# corners of rectangle by center point

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Mariam Ali on 18 Jan 2022
Edited: DGM on 18 Jan 2022
i want to find corners ABCD of rectangular surface by center point and length and width is given in 3D.
center point = [-9.9366,1.6890,1.3800]
for ease attaching the picture
DGM on 18 Jan 2022
Edited: DGM on 18 Jan 2022
This is an underdefined problem. A rectangle is a 2D object. It's a region in a plane. There are an infinite number of planes that intersect a given point in 3D space. In each of those infinite number of planes, there are an infinite number of possible rectangles with the same geometry which share the same center, but vary by rotation. You need more information than just a center point and width/height in order to define a specific rectangle.
If you want the location of all possible vertices, the locus would be a spherical shell centered at the given point, with a radius equal to half the diagonal of the specified 2D geometry.
Mariam Ali on 18 Jan 2022
what i ment that center point of rectangle is given having x y z codinates . hight of rectangle is 1.7 that is in y direction and width is 0.3 which is on z direction and x being the same value of the center point.
now is it possible ?

DGM on 18 Jan 2022
Edited: DGM on 18 Jan 2022
You mean basic addition and subtraction?
c = [-9.9366 1.6890 1.3800];
w = [0 1.7 0.3];
v = c + w/2.*[0 -1 -1; 0 1 -1; 0 1 1; 0 -1 1]
v = 4×3
-9.9366 0.8390 1.2300 -9.9366 2.5390 1.2300 -9.9366 2.5390 1.5300 -9.9366 0.8390 1.5300
patch(v(:,1),v(:,2),v(:,3),'green')
axis equal
grid on
view(3)

Max Heimann on 18 Jan 2022
Do you want the corners of the 2D projection of a rotated plane? In that case you could simply calculate the 3D position of each vertice and discard the 3rd dimension. This requires you to know the rotation of the plane in your 3D space. If you know that your problem is solvable with the builtin sin/cos/tan functions.
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Max Heimann on 18 Jan 2022
Are we talking about a 2D problem or a 3D problem?
Can you explain the 3 components of your center point? From your original question it is defined as:
center_point = [-9.9366,1.6890,1.3800]
Are those the X,Y,Z coordinates of the center point?
Mariam Ali on 18 Jan 2022
its 3D [x,y,z] coordinate.

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