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authorGravatar gingerBill 2016-04-08 21:40:53 +0100
committerGravatar gingerBill 2016-04-08 21:40:53 +0100
commit24d6605d1758445fe9de2dff172b7bceb6d95a39 (patch)
tree2e6502854212f4062ebd5463684bad1e91e309a5
parentgb_math.h - v0.04 - Namespace everything with gb (diff)
Delete gb_math.hpp
-rw-r--r--gb_math.hpp3882
1 files changed, 0 insertions, 3882 deletions
diff --git a/gb_math.hpp b/gb_math.hpp
deleted file mode 100644
index b81bde9..0000000
--- a/gb_math.hpp
+++ /dev/null
@@ -1,3882 +0,0 @@
-// gb_math.hpp - v0.03a - public domain C++11 math library - no warranty implied; use at your own risk
-// A C++11 math library geared towards game development
-// This is meant to be used the gb.hpp library but it doesn't have to be
-
-/*
-Version History:
- 0.04 - Change const position convention
- 0.03a - Remove templated clamp
- 0.03 - Remove templated min/max/clamp
- 0.02b - Typo fixes
- 0.02a - Better `static` keywords
- 0.02 - More Angle Units and templated min/max/clamp/lerp
- 0.01 - Initial Version
-
-LICENSE
- This software is in the public domain. Where that dedication is not
- recognized, you are granted a perpetual, irrevocable license to copy,
- distribute, and modify this file as you see fit.
-
-WARNING
- - This library is _slightly_ experimental and features may not work as expected.
- - This also means that many functions are not documented.
- - This library was developed in conjunction with `gb.hpp`
-
-CONTENTS:
- - Common Macros
- - Assert
- - Types
- - Vector(2,3,4)
- - Complex
- - Quaternion
- - Matrix(2,3,4)
- - Euler_Angles
- - Transform
- - Aabb
- - Sphere
- - Plane
- - Operations
- - Functions & Constants
- - Type Functions
- - Random
-*/
-
-#ifndef GB_MATH_INCLUDE_GB_MATH_HPP
-#define GB_MATH_INCLUDE_GB_MATH_HPP
-
-#if !defined(__cplusplus) && __cplusplus >= 201103L
- #error This library is only for C++11 and above
-#endif
-
-// NOTE(bill): Because static means three different things in C/C++
-// Great Design(!)
-#ifndef global_variable
-#define global_variable static
-#define internal_linkage static
-#define local_persist static
-#endif
-
-#if defined(_MSC_VER)
- #define _ALLOW_KEYWORD_MACROS
-
- #ifndef alignof // Needed for MSVC 2013 'cause Microsoft "loves" standards
- #define alignof(x) __alignof(x)
- #endif
-#endif
-
-
-////////////////////////////////
-/// ///
-/// System OS ///
-/// ///
-////////////////////////////////
-#if defined(_WIN32) || defined(_WIN64)
- #ifndef GB_SYSTEM_WINDOWS
- #define GB_SYSTEM_WINDOWS 1
- #endif
-#elif defined(__APPLE__) && defined(__MACH__)
- #ifndef GB_SYSTEM_OSX
- #define GB_SYSTEM_OSX 1
- #endif
-#elif defined(__unix__)
- #ifndef GB_SYSTEM_UNIX
- #define GB_SYSTEM_UNIX 1
- #endif
-
- #if defined(__linux__)
- #ifndef GB_SYSTEM_LINUX
- #define GB_SYSTEM_LINUX 1
- #endif
- #elif defined(__FreeBSD__) || defined(__FreeBSD_kernel__)
- #ifndef GB_SYSTEM_FREEBSD
- #define GB_SYSTEM_FREEBSD 1
- #endif
- #else
- #error This UNIX operating system is not supported by gb.hpp
- #endif
-#else
- #error This operating system is not supported by gb.hpp
-#endif
-
-
-#if defined(_MSC_VER)
- // Microsoft Visual Studio
- #define GB_COMPILER_MSVC 1
-#elif defined(__clang__)
- // Clang
- #define GB_COMPILER_CLANG 1
-#elif defined(__GNUC__) || defined(__GNUG__) && !(defined(__clang__) || defined(__INTEL_COMPILER))
- // GNU GCC/G++ Compiler
- #define GB_COMPILER_GNU_GCC 1
-#elif defined(__INTEL_COMPILER)
- // Intel C++ Compiler
- #define GB_COMPILER_INTEL 1
-#endif
-
-////////////////////////////////
-/// ///
-/// Environment Bit Size ///
-/// ///
-////////////////////////////////
-#if defined(_WIN32) || defined(_WIN64)
- #if defined(_WIN64)
- #ifndef GB_ARCH_64_BIT
- #define GB_ARCH_64_BIT 1
- #endif
- #else
- #ifndef GB_ARCH_32_BIT
- #define GB_ARCH_32_BIT 1
- #endif
- #endif
-#endif
-
-// TODO(bill): Check if this KEPLER_ENVIRONMENT works on clang
-#if defined(__GNUC__)
- #if defined(__x86_64__) || defined(__ppc64__)
- #ifndef GB_ARCH_64_BIT
- #define GB_ARCH_64_BIT 1
- #endif
- #else
- #ifndef GB_ARCH_32_BIT
- #define GB_ARCH_32_BIT 1
- #endif
- #endif
-#endif
-
-
-
-#ifndef GB_EDIAN_ORDER
-#define GB_EDIAN_ORDER
- #define GB_IS_BIG_EDIAN (!*(unsigned char*)&(unsigned short){1})
- #define GB_IS_LITTLE_EDIAN (!GB_IS_BIG_EDIAN)
-#endif
-
-#ifndef GB_IS_POWER_OF_TWO
-#define GB_IS_POWER_OF_TWO(x) ((x) != 0) && !((x) & ((x) - 1))
-#endif
-
-
-#if !defined(GB_HAS_NO_CONSTEXPR)
- #if defined(_GNUC_VER) && _GNUC_VER < 406 // Less than gcc 4.06
- #define GB_HAS_NO_CONSTEXPR 1
- #elif defined(_MSC_VER) && _MSC_VER < 1900 // Less than Visual Studio 2015/MSVC++ 14.0
- #define GB_HAS_NO_CONSTEXPR 1
- #elif !defined(__GXX_EXPERIMENTAL_CXX0X__) && __cplusplus < 201103L
- #define GB_HAS_NO_CONSTEXPR 1
- #endif
-#endif
-
-#if defined(GB_HAS_NO_CONSTEXPR)
- #define GB_CONSTEXPR
-#else
- #define GB_CONSTEXPR constexpr
-#endif
-
-#ifndef GB_FORCE_INLINE
- #if defined(_MSC_VER)
- #define GB_FORCE_INLINE __forceinline
- #else
- #define GB_FORCE_INLINE __attribute__ ((__always_inline__))
- #endif
-#endif
-
-#if defined(GB_SYSTEM_WINDOWS)
- #define NOMINMAX 1
- #define VC_EXTRALEAN 1
- #define WIN32_EXTRA_LEAN 1
- #define WIN32_LEAN_AND_MEAN 1
-
- #include <windows.h>
- #include <wincrypt.h>
-
- #undef NOMINMAX
- #undef VC_EXTRALEAN
- #undef WIN32_EXTRA_LEAN
- #undef WIN32_LEAN_AND_MEAN
-#else
- //
-#endif
-
-
-#if !defined(GB_ASSERT)
- #if !defined(NDEBUG)
- #define GB_ASSERT(x, ...) ((void)(::gb__assert_handler((x), #x, __FILE__, __LINE__, ##__VA_ARGS__)))
-
- /// Helper function used as a better alternative to assert which allows for
- /// optional printf style error messages
- extern "C" inline void
- gb__assert_handler(bool condition, const char* condition_str,
- const char* filename, size_t line,
- const char* error_text = nullptr, ...)
- {
- if (condition)
- return;
-
- fprintf(stderr, "ASSERT! %s(%lu): %s", filename, line, condition_str);
- if (error_text)
- {
- fprintf(stderr, " - ");
-
- va_list args;
- va_start(args, error_text);
- vfprintf(stderr, error_text, args);
- va_end(args);
- }
- fprintf(stderr, "\n");
- // TODO(bill): Get a better way to abort
- *(int*)0 = 0;
- }
-
- #else
- #define GB_ASSERT(x, ...) ((void)sizeof(x))
- #endif
-#endif
-
-#if !defined(__GB_NAMESPACE_PREFIX) && !defined(GB_NO_GB_NAMESPACE)
- #define __GB_NAMESPACE_PREFIX gb
-#else
- #define __GB_NAMESPACE_PREFIX
-#endif
-
-#if defined(GB_NO_GB_NAMESPACE)
- #define __GB_NAMESPACE_START
- #define __GB_NAMESPACE_END
-#else
- #define __GB_NAMESPACE_START namespace __GB_NAMESPACE_PREFIX {
- #define __GB_NAMESPACE_END } // namespace __GB_NAMESPACE_PREFIX
-#endif
-
-
-#if !defined(GB_BASIC_WITHOUT_NAMESPACE)
-__GB_NAMESPACE_START
-#endif // GB_BASIC_WITHOUT_NAMESPACE
-
-////////////////////////////////
-/// ///
-/// Types ///
-/// ///
-////////////////////////////////
-
-
-#ifndef GB_BASIC_TYPES
-#define GB_BASIC_TYPES
- #if defined(_MSC_VER)
- using u8 = unsigned __int8;
- using s8 = signed __int8;
- using u16 = unsigned __int16;
- using s16 = signed __int16;
- using u32 = unsigned __int32;
- using s32 = signed __int32;
- using u64 = unsigned __int64;
- using s64 = signed __int64;
- #else
- using u8 = unsigned char;
- using s8 = signed char;
- using u16 = unsigned short;
- using s16 = signed short;
- using u32 = unsigned int;
- using s32 = signed int;
- using u64 = unsigned long long;
- using s64 = signed long long;
- #endif
-
- static_assert( sizeof(u8) == 1, "u8 is not 8 bits");
- static_assert(sizeof(u16) == 2, "u16 is not 16 bits");
- static_assert(sizeof(u32) == 4, "u32 is not 32 bits");
- static_assert(sizeof(u64) == 8, "u64 is not 64 bits");
-
- using f32 = float;
- using f64 = double;
-
- #if defined(GB_B8_AS_BOOL)
- using b8 = bool;
- #else
- using b8 = s8;
- #endif
- using b32 = s32;
-
- // NOTE(bill): (std::)size_t is not used not because it's a bad concept but on
- // the platforms that I will be using:
- // sizeof(size_t) == sizeof(usize) == sizeof(ssize)
- // NOTE(bill): This also allows for a signed version of size_t which is similar
- // to ptrdiff_t
- // NOTE(bill): If (u)intptr is a better fit, please use that.
