Available Functions

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Overview

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Variables

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Trigonometric Functions

// Sine wave
sin(t)           // Range: [-1, 1]

// Cosine wave
cos(t)           // Range: [-1, 1]

// Circular motion
10 * cos(t)      // X component
10 * sin(t)      // Y component

// Phase-shifted oscillation
sin(t * 0.5)     // Slower frequency
sin(t + PI/4)    // 45° phase shift

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Available Functions:

• sin(x) - Sine of x (x in radians)
• cos(x) - Cosine of x
• tan(x) - Tangent of x
• asin(x) - Arcsine (inverse sine)
• acos(x) - Arccosine (inverse cosine)
• atan(x) - Arctangent (inverse tangent)
• atan2(y, x) - Two-argument arctangent (returns angle in correct quadrant)

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Example Use Cases:

sin(t * 0.5) * 5

Fx: cos(t) * 10
Fy: sin(t) * 10

atan2(y, x)

Fx: -x
Fy: -2.25 * y

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Hyperbolic Functions

// Hyperbolic tangent
tanh(x)                    // Range: (-1, 1)
                          // Smooth bounded function

// Soft clipping
20 * tanh(sin(t))         // Bounded oscillation

// Sigmoid-like behavior
tanh(t - 5)               // Smooth step at t=5

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Available Functions:

• sinh(x) - Hyperbolic sine: (e^x - e^(-x)) / 2
• cosh(x) - Hyperbolic cosine: (e^x + e^(-x)) / 2
• tanh(x) - Hyperbolic tangent: sinh(x) / cosh(x)
• asinh(x) - Inverse hyperbolic sine
• acosh(x) - Inverse hyperbolic cosine
• atanh(x) - Inverse hyperbolic tangent

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Why Use Hyperbolic Functions?

// Instead of hard clipping:
min(max(value, -1), 1)  // Sharp corners

// Use tanh for smooth saturation:
tanh(value)             // Smooth curve

// Overdamped motion
-z * 0.5 + 20 * tanh(sin(t))

// Growth that stabilizes
10 * tanh(t / 5)

// Catenary curve
cosh(x / 10) - 1

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Exponential and Logarithmic

// Natural exponential
exp(x)                    // e^x

// Exponential decay
exp(-t * 0.5)            // Decay with half-life

// Gaussian-like
exp(-x^2 - y^2)          // Radial decay from origin

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Available Functions:

• exp(x) - Euler’s number raised to x: e^x
• log(x) - Natural logarithm (base e)
• log10(x) - Base-10 logarithm
• log2(x) - Base-2 logarithm
• sqrt(x) - Square root: √x
• cbrt(x) - Cube root: ∛x
• pow(x, y) - x raised to power y (can also use x^y or x**y)

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Operators

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Arithmetic Operators

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Comparison & Logic

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Utility Functions

// Absolute value
abs(x)                   // |x|

// Always positive force
abs(cos(t*0.2))         // Pulsing without negative

// Sign function
sign(x)                  // -1, 0, or 1
sign(x) * abs(x)^2      // Preserve sign in power

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Available Functions:

• abs(x) - Absolute value: |x|
• sign(x) - Sign of x: -1, 0, or 1
• floor(x) - Round down to nearest integer
• ceil(x) - Round up to nearest integer
• round(x) - Round to nearest integer
• trunc(x) - Remove fractional part
• min(a, b, ...) - Smallest value
• max(a, b, ...) - Largest value
• random() - Random value in [0, 1)

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Practical Examples:

-x * abs(cos(t*0.2))

max(0, -z)

floor(t) * 5

(random() - 0.5) * 2

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Mathematical Constants

// Circular motion period
sin(2 * PI * t)         // Period = 1 second

// Exponential decay
exp(-t / E)             // Characteristic time = e

// 45-degree angle
PI / 4                  // Radians

// Convert degrees to radians
angle_deg * PI / 180

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Advanced Techniques

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Composition

// Modulated oscillation
sin(t) * cos(t * 0.1)

// Exponentially decaying oscillation
exp(-t * 0.2) * sin(t * 3)

// Logarithmic spiral
log(t + 1) * cos(t)
log(t + 1) * sin(t)

// Bounded chaotic-like
tanh(sin(t) * cos(t * 1.7) * 3)

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Avoiding Singularities

// BAD: Can divide by zero
x / sqrt(x^2 + y^2)

// GOOD: Add epsilon
x / sqrt(x^2 + y^2 + 0.001)

// BAD: log(0) is undefined
log(t)

// GOOD: Offset to avoid zero
log(t + 1)

// BAD: Negative square root
sqrt(x)

// GOOD: Use absolute value
sqrt(abs(x))

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Performance Optimization

// This is fine - compiled once:
-x / (sqrt(x^2 + y^2 + z^2 + 0.1)^3) + 
 sin(t * 0.5) * tanh(sqrt(x^2 + y^2) / 10)

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Function Categories Summary

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Next Steps