Overview

This is a project to visualise and evaluate matrix transformations / expressions involving 2x2 matricies, 2D vectors, and floats, such as multiplication, inversing, scaling, addition, determinant, dot product and more.

To run it, go to the latest release, or visit the website

Example

Full list of features and controls

Controls

• Enter the expression into the terminal. These get evaluated immediately.
• Use Show <expr> to visualise an expression:
• Click on nodes to ignore them. This also must ignore all its children
• Use left and right arrows to go back and forwards in the visualisation
• Use up and down arrows to speed up and slow down the visuals
• Click right at the end of the visualisation to continue entering expressions in the terminal
• Click K to display the abstract syntax tree.
• Any orange node is a leaf node and indicates that the object at that point will be inserted with no visualisation attatched to the beginning of its existence

Functions

• Mat(a, b, c, d)
• Vec(x, y)
• * (defined for anything including a float)
• + - (defined for vec by vec, mat by mat and float by float)
• * / (defined for mat by vec, mat by mat, vec by float and mat by float)
• ^ (power, defined for float by float. This does not have a visualisation)
• .a .b .x .y (defined for vec)
• .a .b .c .d .w .x .y. .z (defined for mat)
• .i .j (defined for mat, returns i hat and j hat)
• Left(mat) (returns Vec(a, c). This is equivalent to .i)
• Right(mat) (returns Vec(b, d). This is equivalent to .j)
• Top(mat) (returns Vec(a, b))
• Bottom(mat) (returns Vec(c, d))
• Hor(v1, v2) (returns Mat(x1, y1, x2, y2))
• Vert(v1, v2) (returns Mat(x1, x2, y1, y2))
• RotMat(angle) (angle in radians. pi constant is defined)
• RotVec(angle)
• X (defined for vec by vec, represents cross product)
• * (defined for vec by vec, represents dot product)
• Det(mat)
• = (variable assignment)
• Show (used to visualise something)
• ( and )
• Any token not here is interpretted as a variable name

Other features

• Variable assignment and use - pi and I (2x2 identity matrix) are defined.
• Automatic camera which changes based on visuals
• Displays an abstract syntax tree representing your expression
• Ability to trim down your abstract syntax tree to not show specific visuals
• Complete tokeniser and Pratt parser

Examples

Show Mat(1,2,-3,3) * Mat(0.5,-1,1,0.5)

a = Mat(1,2,-3,3)
b = Mat(0.5,-1,1,0.5)
c = Mat(1.0,0.5,-2,0.5)
Show c*(a-b) + b

Show Mat(1.0,0.5,-2,0.5)*(Mat(1,2,-3,3)-Mat(0.5,-1,1,0.5))

a=Vec(12,5)
b=Vec(-2,3)
ap=Vec(-5,-7)
bp=Vec(6,-2)
m=Vert(ap, bp) * Inv(Vert(a,b))

Show m*Vert(a,b)

Show Mat(2,1,-3,(2*-2)+3)

Show Mat(Vec(2,1) * Vec(5 / 2 - 1, 4), -Vec(2,6).y / 2 / 0.8, RotVec(2).x, 1 + 3 - (1 - 2)) * RotVec(5)

Contributing

Contributions are extremely welcome! If you find something you'd like to change, or want to solve an issue, go for it!