- // NOTE(bill): Also, I hate the `_t` suffix
- #if defined(GB_ARCH_64_BIT)
- using ssize = s64;
- using usize = u64;
- #elif defined(GB_ARCH_32_BIT)
- using usize = s32;
- using usize = u32;
- #else
- #error Unknown architecture bit size
- #endif
-
- static_assert(sizeof(usize) == sizeof(size_t),
- "`usize` is not the same size as `size_t`");
- static_assert(sizeof(ssize) == sizeof(usize),
- "`ssize` is not the same size as `usize`");
-
- using intptr = intptr_t;
- using uintptr = uintptr_t;
-
- using ptrdiff = ptrdiff_t;
-
-#endif
-
-#if !defined(GB_U8_MIN)
- #define GB_U8_MIN 0u
- #define GB_U8_MAX 0xffu
- #define GB_S8_MIN (-0x7f - 1)
- #define GB_S8_MAX 0x7f
-
- #define GB_U16_MIN 0u
- #define GB_U16_MAX 0xffffu
- #define GB_S16_MIN (-0x7fff - 1)
- #define GB_S16_MAX 0x7fff
-
- #define GB_U32_MIN 0u
- #define GB_U32_MAX 0xffffffffu
- #define GB_S32_MIN (-0x7fffffff - 1)
- #define GB_S32_MAX 0x7fffffff
-
- #define GB_U64_MIN 0ull
- #define GB_U64_MAX 0xffffffffffffffffull
- #define GB_S64_MIN (-0x7fffffffffffffffll - 1)
- #define GB_S64_MAX 0x7fffffffffffffffll
-#endif
-
-#if defined(GB_ARCH_64_BIT) && !defined(GB_USIZE_MIX)
- #define GB_USIZE_MIX GB_U64_MIN
- #define GB_USIZE_MAX GB_U64_MAX
-
- #define GB_SSIZE_MIX GB_S64_MIN
- #define GB_SSIZE_MAX GB_S64_MAX
-#elif defined(GB_ARCH_32_BIT) && !defined(GB_USIZE_MIX)
- #define GB_USIZE_MIX GB_U32_MIN
- #define GB_USIZE_MAX GB_U32_MAX
-
- #define GB_SSIZE_MIX GB_S32_MIN
- #define GB_SSIZE_MAX GB_S32_MAX
-#endif
-
-#if defined(GB_BASIC_WITHOUT_NAMESPACE) && !defined(U8_MIN)
- #define U8_MIN 0u
- #define U8_MAX 0xffu
- #define S8_MIN (-0x7f - 1)
- #define S8_MAX 0x7f
-
- #define U16_MIN 0u
- #define U16_MAX 0xffffu
- #define S16_MIN (-0x7fff - 1)
- #define S16_MAX 0x7fff
-
- #define U32_MIN 0u
- #define U32_MAX 0xffffffffu
- #define S32_MIN (-0x7fffffff - 1)
- #define S32_MAX 0x7fffffff
-
- #define U64_MIN 0ull
- #define U64_MAX 0xffffffffffffffffull
- #define S64_MIN (-0x7fffffffffffffffll - 1)
- #define S64_MAX 0x7fffffffffffffffll
-
- #if defined(GB_ARCH_64_BIT) && !defined(GB_USIZE_MIX)
- #define USIZE_MIX U64_MIN
- #define USIZE_MAX U64_MAX
-
- #define SSIZE_MIX S64_MIN
- #define SSIZE_MAX S64_MAX
- #elif defined(GB_ARCH_32_BIT) && !defined(GB_USIZE_MIX)
- #define USIZE_MIX U32_MIN
- #define USIZE_MAX U32_MAX
-
- #define SSIZE_MIX S32_MIN
- #define SSIZE_MAX S32_MAX
- #endif
-#endif
-
-
-
-#if !defined(GB_BASIC_WITHOUT_NAMESPACE)
-__GB_NAMESPACE_END
-#endif // GB_BASIC_WITHOUT_NAMESPACE
-
-__GB_NAMESPACE_START
-#ifndef GB_SPECIAL_CASTS
-#define GB_SPECIAL_CASTS
- // IMPORTANT NOTE(bill): Very similar to doing `*(T*)(&u)` but easier/clearer to write
- // however, it can be dangerous if sizeof(T) > sizeof(U) e.g. unintialized memory, undefined behavior
- // *(T*)(&u) ~~ pseudo_cast<T>(u)
- template <typename T, typename U>
- inline T
- pseudo_cast(U const& u)
- {
- return reinterpret_cast<T const&>(u);
- }
-
- // NOTE(bill): Very similar to doing `*(T*)(&u)`
- template <typename Dest, typename Source>
- inline Dest
- bit_cast(Source const& source)
- {
- static_assert(sizeof(Dest) <= sizeof(Source),
- "bit_cast<Dest>(Source const&) - sizeof(Dest) <= sizeof(Source)");
- Dest dest;
- ::memcpy(&dest, &source, sizeof(Dest));
- return dest;
- }
-#endif
-// FORENOTE(bill): There used to be a magic_cast that was equivalent to
-// a C-style cast but I removed it as I could not get it work as intented
-// for everything using only C++ style casts
-
-#if !defined(GB_CASTS_WITHOUT_NAMESPACE)
-__GB_NAMESPACE_END
-#endif // GB_CASTS_WITHOUT_NAMESPACE
-
-__GB_NAMESPACE_START
-////////////////////////////////
-/// ///
-/// Math Types ///
-/// ///
-////////////////////////////////
-
-// TODO(bill): Should the math part be a separate library?
-
-struct Vector2
-{
- union
- {
- struct { f32 x, y; };
- f32 data[2];
- };
-
- inline f32 operator[](usize index) const { return data[index]; }
- inline f32& operator[](usize index) { return data[index]; }
-};
-
-struct Vector3
-{
- union
- {
- struct { f32 x, y, z; };
- struct { f32 r, g, b; };
- Vector2 xy;
- f32 data[3];
- };
-
- inline f32 operator[](usize index) const { return data[index]; }
- inline f32& operator[](usize index) { return data[index]; }
-};
-
-struct Vector4
-{
- union
- {
- struct { f32 x, y, z, w; };
- struct { f32 r, g, b, a; };
- struct { Vector2 xy, zw; };
- Vector3 xyz;
- Vector3 rgb;
- f32 data[4];
- };
-
- inline f32 operator[](usize index) const { return data[index]; }
- inline f32& operator[](usize index) { return data[index]; }
-};
-
-struct Complex
-{
- union
- {
- struct { f32 x, y; };
- struct { f32 real, imag; };
- f32 data[2];
- };
-
- inline f32 operator[](usize index) const { return data[index]; }
- inline f32& operator[](usize index) { return data[index]; }
-};
-
-struct Quaternion
-{
- union
- {
- struct { f32 x, y, z, w; };
- Vector3 xyz;
- f32 data[4];
- };
-
- inline f32 operator[](usize index) const { return data[index]; }
- inline f32& operator[](usize index) { return data[index]; }
-};
-
-struct Matrix2
-{
- union
- {
- struct { Vector2 x, y; };
- Vector2 columns[2];
- f32 data[4];
- };
-
- inline Vector2 operator[](usize index) const { return columns[index]; }
- inline Vector2& operator[](usize index) { return columns[index]; }
-};
-
-struct Matrix3
-{
- union
- {
- struct { Vector3 x, y, z; };
- Vector3 columns[3];
- f32 data[9];
- };
-
- inline Vector3 operator[](usize index) const { return columns[index]; }
- inline Vector3& operator[](usize index) { return columns[index]; }
-};
-
-struct Matrix4
-{
- union
- {
- struct { Vector4 x, y, z, w; };
- Vector4 columns[4];
- f32 data[16];
- };
-
- inline Vector4 operator[](usize index) const { return columns[index]; }
- inline Vector4& operator[](usize index) { return columns[index]; }
-};
-
-struct Angle
-{
- f32 radians;
-};
-
-struct Euler_Angles
-{
- Angle pitch, yaw, roll;
-};
-
-struct Transform
-{
- Vector3 position;
- Quaternion orientation;
- f32 scale;
- // NOTE(bill): Scale is only f32 to make sizeof(Transform) == 32 bytes
-};
-
-struct Aabb
-{
- Vector3 center;
- Vector3 half_size;
-};
-
-struct Oobb
-{
- Matrix4 transform;
- Aabb aabb;
-};
-
-struct Sphere
-{
- Vector3 center;
- f32 radius;
-};
-
-struct Plane
-{
- Vector3 normal;
- f32 distance; // negative distance to origin
-};
-
-////////////////////////////////
-/// ///
-/// Math Type Op Overloads ///
-/// ///
-////////////////////////////////
-
-// Vector2 Operators
-bool operator==(Vector2 a, Vector2 b);
-bool operator!=(Vector2 a, Vector2 b);
-
-Vector2 operator+(Vector2 a);
-Vector2 operator-(Vector2 a);
-
-Vector2 operator+(Vector2 a, Vector2 b);
-Vector2 operator-(Vector2 a, Vector2 b);
-
-Vector2 operator*(Vector2 a, f32 scalar);
-Vector2 operator*(f32 scalar, Vector2 a);
-
-Vector2 operator/(Vector2 a, f32 scalar);
-
-Vector2 operator*(Vector2 a, Vector2 b); // Hadamard Product
-Vector2 operator/(Vector2 a, Vector2 b); // Hadamard Product
-
-Vector2& operator+=(Vector2& a, Vector2 b);
-Vector2& operator-=(Vector2& a, Vector2 b);
-Vector2& operator*=(Vector2& a, f32 scalar);
-Vector2& operator/=(Vector2& a, f32 scalar);
-
-// Vector3 Operators
-bool operator==(Vector3 a, Vector3 b);
-bool operator!=(Vector3 a, Vector3 b);
-
-Vector3 operator+(Vector3 a);
-Vector3 operator-(Vector3 a);
-
-Vector3 operator+(Vector3 a, Vector3 b);
-Vector3 operator-(Vector3 a, Vector3 b);
-
-Vector3 operator*(Vector3 a, f32 scalar);
-Vector3 operator*(f32 scalar, Vector3 a);
-
-Vector3 operator/(Vector3 a, f32 scalar);
-
-Vector3 operator*(Vector3 a, Vector3 b); // Hadamard Product
-Vector3 operator/(Vector3 a, Vector3 b); // Hadamard Product
-
-Vector3& operator+=(Vector3& a, Vector3 b);
-Vector3& operator-=(Vector3& a, Vector3 b);
-Vector3& operator*=(Vector3& a, f32 scalar);
-Vector3& operator/=(Vector3& a, f32 scalar);
-
-// Vector4 Operators
-bool operator==(Vector4 a, Vector4 b);
-bool operator!=(Vector4 a, Vector4 b);
-
-Vector4 operator+(Vector4 a);
-Vector4 operator-(Vector4 a);
-
-Vector4 operator+(Vector4 a, Vector4 b);
-Vector4 operator-(Vector4 a, Vector4 b);
-
-Vector4 operator*(Vector4 a, f32 scalar);
-Vector4 operator*(f32 scalar, Vector4 a);
-
-Vector4 operator/(Vector4 a, f32 scalar);
-
-Vector4 operator*(Vector4 a, Vector4 b); // Hadamard Product
-Vector4 operator/(Vector4 a, Vector4 b); // Hadamard Product
-
-Vector4& operator+=(Vector4& a, Vector4 b);
-Vector4& operator-=(Vector4& a, Vector4 b);
-Vector4& operator*=(Vector4& a, f32 scalar);
-Vector4& operator/=(Vector4& a, f32 scalar);
-
-// Complex Operators
-bool operator==(Complex a, Complex b);
-bool operator!=(Complex a, Complex b);
-
-Complex operator+(Complex a);
-Complex operator-(Complex a);
-
-Complex operator+(Complex a, Complex b);
-Complex operator-(Complex a, Complex b);
-
-Complex operator*(Complex a, Complex b);
-Complex operator*(Complex a, f32 s);
-Complex operator*(f32 s, Complex a);
-
-Complex operator/(Complex a, f32 s);
-
-// Quaternion Operators
-bool operator==(Quaternion a, Quaternion b);
-bool operator!=(Quaternion a, Quaternion b);
-
-Quaternion operator+(Quaternion a);
-Quaternion operator-(Quaternion a);
-
-Quaternion operator+(Quaternion a, Quaternion b);
-Quaternion operator-(Quaternion a, Quaternion b);
-
-Quaternion operator*(Quaternion a, Quaternion b);
-Quaternion operator*(Quaternion a, f32 s);
-Quaternion operator*(f32 s, Quaternion a);
-
-Quaternion operator/(Quaternion a, f32 s);
-
-Vector3 operator*(Quaternion a, Vector3 v); // Rotate v by a
-
-// Matrix2 Operators
-bool operator==(Matrix2 a, Matrix2 b);
-bool operator!=(Matrix2 a, Matrix2 b);
-
-Matrix2 operator+(Matrix2 a);
-Matrix2 operator-(Matrix2 a);
-
-Matrix2 operator+(Matrix2 a, Matrix2 b);
-Matrix2 operator-(Matrix2 a, Matrix2 b);
-
-Matrix2 operator*(Matrix2 a, Matrix2 b);
-Vector2 operator*(Matrix2 a, Vector2 v);
-Matrix2 operator*(Matrix2 a, f32 scalar);
-Matrix2 operator*(f32 scalar, Matrix2 a);
-
-Matrix2 operator/(Matrix2 a, f32 scalar);
-
-Matrix2& operator+=(Matrix2& a, Matrix2 b);
-Matrix2& operator-=(Matrix2& a, Matrix2 b);
-Matrix2& operator*=(Matrix2& a, Matrix2 b);
-
-// Matrix3 Operators
-bool operator==(Matrix3 const& a, Matrix3 const& b);
-bool operator!=(Matrix3 const& a, Matrix3 const& b);
-
-Matrix3 operator+(Matrix3 const& a);
-Matrix3 operator-(Matrix3 const& a);
-
-Matrix3 operator+(Matrix3 const& a, Matrix3 const& b);
-Matrix3 operator-(Matrix3 const& a, Matrix3 const& b);
-
-Matrix3 operator*(Matrix3 const& a, Matrix3 const& b);
-Vector3 operator*(Matrix3 const& a, Vector3 v);
-Matrix3 operator*(Matrix3 const& a, f32 scalar);
