August 13th, 2015, 11:04 AM  #1 
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1  I have a potato chip!
Hi all, Apologies if this is not in the right group... but I tried I have a potato chip! Or rather a cloud of point data that describes an uneven plane in regular intervals. What I need to do, is to find which three points will "Come to rest" on a plane ... if a plane were to be moved against the data set. Now please understand that I am not searching for fullon physics simulation here... No gravity, no acceleration... nothing like that. This is an operation that I need to code... on a rather large data set. So I want to take advantage of procedural tests and iterations to quickly find the three resting points in the data set, and the plane that they describe. Let's look at it one final way.... Let's pretend I dropped a 1000 square mile sheet of glass on to California. Which three mountains would it rest on? Not a math wizard here, so please use small words Thanks in advance for your kind help! 
August 13th, 2015, 12:26 PM  #2  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,511 Thanks: 2514 Math Focus: Mainly analysis and algebra  Quote:
More seriously, it would hit the highest mountain and start the tilt in the direction of its centre of mass until it hit another mountain. Then it again tilts in the direction of its centre of mass until it hits a third. These are not necessarily the three highest mountains. So perhaps the first question is: what is the mass distribution in your glass sheet/plane?  
August 13th, 2015, 01:21 PM  #3 
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1 
The COM is where you'd expect... dead center of the plane... and you could assume dead center of the dataset. And I considered that basic approach... with the understanding that the solution will potentially change as the sheet settles. So the mathematical issues (or perhaps procedural issues) are how to find the *final* three points... not the initial three. Last edited by Ryder; August 13th, 2015 at 01:25 PM. 
August 13th, 2015, 03:39 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,511 Thanks: 2514 Math Focus: Mainly analysis and algebra 
I think you just iterate until the COM falls within the triangle formed by the three supporting points. I don't suppose that there is a closed form for this.

August 13th, 2015, 04:06 PM  #5  
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1  Quote:
Iterate *what*? It's the maths procedure that I'm totally deficient at... and where I need the help Oh, and I don't know what you mean by "closed form". sorry. Thank you! R Last edited by Ryder; August 13th, 2015 at 04:09 PM.  
August 13th, 2015, 04:19 PM  #6 
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1 
Here are the limits of what I think I know... I can look at the dataset and find that highest point... and assign a plane to that point... then I know that I need to tilt the plane toward the COM. But I don't know how to affect this "tilt" (or perhaps best thought of as checking for the shallowest angle to the remaining dataset... biased toward the COM) Once the second point is found, I now need to detect and tilt toward the COM once again, using the two found points as the axis. But once again, I don't know how to affect this tilt... especially in the "correct" direction (toward COM) to check for the next closest peak. It is here that I could really use the help. Thanks again. 
August 14th, 2015, 08:22 AM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,511 Thanks: 2514 Math Focus: Mainly analysis and algebra 
That is exactly the process I am talking about. When I say there isn't a closed form, I mean that there isn't any other way to do it that to go through the process step by step and see where you end up. 
August 14th, 2015, 09:42 AM  #8  
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1  Quote:
I'm looking for maths to get beyond what I already know, and into the realm of practical steps/application. That's why I'm here. Would someone be willing to help? Thank you!  
August 14th, 2015, 09:57 AM  #9 
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1 
To move things along, let's visit the first steps of the process... 1  search the z values of the dataset for the "tallest" value. (Zmax) 2  assign an infinite plane to that value in the form of?? (three points? 0,0, ZMax 1,0,ZMax, 0,1,Zmax?) 3  ??? (here is where I need help) The third step probably has to do with describing an axis where we will later "tilt" the plane toward the COM. Once this axis is described, we can ignore all of the z data on one side of it... and search for the highest second point (Zmax2), as an angle to the plane. Thanks for your kind help. R 
August 19th, 2015, 05:20 PM  #10 
Newbie Joined: Aug 2015 From: California Posts: 7 Thanks: 1 
Wow, nine messages back and forth... and nothing learned. I'll be moving on then... thanks anyway. 

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chip, plane, potato, rest 
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