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Math Functions

Complete reference for mathematical functions available in Nodo expressions.

Basic Math

abs

abs(x)
Returns the absolute value of x.

Examples: 

abs(-5)     → 5
abs(3.2)    → 3.2
abs(0)      → 0

sqrt

sqrt(x)
Returns the square root of x.

Examples: 

sqrt(16)    → 4
sqrt(2)     → 1.414...
sqrt(0)     → 0

pow

pow(base, exponent)
Returns base raised to the power of exponent.

Examples: 

pow(2, 8)   → 256
pow(10, 3)  → 1000
pow(4, 0.5) → 2 (square root)

exp

exp(x)
Returns e^x (Euler's number raised to x).

Examples: 

exp(0)      → 1
exp(1)      → 2.71828...
exp(2)      → 7.38906...

log

log(x)         # Natural logarithm (base e)
log10(x)       # Base 10 logarithm

Examples: 

log(2.71828)   → 1
log10(100)     → 2
log10(1000)    → 3

Rounding

floor

floor(x)
Rounds down to nearest integer.

Examples: 

floor(3.7)  → 3
floor(3.2)  → 3
floor(-2.5) → -3

ceil

ceil(x)
Rounds up to nearest integer.

Examples: 

ceil(3.2)   → 4
ceil(3.7)   → 4
ceil(-2.5)  → -2

round

round(x)
Rounds to nearest integer.

Examples: 

round(3.4)  → 3
round(3.5)  → 4
round(3.6)  → 4

trunc

trunc(x)
Removes decimal part (rounds toward zero).

Examples: 

trunc(3.7)  → 3
trunc(-3.7) → -3

Min/Max

min

min(a, b)
min(a, b, c, ...)
Returns the smallest value.

Examples: 

min(5, 10)      → 5
min(3, 1, 7)    → 1
min(-2, 0, 5)   → -2

max

max(a, b)
max(a, b, c, ...)
Returns the largest value.

Examples: 

max(5, 10)      → 10
max(3, 1, 7)    → 7
max(-2, 0, 5)   → 5

clamp

clamp(value, min, max)
Constrains value between min and max.

Examples: 

clamp(15, 0, 10)    → 10
clamp(-5, 0, 10)    → 0
clamp(5, 0, 10)     → 5

Trigonometry (Degrees)

All trigonometric functions use degrees, not radians.

sin

sin(degrees)
Sine function.

Examples: 

sin(0)      → 0
sin(30)     → 0.5
sin(90)     → 1
sin(180)    → 0

cos

cos(degrees)
Cosine function.

Examples: 

cos(0)      → 1
cos(60)     → 0.5
cos(90)     → 0
cos(180)    → -1

tan

tan(degrees)
Tangent function.

Examples: 

tan(0)      → 0
tan(45)     → 1
tan(90)     → undefined (very large)

asin

asin(value)
Arc sine (inverse sine), returns degrees.

Examples: 

asin(0)     → 0
asin(0.5)   → 30
asin(1)     → 90

acos

acos(value)
Arc cosine (inverse cosine), returns degrees.

Examples: 

acos(1)     → 0
acos(0.5)   → 60
acos(0)     → 90

atan

atan(value)
Arc tangent (inverse tangent), returns degrees.

Examples: 

atan(0)     → 0
atan(1)     → 45
atan(-1)    → -45

atan2

atan2(y, x)
Two-argument arc tangent (handles quadrants correctly).

Examples: 

atan2(1, 1)     → 45
atan2(1, -1)    → 135
atan2(-1, -1)   → -135

Interpolation

lerp

lerp(a, b, t)
Linear interpolation from a to b by factor t (0 to 1).

Examples: 

lerp(0, 10, 0.5)    → 5
lerp(0, 10, 0)      → 0
lerp(0, 10, 1)      → 10
lerp(100, 200, 0.25) → 125

smoothstep

smoothstep(edge0, edge1, x)
Smooth hermite interpolation (ease in/out).