-Matrix3 operator*(f32 scalar, Matrix3 const& a);
-
-Matrix3 operator/(Matrix3 const& a, f32 scalar);
-
-Matrix3& operator+=(Matrix3& a, Matrix3 const& b);
-Matrix3& operator-=(Matrix3& a, Matrix3 const& b);
-Matrix3& operator*=(Matrix3& a, Matrix3 const& b);
-
-// Matrix4 Operators
-bool operator==(Matrix4 const& a, Matrix4 const& b);
-bool operator!=(Matrix4 const& a, Matrix4 const& b);
-
-Matrix4 operator+(Matrix4 const& a);
-Matrix4 operator-(Matrix4 const& a);
-
-Matrix4 operator+(Matrix4 const& a, Matrix4 const& b);
-Matrix4 operator-(Matrix4 const& a, Matrix4 const& b);
-
-Matrix4 operator*(Matrix4 const& a, Matrix4 const& b);
-Vector4 operator*(Matrix4 const& a, Vector4 v);
-Matrix4 operator*(Matrix4 const& a, f32 scalar);
-Matrix4 operator*(f32 scalar, Matrix4 const& a);
-
-Matrix4 operator/(Matrix4 const& a, f32 scalar);
-
-Matrix4& operator+=(Matrix4& a, Matrix4 const& b);
-Matrix4& operator-=(Matrix4& a, Matrix4 const& b);
-Matrix4& operator*=(Matrix4& a, Matrix4 const& b);
-
-// Angle Operators
-bool operator==(Angle a, Angle b);
-bool operator!=(Angle a, Angle b);
-
-Angle operator+(Angle a);
-Angle operator-(Angle a);
-
-Angle operator+(Angle a, Angle b);
-Angle operator-(Angle a, Angle b);
-
-Angle operator*(Angle a, f32 scalar);
-Angle operator*(f32 scalar, Angle a);
-
-Angle operator/(Angle a, f32 scalar);
-
-f32 operator/(Angle a, Angle b);
-
-Angle& operator+=(Angle& a, Angle b);
-Angle& operator-=(Angle& a, Angle b);
-Angle& operator*=(Angle& a, f32 scalar);
-Angle& operator/=(Angle& a, f32 scalar);
-
-// Transform Operators
-// World = Parent * Local
-Transform operator*(Transform const& ps, Transform const& ls);
-Transform& operator*=(Transform& ps, Transform const& ls);
-// Local = World / Parent
-Transform operator/(Transform const& ws, Transform const& ps);
-Transform& operator/=(Transform& ws, Transform const& ps);
-
-namespace angle
-{
-Angle radians(f32 r);
-Angle degrees(f32 d);
-Angle turns(f32 t);
-Angle grads(f32 g);
-Angle gons(f32 g);
-
-f32 as_radians(Angle a);
-f32 as_degrees(Angle a);
-f32 as_turns(Angle a);
-f32 as_grads(Angle a);
-f32 as_gons(Angle a);
-} // namespace angle
-
-//////////////////////////////////
-/// ///
-/// Math Functions & Constants ///
-/// ///
-//////////////////////////////////
-extern Vector2 const VECTOR2_ZERO;
-extern Vector3 const VECTOR3_ZERO;
-extern Vector4 const VECTOR4_ZERO;
-extern Complex const COMPLEX_ZERO;
-extern Quaternion const QUATERNION_IDENTITY;
-extern Matrix2 const MATRIX2_IDENTITY;
-extern Matrix3 const MATRIX3_IDENTITY;
-extern Matrix4 const MATRIX4_IDENTITY;
-extern Euler_Angles const EULER_ANGLES_ZERO;
-extern Transform const TRANSFORM_IDENTITY;
-
-namespace math
-{
-extern f32 const ZERO;
-extern f32 const ONE;
-extern f32 const THIRD;
-extern f32 const TWO_THIRDS;
-extern f32 const E;
-extern f32 const PI;
-extern f32 const TAU;
-extern f32 const SQRT_2;
-extern f32 const SQRT_3;
-extern f32 const SQRT_5;
-
-extern f32 const F32_PRECISION;
-
-// Power
-f32 sqrt(f32 x);
-f32 pow(f32 x, f32 y);
-f32 cbrt(f32 x);
-f32 fast_inv_sqrt(f32 x);
-
-// Trigonometric
-f32 sin(Angle a);
-f32 cos(Angle a);
-f32 tan(Angle a);
-
-Angle arcsin(f32 x);
-Angle arccos(f32 x);
-Angle arctan(f32 x);
-Angle arctan2(f32 y, f32 x);
-
-// Hyperbolic
-f32 sinh(f32 x);
-f32 cosh(f32 x);
-f32 tanh(f32 x);
-
-f32 arsinh(f32 x);
-f32 arcosh(f32 x);
-f32 artanh(f32 x);
-
-// Rounding
-f32 ceil(f32 x);
-f32 floor(f32 x);
-f32 mod(f32 x, f32 y);
-f32 truncate(f32 x);
-f32 round(f32 x);
-
-s32 sign(s32 x);
-s64 sign(s64 x);
-f32 sign(f32 x);
-
-// Other
-f32 abs(f32 x);
-s8 abs( s8 x);
-s16 abs(s16 x);
-s32 abs(s32 x);
-s64 abs(s64 x);
-
-bool is_infinite(f32 x);
-bool is_nan(f32 x);
-
-s32 kronecker_delta(s32 i, s32 j);
-s64 kronecker_delta(s64 i, s64 j);
-f32 kronecker_delta(f32 i, f32 j);
-
-// NOTE(bill): Just incase
-#undef min
-#undef max
-
-f32 min(f32 x, f32 y);
-s32 min(s32 x, s32 y);
-s64 min(s64 x, s64 y);
-
-f32 max(f32 x, f32 y);
-s32 max(s32 x, s32 y);
-s64 max(s64 x, s64 y);
-
-f32 clamp(f32 x, f32 min, f32 max);
-s32 clamp(s32 x, s32 min, s32 max);
-s64 clamp(s64 x, s64 min, s64 max);
-
-// TODO(bill): Should this be a template or just normal function overloading?
-template <typename T>
-T lerp(T const& x, T const& y, f32 t);
-
-bool equals(f32 a, f32 b, f32 precision = F32_PRECISION);
-
-// Vector2 functions
-f32 dot(Vector2 a, Vector2 b);
-f32 cross(Vector2 a, Vector2 b);
-
-f32 magnitude(Vector2 a);
-Vector2 normalize(Vector2 a);
-
-Vector2 hadamard(Vector2 a, Vector2 b);
-
-f32 aspect_ratio(Vector2 a);
-
-// Vector3 functions
-f32 dot(Vector3 a, Vector3 b);
-Vector3 cross(Vector3 a, Vector3 b);
-
-f32 magnitude(Vector3 a);
-Vector3 normalize(Vector3 a);
-
-Vector3 hadamard(Vector3 a, Vector3 b);
-
-// Vector4 functions
-f32 dot(Vector4 a, Vector4 b);
-
-f32 magnitude(Vector4 a);
-Vector4 normalize(Vector4 a);
-
-Vector4 hadamard(Vector4 a, Vector4 b);
-
-// Complex functions
-f32 dot(Complex a, Complex b);
-
-f32 magnitude(Complex a);
-f32 norm(Complex a);
-Complex normalize(Complex a);
-
-Complex conjugate(Complex a);
-Complex inverse(Complex a);
-
-f32 complex_angle(Complex a);
-inline f32 complex_argument(Complex a) { return complex_angle(a); }
-Complex magnitude_angle(f32 magnitude, Angle a);
-inline Complex complex_polar(f32 magnitude, Angle a) { return magnitude_angle(magnitude, a); }
-
-// Quaternion functions
-f32 dot(Quaternion a, Quaternion b);
-Quaternion cross(Quaternion a, Quaternion b);
-
-f32 magnitude(Quaternion a);
-f32 norm(Quaternion a);
-Quaternion normalize(Quaternion a);
-
-Quaternion conjugate(Quaternion a);
-Quaternion inverse(Quaternion a);
-
-Angle quaternion_angle(Quaternion a);
-Vector3 quaternion_axis(Quaternion a);
-Quaternion axis_angle(Vector3 axis, Angle a);
-
-Angle quaternion_roll(Quaternion a);
-Angle quaternion_pitch(Quaternion a);
-Angle quaternion_yaw(Quaternion a);
-
-Euler_Angles quaternion_to_euler_angles(Quaternion a);
-Quaternion euler_angles_to_quaternion(Euler_Angles const& e,
- Vector3 x_axis = {1, 0, 0},
- Vector3 y_axis = {0, 1, 0},
- Vector3 z_axis = {0, 0, 1});
-
-// Spherical Linear Interpolation
-Quaternion slerp(Quaternion x, Quaternion y, f32 t);
-
-// Shoemake's Quaternion Curves
-// Sqherical Cubic Interpolation
-Quaternion squad(Quaternion p,
- Quaternion a,
- Quaternion b,
- Quaternion q,
- f32 t);
-// Matrix2 functions
-Matrix2 transpose(Matrix2 m);
-f32 determinant(Matrix2 m);
-Matrix2 inverse(Matrix2 m);
-Matrix2 hadamard(Matrix2 a, const Matrix2&b);
-Matrix4 matrix2_to_matrix4(Matrix2 m);
-
-// Matrix3 functions
-Matrix3 transpose(Matrix3 const& m);
-f32 determinant(Matrix3 const& m);
-Matrix3 inverse(Matrix3 const& m);
-Matrix3 hadamard(Matrix3 const& a, const Matrix3&b);
-Matrix4 matrix3_to_matrix4(Matrix3 const& m);
-
-// Matrix4 functions
-Matrix4 transpose(Matrix4 const& m);
-f32 determinant(Matrix4 const& m);
-Matrix4 inverse(Matrix4 const& m);
-Matrix4 hadamard(Matrix4 const& a, const Matrix4&b);
-bool is_affine(Matrix4 const& m);
-
-Matrix4 quaternion_to_matrix4(Quaternion a);
-Quaternion matrix4_to_quaternion(Matrix4 const& m);
-
-Matrix4 translate(Vector3 v);
-Matrix4 rotate(Vector3 v, Angle angle);
-Matrix4 scale(Vector3 v);
-Matrix4 ortho(f32 left, f32 right, f32 bottom, f32 top);
-Matrix4 ortho(f32 left, f32 right, f32 bottom, f32 top, f32 z_near, f32 z_far);
-Matrix4 perspective(Angle fovy, f32 aspect, f32 z_near, f32 z_far);
-Matrix4 infinite_perspective(Angle fovy, f32 aspect, f32 z_near);
-
-Matrix4
-look_at_matrix4(Vector3 eye, Vector3 center, Vector3 up = {0, 1, 0});
-
-Quaternion
-look_at_quaternion(Vector3 eye, Vector3 center, Vector3 up = {0, 1, 0});
-
-// Transform Functions
-Vector3 transform_point(Transform const& transform, Vector3 point);
-Transform inverse(Transform const& t);
-Matrix4 transform_to_matrix4(Transform const& t);
-} // namespace math
-
-namespace aabb
-{
-Aabb calculate(void const* vertices, usize num_vertices, usize stride, usize offset);
-
-f32 surface_area(Aabb const& aabb);
-f32 volume(Aabb const& aabb);
-
-Sphere to_sphere(Aabb const& aabb);
-
-bool contains(Aabb const& aabb, Vector3 point);
-bool contains(Aabb const& a, Aabb const& b);
-bool intersects(Aabb const& a, Aabb const& b);
-
-Aabb transform_affine(Aabb const& aabb, Matrix4 const& m);
-} // namespace aabb
-
-namespace sphere
-{
-Sphere calculate_min_bounding_sphere(void const* vertices, usize num_vertices, usize stride, usize offset, f32 step);
-Sphere calculate_max_bounding_sphere(void const* vertices, usize num_vertices, usize stride, usize offset);
-
-f32 surface_area(Sphere s);
-f32 volume(Sphere s);
-
-Aabb to_aabb(Sphere sphere);
-
-bool contains_point(Sphere s, Vector3 point);
-
-f32 ray_intersection(Vector3 from, Vector3 dir, Sphere s);
-} // namespace sphere
-
-namespace plane
-{
-f32 ray_intersection(Vector3 from, Vector3 dir, Plane p);
-
-bool intersection3(Plane p1, Plane p2, Plane p3, Vector3* ip);
-} // namespace plane
-
-
-#if !defined(GB_MATH_NO_RANDOM)
-
-namespace random
-{
-struct Random // NOTE(bill): Mt19937_64
-{
- s64 seed;
- u32 index;
- s64 mt[312];
-};
-
-Random make(s64 seed);
-
-void set_seed(Random* r, s64 seed);
-
-s64 next(Random* r);
-
-void next_from_device(void* buffer, u32 length_in_bytes);
-
-s32 next_s32(Random* r);
-u32 next_u32(Random* r);
-f32 next_f32(Random* r);
-s64 next_s64(Random* r);
-u64 next_u64(Random* r);
-f64 next_f64(Random* r);
-
-s32 uniform_s32(Random* r, s32 min_inc, s32 max_inc);
-u32 uniform_u32(Random* r, u32 min_inc, u32 max_inc);
-f32 uniform_f32(Random* r, f32 min_inc, f32 max_inc);
-s64 uniform_s64(Random* r, s64 min_inc, s64 max_inc);
-u64 uniform_u64(Random* r, u64 min_inc, u64 max_inc);
-f64 uniform_f64(Random* r, f64 min_inc, f64 max_inc);
-
-
-// TODO(bill): Should these noise functions be in the `random` module?
-f32 perlin_3d(f32 x, f32 y, f32 z, s32 x_wrap = 0, s32 y_wrap = 0, s32 z_wrap = 0);
-
-// TODO(bill): Implement simplex noise
-// f32 simplex_2d_octave(f32 x, f32 y, f32 octaves, f32 persistence, f32 scale);
-// f32 simplex_3d_octave(f32 x, f32 y, f32 z, f32 octaves, f32 persistence, f32 scale);
-// f32 simplex_4d_octave(f32 x, f32 y, f32 z, f32 w, f32 octaves, f32 persistence, f32 scale);
-
-} // namespace random
-
-#endif
-
-namespace math
-{
-template <typename T> inline T lerp(T const& x, T const& y, f32 t) { return x + (y - x) * t; }
-} // namespace math
-
-__GB_NAMESPACE_END
-
-#endif // GB_INCLUDE_GB_HPP
-
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-///
-/// So long and thanks for all the fish!
