Playground

Built-in Transformations

Command	Mapping
Scale(s)	\((x,y)\mapsto(sx,sy)\)
XScale(s)	\((x,y)\mapsto(sx,y)\)
YScale(s)	\((x,y)\mapsto(x,sy)\)
XYScale(s,t)	\((x,y)\mapsto(sx,ty)\)
Translate(h,k)	\((x,y)\mapsto(x+h,y+k)\)
Rotate(theta)	\((x,y)\mapsto(x\cos\theta-y\sin\theta, x\sin\theta+y\cos\theta)\)
XShear(t)	\((x,y)\mapsto(x+ty,y)\)
YShear(t)	\((x,y)\mapsto(x,xt+y)\)
M(a,b,c,d,f,g)	\((x,y)\mapsto(ax+by+f,cx+dy+g)\)

Compose functions with · or adjacency, and rememeber that these functions operate from right to left!

Equilize Weights

The "Equilize Weigths" button will set each weight to $1/n$, where $n$ is the number of transformations.

Auto Distribute Weigts

The "Auto Distribute Weights" button will set the weight $p_i$ for the $i$th transformation using the standard matrix $A_i$ and the value $\delta = 0.01$: $$p_i=\frac{\max(\delta, |\det A_i|)}{\sum_{j=1}^k\max(\delta, |\det A_j|)}.$$ The lock button, when enabled, will automatically distribute the weights after any change is made.
For more information on the weights and what they are used for, see here.

Matrices

Info JSON

The "generator" image pane shows the effect of each of the transformations on the unit square constructed with the standard unit vectors $(0,1)$ and $(1,0)$. To show orientation, each square also has an "L" shape connected to the bottom left corner.

The color of each transformes square corresponds to the color show in the "Raw Transformations" pane. The unshaded grey square shows the un-transformed unit square.