anki-3d-engine/AnKi/Math/Functions.h

// Copyright (C) 2009-present, Panagiotis Christopoulos Charitos and contributors.
// All rights reserved.
// Code licensed under the BSD License.
// http://www.anki3d.org/LICENSE

#pragma once

#include <AnKi/Util/Functions.h>
#include <cmath>
#include <cstdlib>

namespace anki {

/// @addtogroup math
/// @{

/// Just PI.
constexpr F32 kPi = 3.14159265358979323846f;

/// Floating point epsilon.
constexpr F32 kEpsilonf = 1.0e-6f;

template<typename T>
inline T sin(const T rad)
{
	return std::sin(rad);
}

template<typename T>
inline T cos(const T rad)
{
	return std::cos(rad);
}

template<typename T>
inline T tan(const T rad)
{
	return std::tan(rad);
}

template<typename T>
inline T acos(const T x)
{
	ANKI_ASSERT(x >= T(-1) && x <= T(1));
	return std::acos(x);
}

template<typename T>
inline T asin(const T x)
{
	return std::asin(x);
}

template<typename T>
inline T atan(const T x)
{
	return std::atan(x);
}

template<typename T>
inline T atan2(const T x, const T y)
{
	return std::atan2(x, y);
}

void sinCos(const F32 a, F32& sina, F32& cosa);
void sinCos(const F64 a, F64& sina, F64& cosa);

template<typename T>
inline T sqrt(const T x) requires(std::is_floating_point<T>::value)
{
	return std::sqrt(x);
}

template<typename T>
inline T sqrt(const T x) requires(std::is_integral<T>::value)
{
	return T(std::sqrt(F64(x)));
}

template<typename T>
inline T square(const T x)
{
	return x * x;
}

template<typename T>
inline T fract(const T x)
{
	return x - std::floor(x);
}

template<typename T>
inline T mod(const T x, const T y)
{
	return x - y * std::floor(x / y);
}

/// Like GLSL's mix.
template<typename T, typename Y>
inline T mix(T x, T y, Y factor)
{
	return x * (T(1) - factor) + y * factor;
}

/// Like GLSL's modf
template<typename T>
inline T modf(T x, T& intPart)
{
	return std::modf(x, &intPart);
}

/// The same as abs/fabs. For ints.
template<typename T>
inline constexpr T absolute(const T f) requires(std::is_integral<T>::value&& std::is_signed<T>::value)
{
	return (f < T(0)) ? -f : f;
}

/// The same as abs/fabs. For floats.
template<typename T>
inline constexpr T absolute(const T f) requires(std::is_floating_point<T>::value&& std::is_same_v<T, double>)
{
	return fabs(f);
}

/// The same as abs/fabs. For floats.
template<typename T>
inline constexpr T absolute(const T f) requires(std::is_floating_point<T>::value&& std::is_same_v<T, float>)
{
	return fabsf(f);
}

template<typename T>
inline constexpr T pow(const T x, const T exp)
{
	return T(std::pow(x, exp));
}

template<typename T>
inline constexpr T log2(const T x)
{
	return T(std::log2(x));
}

template<typename T>
inline constexpr Bool isZero(const T f, const T e = kEpsilonf) requires(std::is_floating_point<T>::value)
{
	return absolute<T>(f) < e;
}

template<typename T>
inline constexpr Bool isZero(const T f) requires(std::is_integral<T>::value)
{
	return f == 0;
}

template<typename T>
inline constexpr T toRad(const T degrees) requires(std::is_floating_point<T>::value)
{
	return degrees * (kPi / T(180));
}

template<typename T>
inline constexpr T toDegrees(const T rad)
{
	return rad * (T(180) / kPi);
}

template<typename T>
inline constexpr T saturate(T v)
{
	return clamp<T>(v, T(0), T(1));
}

/// Returns 1 or -1 based on the sign
template<typename T>
inline constexpr T sign(T v)
{
	return (v > T(0)) ? T(1) : T(-1);
}