-///
-///
-///
-///
-///
-////////////////////////////////
-/// ///
-/// Implemenation ///
-/// ///
-////////////////////////////////
-#if defined(GB_MATH_IMPLEMENTATION)
-
-#include <math.h>
-
-__GB_NAMESPACE_START
-
-////////////////////////////////
-/// ///
-/// Math ///
-/// ///
-////////////////////////////////
-
-Vector2 const VECTOR2_ZERO = Vector2{0, 0};
-Vector3 const VECTOR3_ZERO = Vector3{0, 0, 0};
-Vector4 const VECTOR4_ZERO = Vector4{0, 0, 0, 0};
-Complex const COMPLEX_ZERO = Complex{0, 0};
-Quaternion const QUATERNION_IDENTITY = Quaternion{0, 0, 0, 1};
-Matrix2 const MATRIX2_IDENTITY = Matrix2{1, 0,
- 0, 1};
-Matrix3 const MATRIX3_IDENTITY = Matrix3{1, 0, 0,
- 0, 1, 0,
- 0, 0, 1};
-Matrix4 const MATRIX4_IDENTITY = Matrix4{1, 0, 0, 0,
- 0, 1, 0, 0,
- 0, 0, 1, 0,
- 0, 0, 0, 1};
-Euler_Angles const EULER_ANGLES_ZERO = Euler_Angles{0, 0, 0};
-Transform const TRANSFORM_IDENTITY = Transform{VECTOR3_ZERO, QUATERNION_IDENTITY, 1};
-
-////////////////////////////////
-/// Math Type Op Overloads ///
-////////////////////////////////
-
-// Vector2 Operators
-inline bool
-operator==(Vector2 a, Vector2 b)
-{
- return (a.x == b.x) && (a.y == b.y);
-}
-
-inline bool
-operator!=(Vector2 a, Vector2 b)
-{
- return !operator==(a, b);
-}
-
-inline Vector2
-operator+(Vector2 a)
-{
- return a;
-}
-
-inline Vector2
-operator-(Vector2 a)
-{
- return {-a.x, -a.y};
-}
-
-inline Vector2
-operator+(Vector2 a, Vector2 b)
-{
- return {a.x + b.x, a.y + b.y};
-}
-
-inline Vector2
-operator-(Vector2 a, Vector2 b)
-{
- return {a.x - b.x, a.y - b.y};
-}
-
-inline Vector2
-operator*(Vector2 a, f32 scalar)
-{
- return {a.x * scalar, a.y * scalar};
-}
-
-inline Vector2
-operator*(f32 scalar, Vector2 a)
-{
- return {a.x * scalar, a.y * scalar};
-}
-
-inline Vector2
-operator/(Vector2 a, f32 scalar)
-{
- return {a.x / scalar, a.y / scalar};
-}
-
-inline Vector2
-operator*(Vector2 a, Vector2 b) // Hadamard Product
-{
- return {a.x * b.x, a.y * b.y};
-}
-
-inline Vector2
-operator/(Vector2 a, Vector2 b) // Hadamard Product
-{
- return {a.x / b.x, a.y / b.y};
-}
-
-inline Vector2&
-operator+=(Vector2& a, Vector2 b)
-{
- a.x += b.x;
- a.y += b.y;
-
- return a;
-}
-
-inline Vector2&
-operator-=(Vector2& a, Vector2 b)
-{
- a.x -= b.x;
- a.y -= b.y;
-
- return a;
-}
-
-inline Vector2&
-operator*=(Vector2& a, f32 scalar)
-{
- a.x *= scalar;
- a.y *= scalar;
-
- return a;
-}
-
-inline Vector2&
-operator/=(Vector2& a, f32 scalar)
-{
- a.x /= scalar;
- a.y /= scalar;
-
- return a;
-}
-
-// Vector3 Operators
-inline bool
-operator==(Vector3 a, Vector3 b)
-{
- return (a.x == b.x) && (a.y == b.y) && (a.z == b.z);
-}
-
-inline bool
-operator!=(Vector3 a, Vector3 b)
-{
- return !operator==(a, b);
-}
-
-inline Vector3
-operator+(Vector3 a)
-{
- return a;
-}
-
-inline Vector3
-operator-(Vector3 a)
-{
- return {-a.x, -a.y, -a.z};
-}
-
-inline Vector3
-operator+(Vector3 a, Vector3 b)
-{
- return {a.x + b.x, a.y + b.y, a.z + b.z};
-}
-
-inline Vector3
-operator-(Vector3 a, Vector3 b)
-{
- return {a.x - b.x, a.y - b.y, a.z - b.z};
-}
-
-inline Vector3
-operator*(Vector3 a, f32 scalar)
-{
- return {a.x * scalar, a.y * scalar, a.z * scalar};
-}
-
-inline Vector3
-operator*(f32 scalar, Vector3 a)
-{
- return {a.x * scalar, a.y * scalar, a.z * scalar};
-}
-
-inline Vector3
-operator/(Vector3 a, f32 scalar)
-{
- return {a.x / scalar, a.y / scalar, a.z / scalar};
-}
-
-inline Vector3
-operator*(Vector3 a, Vector3 b) // Hadamard Product
-{
- return {a.x * b.x, a.y * b.y, a.z * b.z};
-}
-
-inline Vector3
-operator/(Vector3 a, Vector3 b) // Hadamard Product
-{
- return {a.x / b.x, a.y / b.y, a.z / b.z};
-}
-
-inline Vector3&
-operator+=(Vector3& a, Vector3 b)
-{
- a.x += b.x;
- a.y += b.y;
- a.z += b.z;
-
- return a;
-}
-
-inline Vector3&
-operator-=(Vector3& a, Vector3 b)
-{
- a.x -= b.x;
- a.y -= b.y;
- a.z -= b.z;
-
- return a;
-}
-
-inline Vector3&
-operator*=(Vector3& a, f32 scalar)
-{
- a.x *= scalar;
- a.y *= scalar;
- a.z *= scalar;
-
- return a;
-}
-
-inline Vector3&
-operator/=(Vector3& a, f32 scalar)
-{
- a.x /= scalar;
- a.y /= scalar;
- a.z /= scalar;
-
- return a;
-}
-
-// Vector4 Operators
-inline bool
-operator==(Vector4 a, Vector4 b)
-{
- return (a.x == b.x) && (a.y == b.y) && (a.z == b.z) && (a.w == b.w);
-}
-
-inline bool
-operator!=(Vector4 a, Vector4 b)
-{
- return !operator==(a, b);
-}
-
-inline Vector4
-operator+(Vector4 a)
-{
- return a;
-}
-
-inline Vector4
-operator-(Vector4 a)
-{
- return {-a.x, -a.y, -a.z, -a.w};
-}
-
-inline Vector4
-operator+(Vector4 a, Vector4 b)
-{
- return {a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w};
-}
-
-inline Vector4
-operator-(Vector4 a, Vector4 b)
-{
- return {a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w};
-}
-
-inline Vector4
-operator*(Vector4 a, f32 scalar)
-{
- return {a.x * scalar, a.y * scalar, a.z * scalar, a.w * scalar};
-}
-
-inline Vector4
-operator*(f32 scalar, Vector4 a)
-{
- return {a.x * scalar, a.y * scalar, a.z * scalar, a.w * scalar};
-}
-
-inline Vector4
-operator/(Vector4 a, f32 scalar)
-{
- return {a.x / scalar, a.y / scalar, a.z / scalar, a.w / scalar};
-}
-
-inline Vector4
-operator*(Vector4 a, Vector4 b) // Hadamard Product
-{
- return {a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w};
-}
-
-inline Vector4
-operator/(Vector4 a, Vector4 b) // Hadamard Product
-{
- return {a.x / b.x, a.y / b.y, a.z / b.z, a.w / b.w};
-}
-
-inline Vector4&
-operator+=(Vector4& a, Vector4 b)
-{
- a.x += b.x;
- a.y += b.y;
- a.z += b.z;
- a.w += b.w;
-
- return a;
-}
-
-inline Vector4&
-operator-=(Vector4& a, Vector4 b)
-{
- a.x -= b.x;
- a.y -= b.y;
- a.z -= b.z;
- a.w -= b.w;
-
- return a;
-}
-
-inline Vector4&
-operator*=(Vector4& a, f32 scalar)
-{
- a.x *= scalar;
- a.y *= scalar;
- a.z *= scalar;
- a.w *= scalar;
-
- return a;
-}
-
-inline Vector4&
-operator/=(Vector4& a, f32 scalar)
-{
- a.x /= scalar;
- a.y /= scalar;
- a.z /= scalar;
- a.w /= scalar;
-
- return a;
-}
-
-// Complex Operators
-inline bool
-operator==(Complex a, Complex b)
-{
- return (a.x == b.x) && (a.y == b.y);
-}
-
-inline bool
-operator!=(Complex a, Complex b)
-{
- return !operator==(a, b);
-}
-
-inline Complex
-operator+(Complex a)
-{
- return a;
-}
-
-inline Complex
-operator-(Complex a)
-{
- return {-a.x, -a.y};
-}
-
-inline Complex
-operator+(Complex a, Complex b)
-{
- return {a.x + b.x, a.y + b.y};
-}
-
-inline Complex
-operator-(Complex a, Complex b)
-{
- return {a.x - b.x, a.y - b.y};
-
-}
-
-inline Complex
-operator*(Complex a, Complex b)
-{
- Complex c = {};
-
- c.x = a.x * b.x - a.y * b.y;
- c.y = a.y * b.x - a.y * b.x;
-
- return c;
-}
-
-inline Complex
-operator*(Complex a, f32 s)
-{
- return {a.x * s, a.y * s};
-}
-
-inline Complex
-operator*(f32 s, Complex a)
-{
- return {a.x * s, a.y * s};
-}
-
-inline Complex
-operator/(Complex a, f32 s)
-{
- return {a.x / s, a.y / s};
-}
-
-// Quaternion Operators
-inline bool
-operator==(Quaternion a, Quaternion b)
-{
- return (a.x == b.x) && (a.y == b.y) && (a.z == b.z) && (a.w == b.w);
-}
-
-inline bool
-operator!=(Quaternion a, Quaternion b)
-{
- return !operator==(a, b);
-}
-
-inline Quaternion
-operator+(Quaternion a)
-{
- return {+a.x, +a.y, +a.z, +a.w};
-}
-
-inline Quaternion
-operator-(Quaternion a)
-{
- return {-a.x, -a.y, -a.z, -a.w};
-}
-
-inline Quaternion
-operator+(Quaternion a, Quaternion b)
-{
- return {a.x + b.x, a.y + b.y, a.z + b.z, a.w + b.w};
-}
-
-inline Quaternion
-operator-(Quaternion a, Quaternion b)
-{
- return {a.x - b.x, a.y - b.y, a.z - b.z, a.w - b.w};
-
-}
-
-inline Quaternion
-operator*(Quaternion a, Quaternion b)
-{
- Quaternion q = {};
-
- q.x = a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y;
- q.y = a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x;
- q.z = a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w;
- q.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z;
-
- return q;
-}
-
-inline Quaternion
-operator*(Quaternion a, f32 s)
-{
- return {a.x * s, a.y * s, a.z * s, a.w * s};
-}
-
-inline Quaternion
-operator*(f32 s, Quaternion a)
-{
- return {a.x * s, a.y * s, a.z * s, a.w * s};
-}
-
-inline Quaternion
-operator/(Quaternion a, f32 s)
-{
- return {a.x / s, a.y / s, a.z / s, a.w / s};
-}
-
-inline Vector3
-operator*(Quaternion a, Vector3 v) // Rotate v by q
-{
- // return (q * Quaternion{v.x, v.y, v.z, 0} * math::conjugate(q)).xyz; // More Expensive
- const Vector3 t = 2.0f * math::cross(a.xyz, v);
- return (v + a.w * t + math::cross(a.xyz, t));
-}
-
-// Matrix2 Operators
-inline bool
-operator==(Matrix2 a, Matrix2 b)
-{
- for (usize i = 0; i < 4; i++)
- {
- if (a[i] != b[i])
- return false;
- }
- return true;
-}
-
-inline bool
-operator!=(Matrix2 a, Matrix2 b)
-{
- return !operator==(a, b);
-}
-
-inline Matrix2
-operator+(Matrix2 a)
-{
- return a;
-}
-
-inline Matrix2
-operator-(Matrix2 a)
-{
- return {-a.x, -a.y};
-}
-
-inline Matrix2
-operator+(Matrix2 a, Matrix2 b)
-{
- Matrix2 mat;
- mat[0] = a[0] + b[0];
- mat[1] = a[1] + b[1];
- return mat;
-}
-
-inline Matrix2
-operator-(Matrix2 a, Matrix2 b)
-{
- Matrix2 mat;
- mat[0] = a[0] - b[0];
- mat[1] = a[1] - b[1];
- return mat;
-}
-
-inline Matrix2
-operator*(Matrix2 a, Matrix2 b)
-{
- Matrix2 result;
- result[0] = a[0] * b[0][0] + a[1] * b[0][1];
