# How to use Delaunay Triangulation to create a plane with constraints?

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youssef hany on 2 Nov 2022
Answered: Jeffrey Clark on 8 Nov 2022
I have four coplanar points shown in red and I want to create a plane bounded by these four points (representing a wall). The green points represent constraints in the wall that I want to be empty in the plane. I want to use Delaunay Triangulation do that but it fails because points are coplanar. what should I do?
Walter Roberson on 2 Nov 2022
It is not clear what "create a plane" means to you ?
You might be interested in some of the functions from the PDE Toolbox, as some of them include creating a mesh for an shapes "excluding" particular shapes.
youssef hany on 2 Nov 2022
Edited: youssef hany on 2 Nov 2022
I mean a 3D plane surface that can be exported to revit, something like that

Jeffrey Clark on 8 Nov 2022
@youssef hany, if all your points are coplanar for one section (in your picture a wall, floor, etc) they can be processed as 2D by dropping the constant dimension and using 2D delaunayTriangulation with constraints for windows, doors (regular and trap). If you are working in arbitrary 3D where coplanar points don't share the same one x, y or z you can rotate each coplanar section to eliminate one dimension using something like:
function Pxy = rotateCoplanar(Pxyz)
Rx = @(t) [ 1 0 0 ...
; 0 cos(t) -sin(t) ...
; 0 sin(t) cos(t) ];
% Ry = @(t) [ cos(t) 0 sin(t) ...
% ; 0 1 0 ...
% ; -sin(t) 0 cos(t) ];
Rz = @(t) [ cos(t) -sin(t) 0 ...
; sin(t) cos(t) 0 ...
; 0 0 1 ];
Pmean = mean(Pxyz,1);
Pnew = Pxyz-Pmean;
uT = cross(Pnew(1,:)-Pnew(3,:),Pnew(2,:)-Pnew(3,:)); uT = uT/norm(uT);
nx = Rz(atan2(uT(1),uT(2)));
uTnx = (nx*uT')';
Pxy = (Rx(atan2(uTnx(2),uTnx(3)))*nx*Pnew')'; Pxy = Pxy(:,1:2);
end

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