Examples: 

smoothstep(0, 1, 0.5)   → 0.5 (but smoother curve)
smoothstep(0, 10, 3)    → ~0.3

Returns 0 if x ≤ edge0, 1 if x ≥ edge1, smooth interpolation between.

Modulo & Sign

mod / %

mod(a, b)
a % b
Modulo (remainder after division).

Examples: 

10 % 3      → 1
7 % 2       → 1
15 % 5      → 0

sign

sign(x)
Returns sign of x: -1, 0, or 1.

Examples: 

sign(10)    → 1
sign(-5)    → -1
sign(0)     → 0

Utility Functions

fract

fract(x)
Returns fractional part of x (x - floor(x)).

Examples: 

fract(3.7)      → 0.7
fract(5.2)      → 0.2
fract(-2.3)     → 0.7

fmod

fmod(x, y)
Floating-point remainder.

Examples: 

fmod(5.5, 2.0)  → 1.5
fmod(7.2, 3.0)  → 1.2

Constants

PI

$PI or pi()
Pi constant (3.14159265359...).

Examples: 

$PI * 2         → 6.283... (2π)
sin($PI / 2)    → 1 (but use sin(90))

E

$E
Euler's number (2.71828...).

Examples: 

$E              → 2.71828...
pow($E, 2)      → 7.389... (e²)

Type Conversion

int

int(x)
Converts to integer (truncates decimals).

Examples: 

int(3.7)        → 3
int(3.2)        → 3
int("42")       → 42

float

float(x)
Converts to floating-point number.

Examples: 

float(42)       → 42.0
float("3.14")   → 3.14

bool

bool(x)
Converts to boolean (0 = false, non-zero = true).

Examples: 

bool(0)         → false
bool(1)         → true
bool(0.1)       → true

str

str(x)
Converts to string.

Examples: 

str(42)         → "42"
str(3.14)       → "3.14"
str(true)       → "true"

Vector Functions

length

length(vector)
Returns magnitude of vector.

Examples: 

length(vec3(3, 4, 0))   → 5
length(vec3(1, 0, 0))   → 1

normalize

normalize(vector)
Returns unit vector (length = 1).

Examples: 

normalize(vec3(3, 4, 0))    → vec3(0.6, 0.8, 0)
normalize(vec3(10, 0, 0))   → vec3(1, 0, 0)

dot

dot(vec1, vec2)
Dot product of two vectors.

Examples: 

dot(vec3(1,0,0), vec3(0,1,0))   → 0 (perpendicular)
dot(vec3(1,0,0), vec3(1,0,0))   → 1 (parallel)

cross

cross(vec1, vec2)
Cross product of two vectors.

Examples: 

cross(vec3(1,0,0), vec3(0,1,0)) → vec3(0,0,1)

distance

distance(vec1, vec2)
Distance between two points.

Examples: 

distance(vec3(0,0,0), vec3(3,4,0))  → 5

Practical Examples

Circular Arrangement

# Position on circle
x = cos($index * 360 / $count) * $radius
z = sin($index * 360 / $count) * $radius

Damped Oscillation

# Sine wave with decay
amplitude = exp(-$index / 10) * $base_amp
offset = sin($index * 36) * amplitude

Responsive Scaling

# Scale based on input range
normalized = ($value - $min) / ($max - $min)
scaled = $out_min + normalized * ($out_max - $out_min)

Grid Snapping

# Snap to nearest grid point
snapped_x = round($x / $grid_size) * $grid_size
snapped_y = round($y / $grid_size) * $grid_size

Falloff

# Distance-based falloff
distance_ratio = distance($point, $center) / $max_distance
falloff = 1.0 - clamp(distance_ratio, 0, 1)
smooth_falloff = smoothstep(0, 1, falloff)

Alternating Pattern

# Switch between two values
value = $index % 2 == 0 ? $value_a : $value_b

See Also

Pro Tip: Combine functions for complex effects: 

offset = smoothstep(0, 1, fract($index / 10)) * sin($index * 36) * $amplitude