- result[1] = a[0] * b[1][0] + a[1] * b[1][1];
- return result;
-}
-
-inline Vector2
-operator*(Matrix2 a, Vector2 v)
-{
- return Vector2{a[0][0] * v.x + a[1][0] * v.y,
- a[0][1] * v.x + a[1][1] * v.y};
-}
-
-inline Matrix2
-operator*(Matrix2 a, f32 scalar)
-{
- Matrix2 mat;
- mat[0] = a[0] * scalar;
- mat[1] = a[1] * scalar;
- return mat;
-}
-
-inline Matrix2
-operator*(f32 scalar, Matrix2 a)
-{
- Matrix2 mat;
- mat[0] = a[0] * scalar;
- mat[1] = a[1] * scalar;
- return mat;
-}
-
-inline Matrix2
-operator/(Matrix2 a, f32 scalar)
-{
- Matrix2 mat;
- mat[0] = a[0] / scalar;
- mat[1] = a[1] / scalar;
- return mat;
-}
-
-inline Matrix2&
-operator+=(Matrix2& a, Matrix2 b)
-{
- return (a = a + b);
-}
-
-inline Matrix2&
-operator-=(Matrix2& a, Matrix2 b)
-{
- return (a = a - b);
-}
-
-inline Matrix2&
-operator*=(Matrix2& a, Matrix2 b)
-{
- return (a = a * b);
-}
-
-
-// Matrix3 Operators
-inline bool
-operator==(Matrix3 const& a, Matrix3 const& b)
-{
- for (usize i = 0; i < 3; i++)
- {
- if (a[i] != b[i])
- return false;
- }
- return true;
-}
-
-inline bool
-operator!=(Matrix3 const& a, Matrix3 const& b)
-{
- return !operator==(a, b);
-}
-
-inline Matrix3
-operator+(Matrix3 const& a)
-{
- return a;
-}
-
-inline Matrix3
-operator-(Matrix3 const& a)
-{
- return {-a.x, -a.y, -a.z};
-}
-
-inline Matrix3
-operator+(Matrix3 const& a, Matrix3 const& b)
-{
- Matrix3 mat;
- mat[0] = a[0] + b[0];
- mat[1] = a[1] + b[1];
- mat[2] = a[2] + b[2];
- return mat;
-}
-
-inline Matrix3
-operator-(Matrix3 const& a, Matrix3 const& b)
-{
- Matrix3 mat;
- mat[0] = a[0] - b[0];
- mat[1] = a[1] - b[1];
- mat[2] = a[2] - b[2];
- return mat;
-}
-
-inline Matrix3
-operator*(Matrix3 const& a, Matrix3 const& b)
-{
- Matrix3 result;
- result[0] = a[0] * b[0][0] + a[1] * b[0][1] + a[2] * b[0][2];
- result[1] = a[0] * b[1][0] + a[1] * b[1][1] + a[2] * b[1][2];
- result[2] = a[0] * b[2][0] + a[1] * b[2][1] + a[2] * b[2][2];
- return result;
-}
-
-inline Vector3
-operator*(Matrix3 const& a, Vector3 v)
-{
- return Vector3{a[0][0] * v.x + a[1][0] * v.y + a[2][0] * v.z,
- a[0][1] * v.x + a[1][1] * v.y + a[2][1] * v.z,
- a[0][2] * v.x + a[1][2] * v.y + a[2][2] * v.z};
-}
-
-inline Matrix3
-operator*(Matrix3 const& a, f32 scalar)
-{
- Matrix3 mat;
- mat[0] = a[0] * scalar;
- mat[1] = a[1] * scalar;
- mat[2] = a[2] * scalar;
- return mat;
-}
-
-inline Matrix3
-operator*(f32 scalar, Matrix3 const& a)
-{
- Matrix3 mat;
- mat[0] = a[0] * scalar;
- mat[1] = a[1] * scalar;
- mat[2] = a[2] * scalar;
- return mat;
-}
-
-inline Matrix3
-operator/(Matrix3 const& a, f32 scalar)
-{
- Matrix3 mat;
- mat[0] = a[0] / scalar;
- mat[1] = a[1] / scalar;
- mat[2] = a[2] / scalar;
- return mat;
-}
-
-inline Matrix3&
-operator+=(Matrix3& a, Matrix3 const& b)
-{
- return (a = a + b);
-}
-
-inline Matrix3&
-operator-=(Matrix3& a, Matrix3 const& b)
-{
- return (a = a - b);
-}
-
-inline Matrix3&
-operator*=(Matrix3& a, Matrix3 const& b)
-{
- return (a = a * b);
-}
-
-
-// Matrix4 Operators
-inline bool
-operator==(Matrix4 const& a, Matrix4 const& b)
-{
- for (usize i = 0; i < 4; i++)
- {
- if (a[i] != b[i])
- return false;
- }
- return true;
-}
-
-inline bool
-operator!=(Matrix4 const& a, Matrix4 const& b)
-{
- return !operator==(a, b);
-}
-
-inline Matrix4
-operator+(Matrix4 const& a)
-{
- return a;
-}
-
-inline Matrix4
-operator-(Matrix4 const& a)
-{
- return {-a.x, -a.y, -a.z, -a.w};
-}
-
-inline Matrix4
-operator+(Matrix4 const& a, Matrix4 const& b)
-{
- Matrix4 mat;
- mat[0] = a[0] + b[0];
- mat[1] = a[1] + b[1];
- mat[2] = a[2] + b[2];
- mat[3] = a[3] + b[3];
- return mat;
-}
-
-inline Matrix4
-operator-(Matrix4 const& a, Matrix4 const& b)
-{
- Matrix4 mat;
- mat[0] = a[0] - b[0];
- mat[1] = a[1] - b[1];
- mat[2] = a[2] - b[2];
- mat[3] = a[3] - b[3];
- return mat;
-}
-
-inline Matrix4
-operator*(Matrix4 const& a, Matrix4 const& b)
-{
- Matrix4 result;
- result[0] = a[0] * b[0][0] + a[1] * b[0][1] + a[2] * b[0][2] + a[3] * b[0][3];
- result[1] = a[0] * b[1][0] + a[1] * b[1][1] + a[2] * b[1][2] + a[3] * b[1][3];
- result[2] = a[0] * b[2][0] + a[1] * b[2][1] + a[2] * b[2][2] + a[3] * b[2][3];
- result[3] = a[0] * b[3][0] + a[1] * b[3][1] + a[2] * b[3][2] + a[3] * b[3][3];
- return result;
-}
-
-inline Vector4
-operator*(Matrix4 const& a, Vector4 v)
-{
- return Vector4{a[0][0] * v.x + a[1][0] * v.y + a[2][0] * v.z + a[3][0] * v.w,
- a[0][1] * v.x + a[1][1] * v.y + a[2][1] * v.z + a[3][1] * v.w,
- a[0][2] * v.x + a[1][2] * v.y + a[2][2] * v.z + a[3][2] * v.w,
- a[0][3] * v.x + a[1][3] * v.y + a[2][3] * v.z + a[3][3] * v.w};
-}
-
-inline Matrix4
-operator*(Matrix4 const& a, f32 scalar)
-{
- Matrix4 mat;
- mat[0] = a[0] * scalar;
- mat[1] = a[1] * scalar;
- mat[2] = a[2] * scalar;
- mat[3] = a[3] * scalar;
- return mat;
-}
-
-inline Matrix4
-operator*(f32 scalar, Matrix4 const& a)
-{
- Matrix4 mat;
- mat[0] = a[0] * scalar;
- mat[1] = a[1] * scalar;
- mat[2] = a[2] * scalar;
- mat[3] = a[3] * scalar;
- return mat;
-}
-
-inline Matrix4
-operator/(Matrix4 const& a, f32 scalar)
-{
- Matrix4 mat;
- mat[0] = a[0] / scalar;
- mat[1] = a[1] / scalar;
- mat[2] = a[2] / scalar;
- mat[3] = a[3] / scalar;
- return mat;
-}
-
-inline Matrix4&
-operator+=(Matrix4& a, Matrix4 const& b)
-{
- return (a = a + b);
-}
-
-inline Matrix4&
-operator-=(Matrix4& a, Matrix4 const& b)
-{
- return (a = a - b);
-}
-
-inline Matrix4&
-operator*=(Matrix4& a, Matrix4 const& b)
-{
- return (a = a * b);
-}
-
-// Angle Operators
-inline bool
-operator==(Angle a, Angle b)
-{
- return a.radians == b.radians;
-}
-
-inline bool
-operator!=(Angle a, Angle b)
-{
- return !operator==(a, b);
-}
-
-inline Angle
-operator+(Angle a)
-{
- return {+a.radians};
-}
-
-inline Angle
-operator-(Angle a)
-{
- return {-a.radians};
-}
-
-inline Angle
-operator+(Angle a, Angle b)
-{
- return {a.radians + b.radians};
-}
-
-inline Angle
-operator-(Angle a, Angle b)
-{
- return {a.radians - b.radians};
-}
-
-inline Angle
-operator*(Angle a, f32 scalar)
-{
- return {a.radians * scalar};
-}
-
-inline Angle
-operator*(f32 scalar, Angle a)
-{
- return {a.radians * scalar};
-}
-
-inline Angle
-operator/(Angle a, f32 scalar)
-{
- return {a.radians / scalar};
-}
-
-inline f32
-operator/(Angle a, Angle b)
-{
- return a.radians / b.radians;
-}
-
-inline Angle&
-operator+=(Angle& a, Angle b)
-{
- return (a = a + b);
-}
-
-inline Angle&
-operator-=(Angle& a, Angle b)
-{
- return (a = a - b);
-}
-
-inline Angle&
-operator*=(Angle& a, f32 scalar)
-{
- return (a = a * scalar);
-}
-
-inline Angle&
-operator/=(Angle& a, f32 scalar)
-{
- return (a = a / scalar);
-}
-
-
-// Transform Operators
-// World = Parent * Local
-Transform
-operator*(Transform const& ps, Transform const& ls)
-{
- Transform ws;
-
- ws.position = ps.position + ps.orientation * (ps.scale * ls.position);
- ws.orientation = ps.orientation * ls.orientation;
- // ws.scale = ps.scale * (ps.orientation * ls.scale); // Vector3 scale
- ws.scale = ps.scale * ls.scale;
-
- return ws;
-}
-
-inline Transform&
-operator*=(Transform& ps, Transform const& ls)
-{
- return (ps = ps * ls);
-}
-
-// Local = World / Parent
-Transform
-operator/(Transform const& ws, Transform const& ps)
-{
- Transform ls;
-
- const Quaternion ps_conjugate = math::conjugate(ps.orientation);
-
- ls.position = (ps_conjugate * (ws.position - ps.position)) / ps.scale;
- ls.orientation = ps_conjugate * ws.orientation;
- // ls.scale = ps_conjugate * (ws.scale / ps.scale); // Vector3 scale
- ls.scale = ws.scale / ps.scale;
-
- return ls;
-}
-
-inline Transform&
-operator/=(Transform& ws, Transform const& ps)
-{
- return (ws = ws / ps);
-}
-
-
-namespace angle
-{
-inline Angle radians(f32 r) { return {r}; }
-inline Angle degrees(f32 d) { return {d * math::TAU / 360.0f}; }
-inline Angle turns(f32 t) { return {t * math::TAU}; }
-inline Angle grads(f32 g) { return {g * math::TAU / 400.0f}; }
-inline Angle gons(f32 g) { return {g * math::TAU / 400.0f}; }
-
-inline f32 as_radians(Angle a) { return a.radians; }
-inline f32 as_degrees(Angle a) { return a.radians * (360.0f / math::TAU); }
-inline f32 as_turns(Angle a) { return a.radians * ( 1.0f / math::TAU); }
-inline f32 as_grads(Angle a) { return a.radians * (400.0f / math::TAU); }
-inline f32 as_gons(Angle a) { return a.radians * (400.0f / math::TAU); }
-} // namespace angle
-
-////////////////////////////////
-/// ///
-/// Math Functions ///
-/// ///
-////////////////////////////////
-
-
-namespace math
-{
-f32 const ZERO = 0.0f;
-f32 const ONE = 1.0f;
-f32 const THIRD = 0.33333333f;
-f32 const TWO_THIRDS = 0.66666667f;
-f32 const E = 2.718281828f;
-f32 const PI = 3.141592654f;
-f32 const TAU = 6.283185307f;
-f32 const SQRT_2 = 1.414213562f;
-f32 const SQRT_3 = 1.732050808f;
-f32 const SQRT_5 = 2.236067978f;
-
-f32 const F32_PRECISION = 1.0e-7f;
-
-// Power
-inline f32 sqrt(f32 x) { return ::sqrtf(x); }
-inline f32 pow(f32 x, f32 y) { return static_cast<f32>(::powf(x, y)); }
-inline f32 cbrt(f32 x) { return static_cast<f32>(::cbrtf(x)); }
-
-inline f32
-fast_inv_sqrt(f32 x)
-{
- const f32 THREE_HALFS = 1.5f;
-
- const f32 x2 = x * 0.5f;
- f32 y = x;
- u32 i = bit_cast<u32>(y); // Evil floating point bit level hacking
- // i = 0x5f3759df - (i >> 1); // What the fuck? Old
- i = 0x5f375a86 - (i >> 1); // What the fuck? Improved!
