane is defined by the equation
dot(X  X0,N) == 0
where X0 is any point in the plane, and N is the normal vector to that plane. Here
P1=M(1,:)
will suffice. You can get the normal vector from a cross product.
N = cross(P1  P3,P2  P3);
Normalize to have unit norm to make things easy...
N = N/norm(N);
Finally, create the new point as
P5 = P4 + 2*dot(P1  P4, N)*N
John



