| Category | Programming |
| Summary | Linear Transformation Finder |
| Started | June 16, 2007 |
| Updated | February 13, 2008 |
| Files |
ltf-0.0.5.zip
(28 KB)
ltf-0.0.5.tar.gz (19 KB) ltf-0.0.5.gem (22 KB) |
Linear Transformation Finder is a Ruby program that works together with Maxima to find linear transformations between vectors that satisfy given constraints. The problem that motivated this project was this:
![[0,0,0] -> [0,0,0]](/images/ltf/t3_all_0.png?1182185928 "[0,0,0] -> [0,0,0]")
![[1,1,1] -> [1/2,1/2,1/2]](/images/ltf/t3_all_1.png?1182185931 "[1,1,1] -> [1/2,1/2,1/2]")
![[0,1,1] -> [1,0,0]](/images/ltf/t3_011.png?1182185920 "[0,1,1] -> [1,0,0]")
![[1,0,1] -> [0,1,0]](/images/ltf/t3_101.png?1182185923 "[1,0,1] -> [0,1,0]")
![[1,1,0] -> [0,0,1]](/images/ltf/t3_110.png?1182185925 "[1,1,0] -> [0,0,1]")
(What this particular transformation should do is spin by π radians around the line x=y=z, and translate in towards the origin a bit.)
I hypothesized that a linear transformation of the following form would work:
![[x,y,z] -> [c1*x + c2*y + c3*z + c4, c5*x + c6*y + c7*z + c8, c9*x + c10*y + c11*z + c12]](/images/ltf/t3_form.png?1182185935 "[x,y,z] -> [c1*x + c2*y + c3*z + c4, c5*x + c6*y + c7*z + c8, c9*x + c10*y + c11*z + c12]")
This is in fact the case, so the problem is finding values for the c* constants that satisfy the above 5 input/output constraints. This is where LTF comes in. LTF reads in a set of constraints, and produces Maxima code which will solve for the constants.
See the main documentation for more information, including the API.