- y = bit_cast<f32>(i);
- y = y * (THREE_HALFS - (x2 * y * y)); // 1st iteration
- // y = y * (THREE_HALFS - (x2 * y * y)); // 2nd iteration, this can be removed
-
- return y;
-}
-
-// Trigonometric
-inline f32 sin(Angle a) { return ::sinf(angle::as_radians(a)); }
-inline f32 cos(Angle a) { return ::cosf(angle::as_radians(a)); }
-inline f32 tan(Angle a) { return ::tanf(angle::as_radians(a)); }
-
-inline Angle arcsin(f32 x) { return angle::radians(::asinf(x)); }
-inline Angle arccos(f32 x) { return angle::radians(::acosf(x)); }
-inline Angle arctan(f32 x) { return angle::radians(::atanf(x)); }
-inline Angle arctan2(f32 y, f32 x) { return angle::radians(::atan2f(y, x)); }
-
-// Hyperbolic
-inline f32 sinh(f32 x) { return ::sinhf(x); }
-inline f32 cosh(f32 x) { return ::coshf(x); }
-inline f32 tanh(f32 x) { return ::tanhf(x); }
-
-inline f32 arsinh(f32 x) { return ::asinhf(x); }
-inline f32 arcosh(f32 x) { return ::acoshf(x); }
-inline f32 artanh(f32 x) { return ::atanhf(x); }
-
-// Rounding
-inline f32 ceil(f32 x) { return ::ceilf(x); }
-inline f32 floor(f32 x) { return ::floorf(x); }
-inline f32 mod(f32 x, f32 y) { return ::fmodf(x, y); }
-inline f32 truncate(f32 x) { return ::truncf(x); }
-inline f32 round(f32 x) { return ::roundf(x); }
-
-inline s32 sign(s32 x) { return x >= 0 ? +1 : -1; }
-inline s64 sign(s64 x) { return x >= 0 ? +1 : -1; }
-inline f32 sign(f32 x) { return x >= 0.0f ? +1.0f : -1.0f; }
-
-// Other
-inline f32
-abs(f32 x)
-{
- u32 i = bit_cast<u32>(x);
- i &= 0x7FFFFFFFul;
- return bit_cast<f32>(i);
-}
-
-inline s8
-abs(s8 x)
-{
- u8 i = bit_cast<u8>(x);
- i &= 0x7Fu;
- return bit_cast<s8>(i);
-}
-
-inline s16
-abs(s16 x)
-{
- u16 i = bit_cast<u16>(x);
- i &= 0x7FFFu;
- return bit_cast<s16>(i);
-}
-
-inline s32
-abs(s32 x)
-{
- u32 i = bit_cast<u32>(x);
- i &= 0x7FFFFFFFul;
- return bit_cast<s32>(i);
-}
-
-inline s64
-abs(s64 x)
-{
- u64 i = bit_cast<u64>(x);
- i &= 0x7FFFFFFFFFFFFFFFull;
- return bit_cast<s64>(i);
-}
-
-inline bool
-is_infinite(f32 x)
-{
- return isinf(x);
-}
-
-inline bool
-is_nan(f32 x)
-{
- return isnan(x);
-}
-
-inline s32
-kronecker_delta(s32 i, s32 j)
-{
- return static_cast<s32>(i == j);
-}
-
-inline s64
-kronecker_delta(s64 i, s64 j)
-{
- return static_cast<s64>(i == j);
-}
-
-inline f32
-kronecker_delta(f32 i, f32 j)
-{
- return static_cast<f32>(i == j);
-}
-
-inline f32
-min(f32 x, f32 y)
-{
- // TODO(bill): Check if this is even good
- return x < y ? x : y;
-}
-
-inline s32
-min(s32 x, s32 y)
-{
- return y + ((x-y) & (x-y)>>31);
-}
-
-inline s64
-min(s64 x, s64 y)
-{
- return y + ((x-y) & (x-y)>>63);
-}
-
-inline f32
-max(f32 x, f32 y)
-{
- // TODO(bill): Check if this is even good
- return x > y ? x : y;
-}
-
-inline s32
-max(s32 x, s32 y)
-{
- return x - ((x-y) & (x-y)>>31);
-}
-
-inline s64
-max(s64 x, s64 y)
-{
- return x - ((x-y) & (x-y)>>63);
-}
-
-inline f32
-clamp(f32 x, f32 min, f32 max)
-{
- const f32 t = x < min ? min : x;
- return t > max ? max : t;
-}
-
-inline s32
-clamp(s32 x, s32 min, s32 max)
-{
- const s32 t = x < min ? min : x;
- return t > max ? max : t;
-}
-
-inline s64
-clamp(s64 x, s64 min, s64 max)
-{
- const s64 t = x < min ? min : x;
- return t > max ? max : t;
-}
-
-inline bool
-equals(f32 a, f32 b, f32 precision)
-{
- return ((b <= (a + precision)) && (b >= (a - precision)));
-}
-
-// Vector2 functions
-inline f32
-dot(Vector2 a, Vector2 b)
-{
- return a.x * b.x + a.y * b.y;
-}
-
-inline f32
-cross(Vector2 a, Vector2 b)
-{
- return a.x * b.y - a.y * b.x;
-}
-
-inline f32
-magnitude(Vector2 a)
-{
- return math::sqrt(math::dot(a, a));
-}
-
-inline Vector2
-normalize(Vector2 a)
-{
- f32 m = magnitude(a);
- if (m > 0)
- return a * (1.0f / m);
- return {};
-}
-
-inline Vector2
-hadamard(Vector2 a, Vector2 b)
-{
- return {a.x * b.x, a.y * b.y};
-}
-
-inline f32
-aspect_ratio(Vector2 a)
-{
- return a.x / a.y;
-}
-
-
-inline Matrix4
-matrix2_to_matrix4(Matrix2 m)
-{
- Matrix4 result = MATRIX4_IDENTITY;
- result[0][0] = m[0][0];
- result[0][1] = m[0][1];
- result[1][0] = m[1][0];
- result[1][1] = m[1][1];
- return result;
-}
-
-// Vector3 functions
-inline f32
-dot(Vector3 a, Vector3 b)
-{
- return a.x * b.x + a.y * b.y + a.z * b.z;
-}
-
-inline Vector3
-cross(Vector3 a, Vector3 b)
-{
- return Vector3{
- a.y * b.z - b.y * a.z, // x
- a.z * b.x - b.z * a.x, // y
- a.x * b.y - b.x * a.y // z
- };
-}
-
-inline f32
-magnitude(Vector3 a)
-{
- return math::sqrt(math::dot(a, a));
-}
-
-inline Vector3
-normalize(Vector3 a)
-{
- f32 m = magnitude(a);
- if (m > 0)
- return a * (1.0f / m);
- return {};
-}
-
-inline Vector3
-hadamard(Vector3 a, Vector3 b)
-{
- return {a.x * b.x, a.y * b.y, a.z * b.z};
-}
-
-inline Matrix4
-matrix3_to_matrix4(Matrix3 const& m)
-{
- Matrix4 result = MATRIX4_IDENTITY;
- result[0][0] = m[0][0];
- result[0][1] = m[0][1];
- result[0][2] = m[0][2];
- result[1][0] = m[1][0];
- result[1][1] = m[1][1];
- result[1][2] = m[1][2];
- result[2][0] = m[2][0];
- result[2][1] = m[2][1];
- result[2][2] = m[2][2];
- return result;
-}
-
-// Vector4 functions
-inline f32
-dot(Vector4 a, Vector4 b)
-{
- return a.x*b.x + a.y*b.y + a.z*b.z + a.w*b.w;
-}
-
-inline f32
-magnitude(Vector4 a)
-{
- return math::sqrt(math::dot(a, a));
-}
-
-inline Vector4
-normalize(Vector4 a)
-{
- f32 m = magnitude(a);
- if (m > 0)
- return a * (1.0f / m);
- return {};
-}
-
-inline Vector4
-hadamard(Vector4 a, Vector4 b)
-{
- return {a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w};
-}
-
-// Complex Functions
-inline f32
-dot(Complex a, Complex b)
-{
- return a.real * b.real + a.imag * b.imag;
-}
-
-inline f32
-magnitude(Complex a)
-{
- return math::sqrt(norm(a));
-}
-
-inline f32
-norm(Complex a)
-{
- return math::dot(a, a);
-}
-
-inline Complex
-normalize(Complex a)
-{
- f32 m = magnitude(a);
- if (m > 0)
- return a / magnitude(a);
- return COMPLEX_ZERO;
-}
-
-inline Complex
-conjugate(Complex a)
-{
- return {a.real, -a.imag};
-}
-
-inline Complex
-inverse(Complex a)
-{
- f32 m = norm(a);
- if (m > 0)
- return conjugate(a) / norm(a);
- return COMPLEX_ZERO;
-}
-
-inline f32
-complex_angle(Complex a)
-{
- return atan2f(a.imag, a.real);
-}
-
-inline Complex
-magnitude_angle(f32 magnitude, Angle a)
-{
- f32 real = magnitude * math::cos(a);
- f32 imag = magnitude * math::sin(a);
- return {real, imag};
-}
-
-// Quaternion functions
-inline f32
-dot(Quaternion a, Quaternion b)
-{
- return math::dot(a.xyz, b.xyz) + a.w*b.w;
-}
-
-inline Quaternion
-cross(Quaternion a, Quaternion b)
-{
- return Quaternion{a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
- a.w * b.y + a.y * b.w + a.z * b.x - a.x * b.z,
- a.w * b.z + a.z * b.w + a.x * b.y - a.y * b.x,
- a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z};
-}
-
-inline f32
-magnitude(Quaternion a)
-{
- return math::sqrt(math::dot(a, a));
-}
-
-inline f32
-norm(Quaternion a)
-{
- return math::dot(a, a);
-}
-
-inline Quaternion
-normalize(Quaternion a)
-{
- f32 m = magnitude(a);
- if (m > 0)
- return a * (1.0f / m);
- return {};
-}
-
-inline Quaternion
-conjugate(Quaternion a)
-{
- return {-a.x, -a.y, -a.z, a.w};
-}
-
-inline Quaternion
-inverse(Quaternion a)
-{
- f32 m = 1.0f / dot(a, a);
- return math::conjugate(a) * m;
-}
-
-inline Angle
-quaternion_angle(Quaternion a)
-{
- return 2.0f * math::arccos(a.w);
-}
-
-inline Vector3
-quaternion_axis(Quaternion a)
-{
- f32 s2 = 1.0f - a.w * a.w;
-
- if (s2 <= 0.0f)
- return {0, 0, 1};
-
- f32 invs2 = 1.0f / math::sqrt(s2);
-
- return a.xyz * invs2;
-}
-
-inline Quaternion
-axis_angle(Vector3 axis, Angle angle)
-{
- Vector3 a = math::normalize(axis);
- f32 s = math::sin(0.5f * angle);
-
- Quaternion q;
- q.xyz = a * s;
- q.w = math::cos(0.5f * angle);
-
- return q;
-}
-
-inline Angle
-quaternion_roll(Quaternion a)
-{
- return math::arctan2(2.0f * a.x * a.y + a.z * a.w,
- a.x * a.x + a.w * a.w - a.y * a.y - a.z * a.z);
-}
-
-inline Angle
-quaternion_pitch(Quaternion a)
-{
- return math::arctan2(2.0f * a.y * a.z + a.w * a.x,
- a.w * a.w - a.x * a.x - a.y * a.y + a.z * a.z);
-}
-
-inline Angle
-quaternion_yaw(Quaternion a)
-{
- return math::arcsin(-2.0f * (a.x * a.z - a.w * a.y));
-
-}
-
-inline Euler_Angles
-quaternion_to_euler_angles(Quaternion a)
-{
- return {quaternion_pitch(a), quaternion_yaw(a), quaternion_roll(a)};
-}
-
-inline Quaternion
-euler_angles_to_quaternion(Euler_Angles const& e,
- Vector3 x_axis,
- Vector3 y_axis,
- Vector3 z_axis)
-{
- Quaternion p = axis_angle(x_axis, e.pitch);
- Quaternion y = axis_angle(y_axis, e.yaw);
- Quaternion r = axis_angle(z_axis, e.roll);
-
- return y * p * r;
-}
-
-
-// Spherical Linear Interpolation
-inline Quaternion
-slerp(Quaternion x, Quaternion y, f32 t)
-{
- Quaternion z = y;
-
- f32 cos_theta = dot(x, y);
-
- if (cos_theta < 0.0f)
- {
- z = -y;
- cos_theta = -cos_theta;
- }
-
- if (cos_theta > 1.0f)
- {
- return Quaternion{lerp(x.x, y.x, t),
- lerp(x.y, y.y, t),
- lerp(x.z, y.z, t),
- lerp(x.w, y.w, t)};
- }
-
- Angle angle = math::arccos(cos_theta);
-
- Quaternion result = math::sin(angle::radians(1.0f) - (t * angle)) * x + math::sin(t * angle) * z;
- return result * (1.0f / math::sin(angle));
-}
-
-// Shoemake's Quaternion Curves
-// Sqherical Cubic Interpolation
-inline Quaternion
-squad(Quaternion p,
- Quaternion a,
- Quaternion b,
- Quaternion q,
- f32 t)
-{
- return slerp(slerp(p, q, t), slerp(a, b, t), 2.0f * t * (1.0f - t));
-}
-
-// Matrix2 functions
-inline Matrix2
-transpose(Matrix2 m)
-{
- Matrix2 result;
- for (usize i = 0; i < 2; i++)
- {
- for (usize j = 0; j < 2; j++)
- result[i][j] = m[j][i];
- }
- return result;
-}
-
-inline f32
-determinant(Matrix2 m)
-{
- return m[0][0] * m[1][1] - m[1][0] * m[0][1];
-}
-
