scatterquad2

scatterquad2(X,Y,Z) finds the volume under the surface defined by the points (X(i),Y(i),Z(i)) with linear interpolation on the Delaunay triangulation of (X,Y) and Z=0 outside the convex hull of (X,Y).

Example:
load seamount
scatterquad2(x,y,z-min(z)) % returns 190.7996
inR = (x>=211.1 & x<=211.4 & y>=-48.35 & y<=-48);
scatterquad2(x,y,(z-min(z)).*inR) % returns 142.3083
scatterquad2(x,y,1) % returns 0.2696

This function is *much* faster than using DBLQUAD with TriScatteredInterp, or similar methods.

For functions that can be evaluated at arbitrary points, use DBLQUAD or QUAD2D instead. For regular grids, instead use TRAPZ twice.