Topic Operators

here are all the symbols which can be categorized by topics

01:Functions

02:Geometry

03: Set Theory * Boolean

04:shortWords

01:Functions

Functions

Watch this first

If you have no idea what is a function, watch XR_XharpRazor talks about the basic concept of functions on our Learning Channel :

Defining a function

since a function takes an input and gives you an output, the glyph resembles a rectangle cup collecting the input and a triangle giving the output. In normal maths, when a function is declared, it is mentioned in words that a specific identifier is a function, here the symbol is used to specify that the identifier is a function.

here let's define the function "f(x) = 2x + 5" :

String Script

almost like in normal math, almost everything is the same,

it is just we need to add the "function definition" symbol

Story Board Script

Here, the input is written above the function identifier, and the output below.

Multiple inputs

a function can also have multiple inputs, such that each parameters need to be separated by comas

What's this random function ?

The function above is a famous function "LERP", or linear-interpolation,

which is a function that takes a starting value, ending value, and a t-value, and it gives you a blend n between the 2 values.

Inverse

since the inverse is the total opposite of the original function, the glyph is just the function definition symbol flipped upside-down.

Derivative & Integral

almost like the normal math we know, it is just the "d" from "dy/dx" has it's own symbol, the rest is just one to one substitution here.

derivative

integral

02:Geometry

Geometry

Geometry Components

Just like declaring a function, declaring a geometry component also requires the co-responding symbol to declare that the next identifier is a point/edge/surface/volume/mesh etc.

dot

(0D)

line

(1D)

surface

(2D)

mesh

(3D)

What is that symbol up there ?

It is one of the grammatic symbols such that it will be covered in the future chapters.

declaring a dot "o" to be (0,0)

Geometry Relationships

Just like Equalities between numbers, geometry objects also has relationships, they behave like our normal math symbols : both operands are on both sides

perpendicular

parallel

congruent

What is that symbol up there ?

It is one of the grammatic symbols such that it will be covered in the future chapters.

saying "line A and line B are perpendicular"

Trigonometry Functions

Just like a function, each function has their own symbols, all is left is the bracket with the input.

sin

cos

tan

asin

cos

atan

03:SetBool

Set Theory & Boolean Aglebra

Why both together ?

turns out that both set theory and boolean algebra have connection in between them, they are somehow intertwined, and they are almost equivalent.

Declaring a set

Just like a function, there is a glyph used to declare a set,

here we also use a bracket with a coma-separated list to list out the content of the set.

The 2 circles resembles the venn diagram, which is an important diagram in set theory all symbols which are within this category will have the "double circle" as its radical.

A set is a single circle, but why 2 ?

soon set operators will act on 2 sets, to make all the symbols more united, all set symbols will have the "double circle" radical.

declaring a set "basket" to be "{apple, orange, lemon}"

Predefined Sets

Some special sets has their own symbols

empty set

universal set

power set

Set Relation

Just like numbers can have relations, sets and elements can also have relations.

belongs to

does not belongs to

is a subset of

is not a subset of

Set & Boolean Operations

These are the operations you can run on sets, under some circumstances, they also work on booleans. In this case, they behave like how we are familiar with set and boolean operations in normal math.