Math Expression Documentation

Math Expression Documentation

This documentation covers the operators that may be used in math expression strings in the FGrade and Function nodes.

We use the Exprtk library for parsing math strings. Although it follows syntax that is common on most graphic calculators, as we detail below, it support many advanced features. Please see their documentation for a full list of functions.

Coordinate Systems

The following variables may be used in any math expression to grade based on these coordinate systems. You can use any combinations of these and even mix multiple coordinate systems.

Name	Form	Variable Name
Cartesian	f(x, y, z)	x, y, z
Cylindrical	f(ρ, φ, z)	rho, phic, z
Spherical	f(r, θ, φ)	r, theta, phis
Signed Distance	f(d)	d

Note: phic corresponds to phi in cylindrical and phis to phi in spherical

Note: d is the signed distance to the surface of the object. Zero is the surface, negative values are inside and positive values are outside. This can used to create conformal gradients.

Operators and Functions Reference

(0) Arithmetic & Assignment Operators

OPERATOR	DEFINITION
+	Addition between x and y. (e.g., x + y)
-	Subtraction between x and y. (e.g., x - y)
*	Multiplication between x and y. (e.g., x * y)
/	Division between x and y. (e.g., x / y)
%	Modulus of x with respect to y. (e.g., x % y)
^	x to the power of y. (e.g., x ^ y)
:=	Assign the value of x to y. (e.g., y := x)
+=	Increment x by the value of the expression on the right-hand side.
-=	Decrement x by the value of the expression on the right-hand side.
*=	Assign the multiplication of x by the value of the expression to x.
/=	Assign the division of x by the value of the expression to x.
%=	Assign x modulo the value of the expression on the right-hand side to x.

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(1) Equalities & Inequalities

OPERATOR	DEFINITION
== or =	True only if x is strictly equal to y. (e.g., x == y)
<> or !=	True only if x does not equal y. (e.g., x != y)
<	True only if x is less than y. (e.g., x < y)
<=	True only if x is less than or equal to y. (e.g., x <= y)
>	True only if x is greater than y. (e.g., x > y)
>=	True only if x is greater than or equal to y. (e.g., x >= y)

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(2) Boolean Operations

OPERATOR	DEFINITION
true	True state or any value other than zero (typically 1).
false	False state, value of exactly zero.
and	Logical AND, True only if x and y are both true. (e.g., x and y)
or	Logical OR, True if either x or y is true. (e.g., x or y)
not	Logical NOT, negates the logical sense of the input. (e.g., not x)
xor	Logical XOR, True only if the logical states of x and y differ.
nand	Logical NAND, True only if either x or y is false.
nor	Logical NOR, True only if both x and y are false.
mand	Multi-input logical AND, True only if all inputs are true.
mor	Multi-input logical OR, True if at least one input is true.

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(3) General Purpose Functions

FUNCTION	DEFINITION
abs	Absolute value of x. (e.g., abs(x))
avg	Average of all inputs. (e.g., avg(x, y, z))
ceil	Smallest integer greater than or equal to x.
floor	Largest integer less than or equal to x.
sqrt	Square root of x, where x >= 0. (e.g., sqrt(x))
log	Natural logarithm of x. (e.g., log(x))
exp	e to the power of x. (e.g., exp(x))
pow	x to the power of y. (e.g., pow(x, y))
max	Largest value of all inputs. (e.g., max(x, y, z))
min	Smallest value of all inputs. (e.g., min(x, y, z))

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(4) Trigonometry Functions

FUNCTION	DEFINITION
sin	Sine of x. (e.g., sin(x))
cos	Cosine of x. (e.g., cos(x))
tan	Tangent of x. (e.g., tan(x))
asin	Arc sine of x, in radians.
acos	Arc cosine of x, in radians.
atan	Arc tangent of x, in radians.
deg2rad	Convert x from degrees to radians. (e.g., deg2rad(x))
rad2deg	Convert x from radians to degrees. (e.g., rad2deg(x))