Translation of a 3D plane

I have a set of 3D points out of which I have fitted a plane using Principal Component Analysis. Now, I want to generate/create a plane parallel to this one at a particular distance or passing through a point and find how these individual points project on that new plane.

Any help or input is appreciated.

The following code is an example.

randn('state',0);
X = mvnrnd([0 0 0], [1 .2 .7; .2 1 0; .7 0 1],50);
plot3(X(:,1),X(:,2),X(:,3),'bo');
grid on;
maxlim = max(abs(X(:)))*1.1;
axis([-maxlim maxlim -maxlim maxlim -maxlim maxlim]);
axis square
view(-23.5,5);

[coeff,score,roots] = princomp(X);
basis = coeff(:,1:2)
normal = coeff(:,3)

n,p] = size(X);
meanX = mean(X,1);
Xfit = repmat(meanX,n,1) + score(:,1:2)*coeff(:,1:2)';
residuals = X - Xfit;

error = abs((X - repmat(meanX,n,1))*normal);
sse = sum(error.^2)

[xgrid,ygrid] = meshgrid(linspace(min(X(:,1)),max(X(:,1)),5), ...
                         linspace(min(X(:,2)),max(X(:,2)),5));
zgrid = (1/normal(3)) .* (meanX*normal - (xgrid.*normal(1) + ygrid.*normal(2)));
h = mesh(xgrid,ygrid,zgrid,'EdgeColor',[0 0 0],'FaceAlpha',0);

hold on
above = (X-repmat(meanX,n,1))*normal > 0;
below = ~above;
nabove = sum(above);
X1 = [X(above,1) Xfit(above,1) nan*ones(nabove,1)];
X2 = [X(above,2) Xfit(above,2) nan*ones(nabove,1)];
X3 = [X(above,3) Xfit(above,3) nan*ones(nabove,1)];
plot3(X1',X2',X3','-', X(above,1),X(above,2),X(above,3),'o', 'Color',[0 .7 0]);
nbelow = sum(below);
X1 = [X(below,1) Xfit(below,1) nan*ones(nbelow,1)];
X2 = [X(below,2) Xfit(below,2) nan*ones(nbelow,1)];
X3 = [X(below,3) Xfit(below,3) nan*ones(nbelow,1)];
plot3(X1',X2',X3','-', X(below,1),X(below,2),X(below,3),'o', 'Color',[1 0 0]);

hold off
maxlim = max(abs(X(:)))*1.1;
axis([-maxlim maxlim -maxlim maxlim -maxlim maxlim]);
axis square
view(-23.5,5);

[David Young]

It's not possible to read your code. Please edit your question, select the code, and click the "{}Code" button, so that it is formatted. Thanks.

[Phanikumar Bhamidipati]

Thank you for pointing that. Corrected. I hope its readable now.

[Andrew Newell]

Is this code not doing what you want?

[Phanikumar Bhamidipati]

This one gives a best fit plane minimizing the MSE. Once that plane is found, I would like to move the plane by a certain distance. that was the original question.

Answer 1

[Tim Zaman]

Try RANSAC, i've got some on that here: http://www.timzaman.nl/?p=190