R2_D2 is is the title I’ve given a brand new MATLAB program that gives animations of 2-by-2 rotation and dilation matrices. I admit I selected “dilations” so the acronym can be memorable, however in any other case the code has little to do with the well-known Star Wars droid.
Contents
Home
This define of a home is featured in Experiments with MATLAB. The info are the 11 blue dots. The coordinates of every dot type a 2-by-1 vector; the 2-by-2 rotation and dilation matrices multiply every of those vectors individually. (The strains between the dots full the image and should not concerned in any computation.)
The home additionally seems in a number of editions of Gil Strang’s textbooks. The duvet of the third version of Strang’s Introduction to Linear Algebra options 9 homes on a quilt made by Gil’s good friend Chris Curtis.
Hand
This define of a hand, which I constructed from measurements of my very own hand, can be utilized in Experiments with MATLAB. There are 37 factors, so Hand is a 2-by-37 matrix.
Rotation
Multiplication by this matrix produces a two-dimensional rotation by an angle theta.
$$ R = left(
start{array}{rr}
cos{theta} & sin{theta}
– sin{theta} & cos{theta}
finish{array}
proper) $$
R is displayed within the first panel. If the home just isn’t rotating in your browser, do this hyperlink: https://blogs.mathworks.com/cleve/recordsdata/house_rotate.gif
Dilation
Dilation is the method of constructing objects bigger or smaller. Multiplication by this diagonal matrix produces a dilation by an element sigma.
$$ S = left(
start{array}{rr}
sigma & 0
0 & sigma
finish{array}
proper) $$
S is displayed within the second panel. The animation can be obtainable at: https://blogs.mathworks.com/cleve/recordsdata/hand_dilate.gif
Each
Right here rotation and dilation are mixed. The product of the rotation and dilation matrices drives the motion. If you’re lacking all of the motion, strive: https://blogs.mathworks.com/cleve/recordsdata/hand_both.gif
R2_D2
While you run R2_D2 by yourself laptop, you may drive the rotations and dilations your self. Mousing exterior of the article creates rotation and mousing inside produces dilation.
The R2_D2 program is offered from https://blogs.mathworks.com/cleve/recordsdata/R2__D2.m.
Additional Studying
If you’re not aware of matrices, or simply need a fast refresher, try the Matrices chapter of Experiments with MATLAB. Train 4.14 is especially useful.
Printed with MATLAB® R2023a
