CODEWITHSUNDEEP
math3dgeometrycomputational-geometry
niro
niro

Reputation: 977

quality analysis of fitted pyramid

sorry for posting this in programing site, but there might be many programming people who are professional in geometry, 3d geometry... so allow this.

I have been given best fitted planes with the original point data. I want to model a pyramid for this data as the data represent a pyramid. My approach of this modeling is

  1. Finding the intersection lines (e.g. AB, CD,..etc) for each pair of adjacent plane
  2. Then, finding the pyramid top (T) by intersecting the previously found lines as these lines don’t pass through a single point
  3. Intersecting the available side planes with a desired horizontal plane to get the basement

In figure – black triangles are original best fitted triangles; red and blue triangles are model triangles

I want to show that the points are well fitted for the pyramid model than that it fitted for the given best fitted planes. (Assume original planes are updated as shown)

Actually step 2 is done using weighted least square process. Each intersection line is assigned with a weight. Weight is proportional to the angle between normal vectors of corresponding planes. in this step, I tried to find the point which is closest to all the intersection lines i.e. point T. according to the weights, line positions might change with respect to the influence of high weight line. That mean, original planes could change little bit. So I want to show that these new positions of planes are well fitted for the original point data than original planes.

Any idea to show this? I am thinking to use RMSE and show before and after RMSE. But again I think I should use weighted RMSE as all the planes refereeing to the point T are influenced so that I should cope this as a global case rather than looking individual planes….. But I can’t figure out a way to show this. Or maybe I should use some other measure… So, I am confused and no idea to show this.. Please help me…

enter image description here

Upvotes: 0

Views: 202

Answers (1)

comingstorm
comingstorm

Reputation: 26117

If you are given the best-fit planes, why not intersect the three of them to get a single unambiguous T, then determine the lines AT, BT, and CT?

This is not a rhetorical question, by the way. Your actual question seems to be for reassurance that your procedure yields "well-fitted" results, but you have not explained or described what kind of fit you're looking for!

Unfortunately, without this information, your question cannot be answered as asked. If you describe your goals, we may be able to help you achieve them -- or, if you have not yet articulated them for yourself, that exercise may be enough to let you answer your own question...

That said, I will mention that the only difference between the planes you started with and the planes your procedure ends up with should be due to floating point error. This is because, geometrically speaking, all three lines should intersect at the same point as the planes that generated them.

Upvotes: 1

Related Questions