Linear Transform Visualizer

A small interactive demo written in Odin with raylib. It visualizes 2D linear transformations by showing how the standard grid and basis vectors change under arbitrary basis vectors.

Run

Requires the Odin compiler and raylib (raylib is bundled with Odin's vendor:raylib).

# Build
odin build . -out:odin_graph

# Run
./odin_graph

# Or build and run in one step
odin run .

How to use

Input basis vectors

In the bottom input box of the window, type four numbers separated by spaces:

i_x i_y j_x j_y

For example:

1 0 1 1

Press Enter to apply. The new transformation is composed (stacked) with the current one.

Preset commands

You can also type common transformations directly. These work in both the window input box and the terminal.

Command	Matrix	Effect
`shear` or `shear x`	`1 0 1 1`	Horizontal shear
`shear y`	`1 1 0 1`	Vertical shear
`rotate 90`	`0 -1 1 0`	Rotate 90° counter-clockwise
`rotate -90`	`0 1 -1 0`	Rotate 90° clockwise
`rotate 180`	`-1 0 0 -1`	Rotate 180°
`rotate 45`	`0.707 -0.707 0.707 0.707`	Rotate 45° counter-clockwise
`scale 2`	`2 0 0 2`	Uniform scale by 2
`scale 0.5`	`0.5 0 0 0.5`	Uniform scale by 0.5
`scale 3`	`3 0 0 3`	Uniform scale by 3
`flip x`	`1 0 0 -1`	Reflect across x-axis
`flip y`	`-1 0 0 1`	Reflect across y-axis
`identity` or `id`	`1 0 0 1`	Identity (same as reset)

Navigation

Left arrow < – go back to the previous transformation state
Right arrow > – go forward to the next transformation state
The bottom counter shows the current step and total number of steps

Both arrow transitions are animated.

Reset

Type reset or r in the input box (or terminal) and press Enter to add an identity step and return to the standard basis.

Terminal input

You can also type basis vectors into the terminal where you launched the program. The terminal supports the same format and the reset/quit commands.

> 1 0 1 1
> 1 1 0 1
> reset
> q

Exit

Press ESC
Close the window
Type quit, exit, or q

What's shown

Gray grid – original standard grid
Blue grid – transformed grid; density is recalculated each frame to fill the screen
Red arrow – transformed i-hat
Green arrow – transformed j-hat
Top-left panel – i-hat/j-hat values, legend, the full transformation chain (M2 × M1), each step's input matrix, cumulative matrix, expanded matrix multiplication, and component-wise formula

Project structure

.
├── main.odin      # Source code
├── .gitignore     # Git ignore rules
└── README.md      # This file