How to calculate the volume under two intersection surface?

Question

I like to calculate the volume under the two intersection plane. The two plane is draw use this code.

P1 = [575,0,400];
P2 = [287.5,0,662];
P3 = [575,3500,154];
normal = cross(P1-P2, P1-P3)
syms x y z
P = [x, y, z]
ep1=dot(normal, P-P1)
%  get the equation
Z = solve(ep1,z) 
% draw the first plane
ezsurf(Z,[287.5,575,0,3500])
hold on
% draw the second horizontal plane
[x,y]=meshgrid(0:500:3500)
z = ones(8,8)*440
surf(x, y, z)

So I must calculate the volume under the first plane. I used this code, but I don't know how to construct matrix Zm used the the symbols equation Z. And how can I use meshgrid and surf not ezsurf draw the first plane.

%f=@(x,y)(interp2(Zm,Xq,Yq))
% I want to calculate volume under the plane  ranged by Xmin=2.875, Xmax=575,Ymin=0,Ymax=3500 
%volume = quad2d(f,(287.5),575,0,3500)
%volume = integral2(f,287.5,575,0,3500)

Thanks a lot.

Kyle Kyle · Accepted Answer · 2019-02-21T04:18:32

As an alternative strategy that might be easier to understand I would suggest, instead of interpolating, using some geometry formulas to calculate the area. You can break down the 3D shape into a simple triangular prism and an irregular tetrahedron. There are well defined generalized formulas for both of these. http://mathcentral.uregina.ca/QQ/database/QQ.09.03/peter2.html

How to calculate the volume under two intersection surface?

1 Answers