How to find a cross section of a 'Boundary' plot with non planar data?

Hi MATLAB Community,

I have a boundary which I have plot to create a volume defined from a series of data points in 3D space, as shown by the red volume in the below image, and I am looking to find the area of this volume at the intersection with a plane, as visualised by the blue rectangle. Since the points defining the volume do not lie on distinct planes, I can't select values with a specific Y axis value and create a 2D plot of them. Can anyone point me in the right direction for a method that may be used to create this intersection and find its area?

Thanks,

Tim

Answer 1

[Bruno Luong]

Assuming the plane is z=0 (otherwise you should so a solid coordinates transformation to bring to this assumption)

You have to loop on the (triangular) faces and search for face that have 3 vertices with z change sign.

For those faces, pick the 2 edges (it must have 2) that have 2 vetices (x1,y1,z1) and (x2,y2,z2) with changing sign of z.

The intersection to the plane z=0 is :

(x,y) = ((x1,y1)*z2 - (x2,2)*z1)/(z2-z1) 

Form a graph that links (x,y), you should get a polygon in 2D. Use polyarea to find the area.