How to discretize a surface/volume in space?

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Cole
Cole 2014 年 8 月 21 日
コメント済み: Sean de Wolski 2014 年 8 月 21 日
Hi,
I have a problem that I'm trying to solve in the most efficient way. I have a series of planes in space which represent quartz veins in a mining context. In the synthetic example that I'm working on, they're approximately 5m x 5m and have a thickness of 20mm (obviously this varies as they draw from a distribution).
These "veins" exist in a larger volume called a mining domain. The mining domain is divided into 10 x 10 x 10 meter blocks. I want to solve for the volume of "vein" in each block so I can calculate the grade per block. I attempted to do this with matrix algebra but it's proving to be too difficult because of veins that lie within multiple blocks or because of veins which terminate within a block etc.
I've decided the best way to solve this problem is to hit it with a hammer. I'm going to discretize the veins into small points with a known area/volume then count the number of points in each block. There will be some error involved with this but it will be small enough to ignore for what I'm doing.
What's the most efficient way to discretize a volume in Matlab? My "veins" are defined by 4 corner points with an x,y,z location and each also has a thickness parameter. I think the best way to solve the problem would be to discretize the plane in 2D, count the points then solve for volume using the known thickness.
I'm just having trouble coding this efficiently.
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Sean de Wolski
Sean de Wolski 2014 年 8 月 21 日
Can you provide sample data?

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