-inline Matrix2
-inverse(Matrix2 m)
-{
- f32 inv_det = 1.0f / (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
- Matrix2 result;
- result[0][0] = m[1][1] * inv_det;
- result[0][1] = -m[0][1] * inv_det;
- result[1][0] = -m[1][0] * inv_det;
- result[1][1] = m[0][0] * inv_det;
- return result;
-}
-
-inline Matrix2
-hadamard(Matrix2 a, const Matrix2&b)
-{
- Matrix2 result;
- result[0] = a[0] * b[0];
- result[1] = a[1] * b[1];
- return result;
-}
-
-// Matrix3 functions
-inline Matrix3
-transpose(Matrix3 const& m)
-{
- Matrix3 result;
-
- for (usize i = 0; i < 3; i++)
- {
- for (usize j = 0; j < 3; j++)
- result[i][j] = m[j][i];
- }
- return result;
-}
-
-inline f32
-determinant(Matrix3 const& m)
-{
- return (+m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
- -m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
- +m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]));
-}
-
-inline Matrix3
-inverse(Matrix3 const& m)
-{
- f32 inv_det = 1.0f / (
- + m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
- - m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
- + m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]));
-
- Matrix3 result;
-
- result[0][0] = +(m[1][1] * m[2][2] - m[2][1] * m[1][2]) * inv_det;
- result[1][0] = -(m[1][0] * m[2][2] - m[2][0] * m[1][2]) * inv_det;
- result[2][0] = +(m[1][0] * m[2][1] - m[2][0] * m[1][1]) * inv_det;
- result[0][1] = -(m[0][1] * m[2][2] - m[2][1] * m[0][2]) * inv_det;
- result[1][1] = +(m[0][0] * m[2][2] - m[2][0] * m[0][2]) * inv_det;
- result[2][1] = -(m[0][0] * m[2][1] - m[2][0] * m[0][1]) * inv_det;
- result[0][2] = +(m[0][1] * m[1][2] - m[1][1] * m[0][2]) * inv_det;
- result[1][2] = -(m[0][0] * m[1][2] - m[1][0] * m[0][2]) * inv_det;
- result[2][2] = +(m[0][0] * m[1][1] - m[1][0] * m[0][1]) * inv_det;
-
- return result;
-}
-
-inline Matrix3
-hadamard(Matrix3 const& a, const Matrix3&b)
-{
- Matrix3 result;
- result[0] = a[0] * b[0];
- result[1] = a[1] * b[1];
- result[2] = a[2] * b[2];
- return result;
-}
-
-// Matrix4 functions
-inline Matrix4
-transpose(Matrix4 const& m)
-{
- Matrix4 result;
-
- for (usize i = 0; i < 4; i++)
- {
- for (usize j = 0; j < 4; j++)
- result[i][j] = m[j][i];
- }
- return result;
-}
-
-f32
-determinant(Matrix4 const& m)
-{
- f32 coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
- f32 coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
- f32 coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
-
- f32 coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
- f32 coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
- f32 coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
-
- f32 coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
- f32 coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
- f32 coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
-
- f32 coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
- f32 coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
- f32 coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
-
- f32 coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
- f32 coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
- f32 coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
-
- f32 coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
- f32 coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
- f32 coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
-
- Vector4 fac0 = {coef00, coef00, coef02, coef03};
- Vector4 fac1 = {coef04, coef04, coef06, coef07};
- Vector4 fac2 = {coef08, coef08, coef10, coef11};
- Vector4 fac3 = {coef12, coef12, coef14, coef15};
- Vector4 fac4 = {coef16, coef16, coef18, coef19};
- Vector4 fac5 = {coef20, coef20, coef22, coef23};
-
- Vector4 vec0 = {m[1][0], m[0][0], m[0][0], m[0][0]};
- Vector4 vec1 = {m[1][1], m[0][1], m[0][1], m[0][1]};
- Vector4 vec2 = {m[1][2], m[0][2], m[0][2], m[0][2]};
- Vector4 vec3 = {m[1][3], m[0][3], m[0][3], m[0][3]};
-
- Vector4 inv0 = vec1 * fac0 - vec2 * fac1 + vec3 * fac2;
- Vector4 inv1 = vec0 * fac0 - vec2 * fac3 + vec3 * fac4;
- Vector4 inv2 = vec0 * fac1 - vec1 * fac3 + vec3 * fac5;
- Vector4 inv3 = vec0 * fac2 - vec1 * fac4 + vec2 * fac5;
-
- Vector4 signA = {+1, -1, +1, -1};
- Vector4 signB = {-1, +1, -1, +1};
- Matrix4 inverse = {inv0 * signA, inv1 * signB, inv2 * signA, inv3 * signB};
-
- Vector4 row0 = {inverse[0][0], inverse[1][0], inverse[2][0], inverse[3][0]};
-
- Vector4 dot0 = m[0] * row0;
- f32 dot1 = (dot0[0] + dot0[1]) + (dot0[2] + dot0[3]);
- return dot1;
-}
-
-Matrix4
-inverse(Matrix4 const& m)
-{
- f32 coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
- f32 coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
- f32 coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
- f32 coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
- f32 coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
- f32 coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
- f32 coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
- f32 coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
- f32 coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
- f32 coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
- f32 coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
- f32 coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
- f32 coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
- f32 coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
- f32 coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
- f32 coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
- f32 coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
- f32 coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
-
- Vector4 fac0 = {coef00, coef00, coef02, coef03};
- Vector4 fac1 = {coef04, coef04, coef06, coef07};
- Vector4 fac2 = {coef08, coef08, coef10, coef11};
- Vector4 fac3 = {coef12, coef12, coef14, coef15};
- Vector4 fac4 = {coef16, coef16, coef18, coef19};
- Vector4 fac5 = {coef20, coef20, coef22, coef23};
-
- Vector4 vec0 = {m[1][0], m[0][0], m[0][0], m[0][0]};
- Vector4 vec1 = {m[1][1], m[0][1], m[0][1], m[0][1]};
- Vector4 vec2 = {m[1][2], m[0][2], m[0][2], m[0][2]};
- Vector4 vec3 = {m[1][3], m[0][3], m[0][3], m[0][3]};
-
- Vector4 inv0 = vec1 * fac0 - vec2 * fac1 + vec3 * fac2;
- Vector4 inv1 = vec0 * fac0 - vec2 * fac3 + vec3 * fac4;
- Vector4 inv2 = vec0 * fac1 - vec1 * fac3 + vec3 * fac5;
- Vector4 inv3 = vec0 * fac2 - vec1 * fac4 + vec2 * fac5;
-
- Vector4 signA = {+1, -1, +1, -1};
- Vector4 signB = {-1, +1, -1, +1};
- Matrix4 inverse = {inv0 * signA, inv1 * signB, inv2 * signA, inv3 * signB};
-
- Vector4 row0 = {inverse[0][0], inverse[1][0], inverse[2][0], inverse[3][0]};
-
- Vector4 dot0 = m[0] * row0;
- f32 dot1 = (dot0[0] + dot0[1]) + (dot0[2] + dot0[3]);
-
- f32 oneOverDeterminant = 1.0f / dot1;
-
- return inverse * oneOverDeterminant;
-}
-
-inline Matrix4
-hadamard(Matrix4 const& a, Matrix4 const& b)
-{
- Matrix4 result;
-
- result[0] = a[0] * b[0];
- result[1] = a[1] * b[1];
- result[2] = a[2] * b[2];
- result[3] = a[3] * b[3];
-
- return result;
-}
-
-inline bool
-is_affine(Matrix4 const& m)
-{
- // E.g. No translation
- return (equals(m.columns[3].x, 0)) &
- (equals(m.columns[3].y, 0)) &
- (equals(m.columns[3].z, 0)) &
- (equals(m.columns[3].w, 1.0f));
-}
-
-
-inline Matrix4
-quaternion_to_matrix4(Quaternion q)
-{
- Matrix4 mat = MATRIX4_IDENTITY;
-
- Quaternion a = math::normalize(q);
-
- f32 xx = a.x * a.x;
- f32 yy = a.y * a.y;
- f32 zz = a.z * a.z;
- f32 xy = a.x * a.y;
- f32 xz = a.x * a.z;
- f32 yz = a.y * a.z;
- f32 wx = a.w * a.x;
- f32 wy = a.w * a.y;
- f32 wz = a.w * a.z;
-
- mat[0][0] = 1.0f - 2.0f * (yy + zz);
- mat[0][1] = 2.0f * (xy + wz);
- mat[0][2] = 2.0f * (xz - wy);
-
- mat[1][0] = 2.0f * (xy - wz);
- mat[1][1] = 1.0f - 2.0f * (xx + zz);
- mat[1][2] = 2.0f * (yz + wx);
-
- mat[2][0] = 2.0f * (xz + wy);
- mat[2][1] = 2.0f * (yz - wx);
- mat[2][2] = 1.0f - 2.0f * (xx + yy);
-
- return mat;
-}
-
-Quaternion
-matrix4_to_quaternion(Matrix4 const& m)
-{
- f32 four_x_squared_minus_1 = m[0][0] - m[1][1] - m[2][2];
- f32 four_y_squared_minus_1 = m[1][1] - m[0][0] - m[2][2];
- f32 four_z_squared_minus_1 = m[2][2] - m[0][0] - m[1][1];
- f32 four_w_squared_minus_1 = m[0][0] + m[1][1] + m[2][2];
-
- s32 biggestIndex = 0;
- f32 four_biggest_squared_minus_1 = four_w_squared_minus_1;
- if (four_x_squared_minus_1 > four_biggest_squared_minus_1)
- {
- four_biggest_squared_minus_1 = four_x_squared_minus_1;
- biggestIndex = 1;
- }
- if (four_y_squared_minus_1 > four_biggest_squared_minus_1)
- {
- four_biggest_squared_minus_1 = four_y_squared_minus_1;
- biggestIndex = 2;
- }
- if (four_z_squared_minus_1 > four_biggest_squared_minus_1)
- {
- four_biggest_squared_minus_1 = four_z_squared_minus_1;
- biggestIndex = 3;
- }
-
- f32 biggestVal = math::sqrt(four_biggest_squared_minus_1 + 1.0f) * 0.5f;
- f32 mult = 0.25f / biggestVal;
-
- Quaternion q = QUATERNION_IDENTITY;
-
- switch (biggestIndex)
- {
- case 0:
- {
- q.w = biggestVal;
- q.x = (m[1][2] - m[2][1]) * mult;
- q.y = (m[2][0] - m[0][2]) * mult;
- q.z = (m[0][1] - m[1][0]) * mult;
- }
- break;
- case 1:
- {
- q.w = (m[1][2] - m[2][1]) * mult;
- q.x = biggestVal;
- q.y = (m[0][1] + m[1][0]) * mult;
- q.z = (m[2][0] + m[0][2]) * mult;
- }
- break;
- case 2:
- {
- q.w = (m[2][0] - m[0][2]) * mult;
- q.x = (m[0][1] + m[1][0]) * mult;
- q.y = biggestVal;
- q.z = (m[1][2] + m[2][1]) * mult;
- }
- break;
- case 3:
- {
- q.w = (m[0][1] - m[1][0]) * mult;
- q.x = (m[2][0] + m[0][2]) * mult;
- q.y = (m[1][2] + m[2][1]) * mult;
- q.z = biggestVal;
- }
- break;
- default: // Should never actually get here. Just for sanities sake.
