Topic Operators
here are all the symbols which can be categorized by topics
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
OR
What's this random function ?
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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
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 grammatical (/ fundamental) symbols that will be covered in future chapters.
Examples
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 grammatical (/ fundamental) symbols that will be covered in future chapters.
Examples
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
Zoi - 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.
define set
[ zoi - dæf ]
Glyph Derivation
The 2 circles resemble the Venn diagram, which is an important diagram in set theory.
All symbols that 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.
Examples
declaring a set "basket" to be "{apple, orange, lemon}"
Predefined Sets
Some special sets has their own symbols
empty set
[ zoi - no ]
universal set
[ zoi - ni ]
power set
[ zoi - næ ]
Set Relation
Just like numbers can have relations, sets and elements can also have relations.
is an element of
[ zoi - æru ]
is not an element of
[ zoi - æra ]
is a subset of
[ zoi - ærui ]
is not a subset of
[ zoi - ærai ]
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.
not
[zoi - rooo]
[ zoi - ro ]
union / or
[ zoi - riii ]
[ zoi - ri ]
subtract
[ zoi - rioo ]
[ zoi - rio ]
xor
[ zoi - rioi ]
intersect / and
[ zoi - roio ]
[zoi - royo]
The Connection between Set and Boolean
First let's take a look at how does the union operator works :
"A union B" can be interpret as "if you are in set A OR set B, you will be selected"
the selected elements will need to be in A OR B, and this is why the set operator "union" is also a boolean operator "or".
Shortcut words
These symbols acts like substitutions of phrases, which can be helpful in proofing, documentation, etc
because
therefore
for all
there exist
given that
Glyph Derivation
Some of the symbols are derived from some of the grammatic symbols, which will be covered in future chapters