harfang3d/harfang/foundation/math.h

// HARFANG(R) Copyright (C) 2021 Emmanuel Julien, NWNC HARFANG. Released under GPL/LGPL/Commercial Licence, see licence.txt for details.

#pragma once

#include <cstddef>
#include <cstdint>
#include <limits>

namespace hg {

static const float Pi = 3.1415926535F;

static const float HalfPi = Pi / 2.F;
static const float TwoPi = Pi * 2.F;

/// Return the absolute value of the function input.
template <class T> constexpr T inline Abs(const T &v) {
	return v < 0 ? -v : v;
}

/// Return the minimum of two values.
template <class T> constexpr T inline Min(const T &a, const T &b) {
	return a < b ? a : b;
}

template <class T> constexpr T inline Min(const T &a, const T &b, const T &c) {
	return Min(Min(a, b), c);
}

/// Return the maximum of two values.
template <class T> constexpr T inline Max(const T &a, const T &b) {
	return a > b ? a : b;
}

template <class T> constexpr T inline Max(const T &a, const T &b, const T &c) {
	return Max(Max(a, b), c);
}

/// Clip a value to the specified inclusive interval.
template <class T> constexpr T inline Clamp(const T &v, const T &min, const T &max) {
	return v < min ? min : (v > max ? max : v);
}

/// Linear interpolate between two vectors on the [0;1] interval.
/// @see LinearInterpolate.
template <class T> constexpr T inline Lerp(const T &a, const T &b, float k) {
	return T(a * (1.F - k) + b * k);
}

template <class T> T inline Wrap(T v, T range_start, T range_end) {
	const T start = Min(range_start, range_end);
	const T end = Max(range_start, range_end);
	const T dt = end - start;

	while (v < start) {
		v += dt;
	}

	while (v > end) {
		v -= dt;
	}

	return v;
}

float Sqrt(float v);

inline bool Equal(float a, float b) {
	return Abs(a - b) <= std::numeric_limits<float>::epsilon();
}

inline bool NotEqual(float a, float b) {
	return Abs(a - b) > std::numeric_limits<float>::epsilon();
}

inline bool AlmostEqual(float a, float b, float e = 0.00001F) {
	return Abs(a - b) <= e;
}

inline bool EqualZero(float a) {
	return Abs(a) <= std::numeric_limits<float>::epsilon();
}

inline bool NotEqualZero(float a) {
	return Abs(a) > std::numeric_limits<float>::epsilon();
}

inline bool AlmostEqualZero(float a, float e) {
	return Abs(a) <= e;
}

float Pow(float v, float exp);

float Ceil(float);
float Floor(float);
float Round(float);
float Mod(float);

float Frac(float);

float RangeAdjust(float v, float old_min, float old_max, float new_min, float new_max);

float Quantize(float v, float q);

float Sin(float);
float ASin(float);
float Cos(float);
float ACos(float);
float Tan(float);
float ATan(float);

bool IsFinite(float);

template <typename T> constexpr T LinearInterpolate(T y0, T y1, float t) {
	return y0 + (y1 - y0) * t;
}

/// Compute the cosine interpolated value between `y0` and `y1` at `t`.
/// @see LinearInterpolate, CubicInterpolate and HermiteInterpolate.
template <typename T> T CosineInterpolate(T y0, T y1, float t) {
	const float t2 = (1.F - Cos(t * Pi)) / 2.F;
	return y0 * (1.F - t2) + y1 * t2;
}

/// Perform a cubic interpolation across four values with `t` in the [0;1] range between `y1` and `y2`.
/// @see LinearInterpolate, CosineInterpolate and HermiteInterpolate.
template <typename T> T CubicInterpolate(T y0, T y1, T y2, T y3, float t) {
	const float t2 = t * t;
	T a0 = y3 - y2 - y0 + y1, a1 = y0 - y1 - a0, a2 = y2 - y0, a3 = y1;
	return a0 * t * t2 + a1 * t2 + a2 * t + a3;
}

/*
	tension: 1 is high, 0 normal, -1 is low
	bias: 0 is even, positive is towards first segment, negative towards the other
*/
template <typename T> T HermiteInterpolate(T y0, T y1, T y2, T y3, float t, float tension, float bias) {
	const float t2 = t * t;
	const float t3 = t2 * t;
	T t0 = (y1 - y0) * (1.F + bias) * (1.F - tension) / 2.F;
	t0 += (y2 - y1) * (1.F - bias) * (1.F - tension) / 2.F;
	T t1 = (y2 - y1) * (1.F + bias) * (1.F - tension) / 2.F;
	t1 += (y3 - y2) * (1.F - bias) * (1.F - tension) / 2.F;
	const float a0 = 2.F * t3 - 3.F * t2 + 1.F;
	const float a1 = t3 - 2.F * t2 + t;
	const float a2 = t3 - t2;
	const float a3 = -2.F * t3 + 3.F * t2;
	return y1 * a0 + t0 * a1 + t1 * a2 + y2 * a3;
}

template <class T> T LinearInterpolateArray(uint32_t count, const T values[], float t) {
	const float s = t * static_cast<float>(count - 1);
	uint32_t lo = static_cast<uint32_t>(s), hi = lo + 1;

	lo = Clamp<uint32_t>(lo, 0, count - 1);
	hi = Clamp<uint32_t>(hi, 0, count - 1);

	return LinearInterpolate(values[lo], values[hi], s - static_cast<float>(lo));
}

template <typename T> inline T getPOT(T v) {
	T n = 1;
	while (n < v) {
		n *= 2;
	}
	return n;
}

template <typename T> inline bool isPOT(T v) {
	return v == getPOT(v);
}

} // namespace hg