/// Same as smoothstep in glsl
template<typename T>
inline constexpr T smoothstep(T edge0, T edge1, T value)
{
	value = clamp((value - edge0) / (edge1 - edge0), T(0), T(1));
	return value * value * (T(3) - T(2) * value);
}

/// Linear interpolation between values
/// @param[in] from Starting value
/// @param[in] to Ending value
/// @param[in] u The percentage from the from "from" value. Values from [0.0, 1.0]
template<typename T>
inline constexpr T linearInterpolate(const T& from, const T& to, F32 u)
{
	return from * T(1.0f - u) + to * T(u);
}

/// Cosine interpolation
/// @param[in] from Starting value
/// @param[in] to Ending value
/// @param[in] u The percentage from the from "from" value. Values from [0.0, 1.0]
template<typename T>
inline T cosInterpolate(const T& from, const T& to, F32 u)
{
	const F32 u2 = (1.0f - cos<F32>(u * kPi)) / 2.0f;
	return from * T(1.0f - u2) + to * T(u2);
}

/// Cubic interpolation
/// @param[in] a Point a
/// @param[in] b Point b
/// @param[in] c Point c
/// @param[in] d Point d
/// @param[in] u The percentage from the from b point to d point. Value from [0.0, 1.0]
template<typename T>
inline constexpr T cubicInterpolate(const T& a, const T& b, const T& c, const T& d, F32 u)
{
	const F32 u2 = u * u;
	const T a0 = d - c - a + b;
	const T a1 = a - b - a0;
	const T a2 = c - a;
	const T a3 = b;

	return (a0 * u * u2 + a1 * u2 + a2 * u + a3);
}

/// Pack 4 color components to R10G10B10A2 SNORM format.
inline U32 packColorToR10G10B10A2SNorm(F32 r, F32 g, F32 b, F32 a)
{
	union SignedR10G10B10A10
	{
		struct
		{
			I32 m_x : 10;
			I32 m_y : 10;
			I32 m_z : 10;
			I32 m_w : 2;
		} m_unpacked;
		U32 m_packed;
	};

#if ANKI_COMPILER_GCC_COMPATIBLE
#	pragma GCC diagnostic push
#	pragma GCC diagnostic ignored "-Wconversion"
#endif

	SignedR10G10B10A10 out;
	out.m_unpacked.m_x = I32(round(r * 511.0f));
	out.m_unpacked.m_y = I32(round(g * 511.0f));
	out.m_unpacked.m_z = I32(round(b * 511.0f));
	out.m_unpacked.m_w = I32(round(a * 1.0f));

#if ANKI_COMPILER_GCC_COMPATIBLE
#	pragma GCC diagnostic pop
#endif

	return out.m_packed;
}

template<typename TVec4>
inline U32 packSnorm4x8(const TVec4& v)
{
	union
	{
		I8 in[4];
		U32 out;
	} u;

	const TVec4 result = (v.clamp(-1.0f, 1.0f) * 127.0f).round();

	u.in[0] = I8(result[0]);
	u.in[1] = I8(result[1]);
	u.in[2] = I8(result[2]);
	u.in[3] = I8(result[3]);

	return u.out;
}

/// Compute the abs triangle area.
template<typename TVec>
inline F32 computeTriangleArea(const TVec& a, const TVec& b, const TVec& c)
{
	const TVec ab = b - a;
	const TVec ac = c - a;
	const F32 area = ab.cross(ac).length() / 2.0f;
	return absolute(area);
}
/// @}

} // end namespace anki

// Now lay out functions that include other math headers

#include <AnKi/Math/Vec.h>

namespace anki {

template<typename T>
TVec<T, 3> sphericalToCartesian(T polar, T azimuth)
{
	TVec<T, 3> out;
	out.x() = cos(polar) * sin(azimuth);
	out.y() = cos(polar) * cos(azimuth);
	out.z() = sin(polar);
	return out;
}

} // end namespace anki