zalo/zalo.github.io

A home for knowledge that is hard to find elsewhere

Sublucid Geometry

A technical blog with a small number of nifty geometric tricks that are hard to find elsewhere.

The source for all of the examples can be found in the assets/js/ directory.

zalo.github.io's Issues

3D line fit using SVD

re https://zalo.github.io/blog/line-fitting/#

There are a variety of iterative solutions available, but they often depend on an operation called the Singular Value Decomposition or SVD

I'm trying to collect examples of SVD use here
https://www.geogebra.org/m/Sc6ybzdu

This one
https://www.geogebra.org/m/Sc6ybzdu#material/hmTzuJ2d

uses the method from the first answer here I think
https://stackoverflow.com/questions/2298390/fitting-a-line-in-3d

which suggests it's a closed form problem with SVD, not iterative. Do the iterative methods calculate something better?

Thanks for your help, just trying to understand SVD a little better :)

Here's the rough code from my example for reference:

U=svd(1)
Σ=svd(2)

singularVectorForLargestSingularValue=Element(Transpose(U),b)
singularVectorForSmallestSingularValue=Element(Transpose(U),a)

directionVector= (singularVectorForLargestSingularValue(1),singularVectorForLargestSingularValue(2),singularVectorForLargestSingularValue(3))

bestFitLine = Line(Centroid,directionVector)

otp

otp

Originally posted by @virusoff271189 in harryshi/TeleSafe2#1 (comment)

missing images?

Hi

I was browsing through your blog, great stuff but it seems like the pages are either missing images or something is wrong with the page structures. I see white rectangles in the pages but no images there.

thanks

Segment-Segment Distance in 3D - Sublucid Geometry

Segment-Segment Distance in 3D - Sublucid Geometry

One of my favorite functions projects points onto line segments.

https://zalo.github.io/blog/closest-point-between-segments/

Line Fitting in 3D - Sublucid Geometry

Line Fitting in 3D - Sublucid Geometry

Orthogonal Regression is the process of finding the line that best fits a set of points by minimizing their squared orthogonal distances to it.

https://zalo.github.io/blog/line-fitting/

Constraints - Sublucid Geometry

Constraints - Sublucid Geometry

The essence of constraint is projection.

https://zalo.github.io/blog/constraints/

Inverse Kinematics - Sublucid Geometry

Inverse Kinematics - Sublucid Geometry

Inverse Kinematics is the process of finding a set of joint angles that reach a goal position.

https://zalo.github.io/blog/inverse-kinematics/