Math expressions in OpenVCAD

OpenVCAD compiles math expression strings at runtime with the ExprTk library. The same syntax is used wherever you pass an expression string—for example FloatAttribute, Vec4Attribute, and VolumeFractionsAttribute in the attribute-modeling workflow, and other nodes that accept spatial formulas.

Note

Syntax matches most graphing-calculator conventions, with many advanced features available. See the ExprTk documentation for the full language specification.

Coordinate systems

The following variables may be used in any math expression. You can combine multiple coordinate systems in a single expression.

Name	Form	Variable names
Cartesian	f(x, y, z)	x, y, z
Cylindrical	f(rho, phic, z)	rho, phic, z
Spherical	f(r, theta, phis)	r, theta, phis
Signed distance	f(d)	d

Note

phic is the azimuthal angle in cylindrical coordinates; phis is the polar angle in spherical coordinates. Both use radians.

Note

d is the signed distance to the object surface: zero on the surface, negative inside, positive outside. This supports conformal (surface-following) gradients.

Cylindrical definitions

• rho = sqrt(x^2 + y^2) — distance from the Z axis

• phic = atan2(y, x) — azimuth in the XY plane (radians, about -π to +π)

• z — same as Cartesian z

Spherical definitions

• r = sqrt(x^2 + y^2 + z^2) — distance from the origin

• theta = atan2(y, x) — azimuth in the XY plane (radians)

• phis = acos(z / r) — polar angle from +Z (radians, 0 to π)

Arithmetic and assignment operators

Operator	Definition
+	Addition (x + y)
-	Subtraction (x - y)
*	Multiplication (x * y)
/	Division (x / y)
%	Modulus (x % y)
^	Exponentiation (x ^ y)
:=	Assignment (y := x)
+=, -=, *=, /=, %=	Compound assignment

Equalities and inequalities

Operator	Definition
== or =	Equal (x == y)
<> or !=	Not equal
<, <=, >, >=	Inequality comparisons

Boolean operations

Operator	Definition
true / false	Boolean literals
and, or, not	Logical operators
xor, nand, nor, mand, mor	Extended logical ops

General-purpose functions

Function	Definition
abs(x)	Absolute value
avg(x, y, ...)	Mean of arguments
ceil(x), floor(x)	Rounding
sqrt(x)	Square root (x ≥ 0)
log(x), exp(x)	Log and exponential
pow(x, y)	Power
max(...), min(...)	Extrema
clamp(lo, x, hi)	Clamp x to [lo, hi]

Trigonometry

Arguments are in radians unless you convert with deg2rad / rad2deg.

Function	Definition
sin, cos, tan	Basic trig
asin, acos, atan	Inverses
deg2rad(x), rad2deg(x)	Unit conversion

Constants

Name	Role
pi	Built-in
e	Built-in

You can also use numeric literals (e.g. 3.14159).

Tips

• Grouping uses parentheses: (x + y) * z.

• Mixing coordinates is valid, e.g. rho * sin(phis) + z.

• Colors and fractions often need clamp: clamp(0, expr, 1) for channels that must stay in [0, 1].