Lets see - Simpson's rule. Isn't that something like subdivide the domain, then multiply the area of each part by the area of the part, sum and divide by the total area? You can use Post(... "connections") to average the values at the vertices of the each triangle, leaving the result associated with the triangles, rather than the vertices; Measure(... "elements") gives you the area of each triangle, and without the "elements" argument gives you the total surface area. You can use Compute to do the multiplication of average scalar value*area for each triangle, then sum the results by using Statistics to get the mean value and multiplying by the number of values (which Inquire(... "items", "data)) wil give you. Then multiply these three values, and you have an approximate integral.
In the attached example I have generated a bogus scalar field, done your trick of isosurfacing the distance to the normal, and doing the integration. Greg (See attached file: integrate_example.cfg)(See attached file: integrate_example.net) Greg Ball <[EMAIL PROTECTED]>@opendx.watson.ibm.com on 09/17/2001 03:25:37 PM Please respond to [email protected] Sent by: [EMAIL PROTECTED] To: [email protected] cc: Subject: [opendx-users] Numerical integration with DX Hi DX weenies, I've been lurking on this list for a while and I have found the answers posted here to be very informative, so thanks for that. Till now my own experience with DX has gone pretty smoothly. Now I am looking for a capability which doesn't seem to be mentioned in the documentation, or the archives. Apologies if I have missed something obvious here. What I want to do is perform surface integration on a 2-d surface in 3-space. I have a scalar component on a field in 3-space, with regular connections. Right now, I am marking positions, calculating the distance from the origin, taking that through isosurface, and marking the scalar component again. This gives me a new field. The positions are irregular and are in the form of a sphere. The scalar field is interpolated onto this sphere. It looks fine when rendered. Now I want to calculate the integral of the scalar over the surface. It seems that in terms of the computational work I'm almost there, but I can't figure out how to proceed. Any help appreciated. Thanks, Greg Ball -- Astronomy Dept. Harvard University
integrate_example.cfg
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integrate_example.net
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