Math

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🧮 Math Utilities

The Formic API provides a set of mathematical utilities for handling tabulated functions — functions defined by discrete data points and evaluated via interpolation. These utilities are essential for physics simulations, thermodynamic tables, and any situation where continuous formulas are too complex or unknown.

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📊 Overview

Class	Purpose
OneDTabulatedFunction	Represents a 1D function defined by sampled points
ReversibleOneDTabulatedFunction	A 1D function with both forward and inverse lookup
TwoDTabulatedFunction	Represents a 2D function with bilinear interpolation

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🔹 OneDTabulatedFunction

A one-dimensional tabulated function f(x) built from discrete (x, y) pairs. It supports both linear and logarithmic step modes for sampling or evaluation.

🧩 Example Usage

TreeMap<Float, Float> data = new TreeMap<>();
data.put(100f, 1.2f);
data.put(200f, 1.8f);
data.put(300f, 2.5f);

OneDTabulatedFunction func = new OneDTabulatedFunction(
    data,
    100f, // step size
    StepMode.LINEAR,
    true  // clamp to range
);

float result = func.evaluate(250f); // Interpolated value ≈ 2.15

💡 Step Modes

• LINEAR — uniform spacing in regular space
• LOG — uniform spacing in logarithmic space (useful for exponential relationships)

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🔹 ReversibleOneDTabulatedFunction

A bidirectional version of the 1D function, which automatically builds both f(x) and its inverse f⁻¹(y). This is particularly useful when modeling relationships like temperature ↔ pressure or density ↔ energy.

🧠 Core Idea

This class constructs two interpolated functions:

• f(x) — forward table (e.g. temperature → pressure)
• inverse_f(x) — reverse table (e.g. pressure → temperature)

Both are generated with configurable step modes and sampling resolutions.

🧩 Example Usage

// Define a simple relationship: P = x^2
ReversibleOneDTabulatedFunction pressureTemperature =
    new ReversibleOneDTabulatedFunction(
        x -> x * x,         // f(x)
        0f, 100f,           // domain
        StepMode.LINEAR,    // forward step mode
        1f,                 // forward step
        StepMode.LOG,       // inverse step mode
        0.02f               // inverse step
    );

float P = pressureTemperature.getF(50f);       // Forward: P = 2500
float T = pressureTemperature.getInverseF(2500f); // Inverse: T ≈ 50

⚙️ How It Works

1. Samples the forward function f(x) between min and max using the chosen StepMode.
2. Inverts the mapping to produce a smooth lookup from y → x.
3. Interpolates during evaluation for continuous results.

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🔹 TwoDTabulatedFunction

Represents a two-dimensional tabulated surface f(x, y) — ideal for simulations like:

• Pressure as a function of temperature and density
• Reaction rates across two parameters
• Terrain, atmosphere, or fluid property maps

🧩 Example Usage

TwoDTabulatedFunction table = new TwoDTabulatedFunction(
    new float[]{0, 50, 100},          // X-axis (temperature)
    new float[]{0, 1, 2},             // Y-axis (density)
    new float[][]{
        {1.0f, 1.5f, 2.0f},           // f(x=0)
        {2.0f, 2.5f, 3.0f},           // f(x=50)
        {3.0f, 3.5f, 4.0f}            // f(x=100)
    }
);

float value = table.evaluate(25f, 1.5f); // Bilinear interpolation

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🧠 Summary

Utility	Type	Key Feature
OneDTabulatedFunction	1D	Simple interpolation over sampled data
ReversibleOneDTabulatedFunction	1D	Supports both forward and inverse lookup
TwoDTabulatedFunction	2D	Bilinear interpolation across a grid

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🔗 Related Pages:

• Data Loaders — load tabulated datasets from datapacks
• Formic API Home

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