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MathUtils is a small static utility class with a linear range mapping function and the mathematical constant pi. All members are static — no instance is needed. It is commonly used to convert between coordinate spaces, drive wave-based animations, and scale game values such as health or progress bars. 
#include "include/headers/MathUtils.h"  // included automatically via Fazen.h

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Members

MemberTypeValue / SignatureDescription
pistatic constexpr double3.141592653589793238Mathematical constant π
Mapstatic floatMap(float value, float x1, float x2, float y1, float y2)Linearly maps value from [y1, y2] to [x1, x2] (inverse of parameter-name convention)

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static constexpr double pi

A compile-time constant equal to 3.141592653589793238. Use it with std::sin, std::cos, or any formula that requires radians.

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static float Map(float value, float x1, float x2, float y1, float y2)

Linearly scales value from the range [y1, y2] back to the range [x1, x2]. Despite the parameter naming convention suggesting a forward [x1,x2] → [y1,y2] mapping, the implementation computes the inverse direction. Values outside [y1, y2] are extrapolated linearly.

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Map() Formula

The implementation computes slope m and intercept b from the x/y ranges, then solves the inverse: 
m = (y2 - y1) / (x2 - x1)
b = y1 - m * x1
result = (value - b) / m
Substituting b and simplifying: 
result = (value - y1) * (x2 - x1) / (y2 - y1) + x1
When value equals y1 the result is x1; when value equals y2 the result is x2.

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Parameters

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value
float
required
The input value to map. Treated as a point within or outside the [y1, y2] range.
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x1
float
required
The lower bound of the output range. Returned when value equals y1.
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x2
float
required
The upper bound of the output range. Returned when value equals y2. Must not equal x1 (would produce a division by zero via slope m).
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y1
float
required
The lower bound of the input range. When value equals y1, the result is x1.
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y2
float
required
The upper bound of the input range. When value equals y2, the result is x2. Must not equal y1 (division by zero in the inverse step).

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Usage Examples

// Convert a screen-space pixel X value (y-range) back to console cell index (x-range)
// e.g. pixel 480 in [0,960] maps to cell 40 in [0,80]
float cellX = MathUtils::Map(pixelX, 0, 80, 0, 960);

// Animate a sine wave: sin(t) is in [-1,1] (y-range), map to rows [5,35] (x-range)
float t = frameCount * 0.05f;
float y = MathUtils::Map(std::sin(t), 5.0f, 35.0f, -1.0f, 1.0f);
Point wave(50.0f, y, yellowF);
In the sine wave example, std::sin(t) is the input value drawn from the [y1, y2] range [-1, 1]. The output is scaled to the [x1, x2] range [5, 35], producing smooth oscillation between rows 5 and 35.

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