- {
- GB_ASSERT(false, "How did you get here?!");
- }
- break;
- }
-
- return q;
-}
-
-
-inline Matrix4
-translate(Vector3 v)
-{
- Matrix4 result = MATRIX4_IDENTITY;
- result[3].xyz = v;
- result[3].w = 1;
- return result;
-}
-
-inline Matrix4
-rotate(Vector3 v, Angle angle)
-{
- const f32 c = math::cos(angle);
- const f32 s = math::sin(angle);
-
- const Vector3 axis = math::normalize(v);
- const Vector3 t = (1.0f - c) * axis;
-
- Matrix4 rot = MATRIX4_IDENTITY;
-
- rot[0][0] = c + t.x * axis.x;
- rot[0][1] = 0 + t.x * axis.y + s * axis.z;
- rot[0][2] = 0 + t.x * axis.z - s * axis.y;
- rot[0][3] = 0;
-
- rot[1][0] = 0 + t.y * axis.x - s * axis.z;
- rot[1][1] = c + t.y * axis.y;
- rot[1][2] = 0 + t.y * axis.z + s * axis.x;
- rot[1][3] = 0;
-
- rot[2][0] = 0 + t.z * axis.x + s * axis.y;
- rot[2][1] = 0 + t.z * axis.y - s * axis.x;
- rot[2][2] = c + t.z * axis.z;
- rot[2][3] = 0;
-
- return rot;
-}
-
-inline Matrix4
-scale(Vector3 v)
-{
- return { v.x, 0, 0, 0,
- 0, v.y, 0, 0,
- 0, 0, v.z, 0,
- 0, 0, 0, 1 };
-}
-
-inline Matrix4
-ortho(f32 left, f32 right, f32 bottom, f32 top)
-{
- return ortho(left, right, bottom, top, -1.0f, 1.0f);
-}
-
-inline Matrix4
-ortho(f32 left, f32 right, f32 bottom, f32 top, f32 z_near, f32 z_far)
-{
- Matrix4 result = MATRIX4_IDENTITY;
-
- result[0][0] = 2.0f / (right - left);
- result[1][1] = 2.0f / (top - bottom);
- result[2][2] = -2.0f / (z_far - z_near);
- result[3][0] = -(right + left) / (right - left);
- result[3][1] = -(top + bottom) / (top - bottom);
- result[3][2] = -(z_far + z_near) / (z_far - z_near);
-
- return result;
-}
-
-inline Matrix4
-perspective(Angle fovy, f32 aspect, f32 z_near, f32 z_far)
-{
- GB_ASSERT(math::abs(aspect) > 0.0f,
- "math::perspective `fovy` is %f rad", angle::as_radians(fovy));
-
- f32 tan_half_fovy = math::tan(0.5f * fovy);
-
- Matrix4 result = {};
- result[0][0] = 1.0f / (aspect * tan_half_fovy);
- result[1][1] = 1.0f / (tan_half_fovy);
- result[2][2] = -(z_far + z_near) / (z_far - z_near);
- result[2][3] = -1.0f;
- result[3][2] = -2.0f * z_far * z_near / (z_far - z_near);
-
- return result;
-}
-
-inline Matrix4
-infinite_perspective(Angle fovy, f32 aspect, f32 z_near)
-{
- f32 range = math::tan(0.5f * fovy) * z_near;
- f32 left = -range * aspect;
- f32 right = range * aspect;
- f32 bottom = -range;
- f32 top = range;
-
- Matrix4 result = {};
-
- result[0][0] = (2.0f * z_near) / (right - left);
- result[1][1] = (2.0f * z_near) / (top - bottom);
- result[2][2] = -1.0f;
- result[2][3] = -1.0f;
- result[3][2] = -2.0f * z_near;
-
- return result;
-}
-
-
-inline Matrix4
-look_at_matrix4(Vector3 eye, Vector3 center, Vector3 up)
-{
- const Vector3 f = math::normalize(center - eye);
- const Vector3 s = math::normalize(math::cross(f, up));
- const Vector3 u = math::cross(s, f);
-
- Matrix4 result = MATRIX4_IDENTITY;
-
- result[0][0] = +s.x;
- result[1][0] = +s.y;
- result[2][0] = +s.z;
-
- result[0][1] = +u.x;
- result[1][1] = +u.y;
- result[2][1] = +u.z;
-
- result[0][2] = -f.x;
- result[1][2] = -f.y;
- result[2][2] = -f.z;
-
- result[3][0] = -math::dot(s, eye);
- result[3][1] = -math::dot(u, eye);
- result[3][2] = +math::dot(f, eye);
-
- return result;
-}
-
-
-inline Quaternion
-look_at_quaternion(Vector3 eye, Vector3 center, Vector3 up)
-{
- if (math::equals(math::magnitude(center - eye), 0, 0.001f))
- return QUATERNION_IDENTITY; // You cannot look at where you are!
-
-#if 1
- return matrix4_to_quaternion(look_at_matrix4(eye, center, up));
-#else
- // TODO(bill): Thoroughly test this look_at_quaternion!
- // Is it more efficient that that a converting a Matrix4 to a Quaternion?
- Vector3 forward_l = math::normalize(center - eye);
- Vector3 forward_w = {1, 0, 0};
- Vector3 axis = math::cross(forward_l, forward_w);
-
- f32 angle = math::acos(math::dot(forward_l, forward_w));
-
- Vector3 third = math::cross(axis, forward_w);
- if (math::dot(third, forward_l) < 0)
- angle = -angle;
-
- Quaternion q1 = math::axis_angle(axis, angle);
-
- Vector3 up_l = q1 * math::normalize(up);
- Vector3 right = math::normalize(math::cross(forward_l, up));
- Vector3 up_w = math::normalize(math::cross(right, forward_l));
-
- Vector3 axis2 = math::cross(up_l, up_w);
- f32 angle2 = math::acos(math::dot(up_l, up_w));
-
- Quaternion q2 = math::axis_angle(axis2, angle2);
-
- return q2 * q1;
-#endif
-}
-
-// Transform Functions
-inline Vector3
-transform_point(Transform const& transform, Vector3 point)
-{
- return (math::conjugate(transform.orientation) * (transform.position - point)) / transform.scale;
-}
-
-inline Transform
-inverse(Transform const& t)
-{
- const Quaternion inv_orientation = math::conjugate(t.orientation);
-
- Transform inv_transform;
-
- inv_transform.position = (inv_orientation * -t.position) / t.scale;
- inv_transform.orientation = inv_orientation;
- // inv_transform.scale = inv_orientation * (Vector3{1, 1, 1} / t.scale); // Vector3 scale
- inv_transform.scale = 1.0f / t.scale;
-
- return inv_transform;
-}
-
-inline Matrix4
-transform_to_matrix4(Transform const& t)
-{
- return math::translate(t.position) *
- math::quaternion_to_matrix4(t.orientation) *
- math::scale({t.scale, t.scale, t.scale});
-}
-} // namespace math
-
-
-namespace aabb
-{
-inline Aabb
-calculate(void const* vertices, usize num_vertices, usize stride, usize offset)
-{
- Vector3 min;
- Vector3 max;
- const u8* vertex = reinterpret_cast<const u8*>(vertices);
- vertex += offset;
- Vector3 position = pseudo_cast<Vector3>(vertex);
- min.x = max.x = position.x;
- min.y = max.y = position.y;
- min.z = max.z = position.z;
- vertex += stride;
-
- for (usize i = 1; i < num_vertices; i++)
- {
- position = pseudo_cast<Vector3>(vertex);
- vertex += stride;
-
- Vector3 p = position;
- min.x = math::min(p.x, min.x);
- min.y = math::min(p.y, min.y);
- min.z = math::min(p.z, min.z);
- max.x = math::max(p.x, max.x);
- max.y = math::max(p.y, max.y);
- max.z = math::max(p.z, max.z);
- }
-
- Aabb aabb;
-
- aabb.center = 0.5f * (min + max);
- aabb.half_size = 0.5f * (max - min);
-
- return aabb;
-}
-
-inline f32
-surface_area(Aabb const& aabb)
-{
- Vector3 h = aabb.half_size * 2.0f;
- f32 s = 0.0f;
- s += h.x * h.y;
- s += h.y * h.z;
- s += h.z * h.x;
- s *= 3.0f;
- return s;
-}
-
-inline f32
-volume(Aabb const& aabb)
-{
- Vector3 h = aabb.half_size * 2.0f;
- return h.x * h.y * h.z;
-}
-
-inline Sphere
-to_sphere(Aabb const& aabb)
-{
- Sphere s;
- s.center = aabb.center;
- s.radius = math::magnitude(aabb.half_size);
- return s;
-}
-
-
-inline bool
-contains(Aabb const& aabb, Vector3 point)
-{
- Vector3 distance = aabb.center - point;
-
- // NOTE(bill): & is faster than &&
- return (math::abs(distance.x) <= aabb.half_size.x) &
- (math::abs(distance.y) <= aabb.half_size.y) &
- (math::abs(distance.z) <= aabb.half_size.z);
-}
-
-inline bool
-contains(Aabb const& a, Aabb const& b)
-{
- Vector3 dist = a.center - b.center;
-
- // NOTE(bill): & is faster than &&
- return (math::abs(dist.x) + b.half_size.x <= a.half_size.x) &
- (math::abs(dist.y) + b.half_size.y <= a.half_size.y) &
- (math::abs(dist.z) + b.half_size.z <= a.half_size.z);
-}
-
-
-inline bool
-intersects(Aabb const& a, Aabb const& b)
-{
- Vector3 dist = a.center - b.center;
- Vector3 sum_half_sizes = a.half_size + b.half_size;
-
- // NOTE(bill): & is faster than &&
- return (math::abs(dist.x) <= sum_half_sizes.x) &
- (math::abs(dist.y) <= sum_half_sizes.y) &
- (math::abs(dist.z) <= sum_half_sizes.z);
-}
-
-inline Aabb
-transform_affine(Aabb const& aabb, Matrix4 const& m)
-{
- GB_ASSERT(math::is_affine(m),
- "Passed Matrix4 must be an affine matrix");
-
- Aabb result;
- Vector4 ac;
- ac.xyz = aabb.center;
- ac.w = 1;
- result.center = (m * ac).xyz;
-
- Vector3 hs = aabb.half_size;
- f32 x = math::abs(m[0][0] * hs.x + math::abs(m[0][1]) * hs.y + math::abs(m[0][2]) * hs.z);
- f32 y = math::abs(m[1][0] * hs.x + math::abs(m[1][1]) * hs.y + math::abs(m[1][2]) * hs.z);
- f32 z = math::abs(m[2][0] * hs.x + math::abs(m[2][1]) * hs.y + math::abs(m[2][2]) * hs.z);
-
- result.half_size.x = math::is_infinite(math::abs(hs.x)) ? hs.x : x;
- result.half_size.y = math::is_infinite(math::abs(hs.y)) ? hs.y : y;
- result.half_size.z = math::is_infinite(math::abs(hs.z)) ? hs.z : z;
-
- return result;
-}
-} // namespace aabb
-
-namespace sphere
-{
-Sphere
-calculate_min_bounding(void const* vertices, usize num_vertices, usize stride, usize offset, f32 step)
-{
-#if !defined(GB_MATH_NO_RANDOM)
- auto gen = random::make(0);
-#endif
-
- u8 const* vertex = reinterpret_cast<u8 const*>(vertices);
- vertex += offset;
-
- Vector3 position = pseudo_cast<Vector3>(vertex[0]);
- Vector3 center = position;
- center += pseudo_cast<Vector3>(vertex[1 * stride]);
- center *= 0.5f;
-
- Vector3 d = position - center;
- f32 max_dist_sq = math::dot(d, d);
- f32 radius_step = step * 0.37f;
-
- bool done;
- do
- {
- done = true;
-#if !defined(GB_MATH_NO_RANDOM)
- for (u32 i = 0, index = random::uniform_u32(&gen, 0, num_vertices-1);
- i < num_vertices;
- i++, index = (index + 1)%num_vertices)
-#else
- for (u32 i = 0, index = num_vertices/2;
- i < num_vertices;
- i++, index = (index + 1)%num_vertices)
-#endif
- {
- Vector3 position = pseudo_cast<Vector3>(vertex[index * stride]);
-
- d = position - center;
- f32 dist_sq = math::dot(d, d);
-
- if (dist_sq > max_dist_sq)
- {
- done = false;
-
- center = d * radius_step;
- max_dist_sq = math::lerp(max_dist_sq, dist_sq, step);
-
- break;
- }
- }
- }
- while (!done);
-
- Sphere result;
-
- result.center = center;
- result.radius = math::sqrt(max_dist_sq);
-
- return result;
-}
-
-Sphere
-calculate_max_bounding(void const* vertices, usize num_vertices, usize stride, usize offset)
-{
- Aabb aabb = aabb::calculate(vertices, num_vertices, stride, offset);
-
- Vector3 center = aabb.center;
-
- f32 max_dist_sq = 0.0f;
- const u8* vertex = reinterpret_cast<const u8*>(vertices);
- vertex += offset;
-
- for (usize i = 0; i < num_vertices; i++)
- {
- Vector3 position = pseudo_cast<Vector3>(vertex);
- vertex += stride;
-
- Vector3 d = position - center;
- f32 dist_sq = math::dot(d, d);
- max_dist_sq = math::max(dist_sq, max_dist_sq);
- }
-
- Sphere sphere;
- sphere.center = center;
- sphere.radius = math::sqrt(max_dist_sq);
-
- return sphere;
-}
-
-inline f32
-surface_area(Sphere s)
-{
- return 2.0f * math::TAU * s.radius * s.radius;
-}
-
-inline f32
-volume(Sphere s)
-{
- return math::TWO_THIRDS * math::TAU * s.radius * s.radius * s.radius;
-}
-
-inline Aabb
-to_aabb(Sphere s)
-{
- Aabb a;
- a.center = s.center;
- a.half_size.x = s.radius * math::SQRT_3;
- a.half_size.y = s.radius * math::SQRT_3;
- a.half_size.z = s.radius * math::SQRT_3;
- return a;
-}
-
-inline bool
-contains_point(Sphere s, Vector3 point)
-{
- Vector3 dr = point - s.center;
- f32 distance = math::dot(dr, dr);
- return distance < s.radius * s.radius;
-}
-
-inline f32
-ray_intersection(Vector3 from, Vector3 dir, Sphere s)
-{
- Vector3 v = s.center - from;
- f32 b = math::dot(v, dir);
- f32 det = (s.radius * s.radius) - math::dot(v, v) + (b * b);
-
- if (det < 0.0 || b < s.radius)
- return -1.0f;
- return b - math::sqrt(det);
-}
-} // namespace sphere
-
-namespace plane
-{
-inline f32
-ray_intersection(Vector3 from, Vector3 dir, Plane p)
-{
- f32 nd = math::dot(dir, p.normal);
- f32 orpn = math::dot(from, p.normal);
- f32 dist = -1.0f;
-
- if (nd < 0.0f)
- dist = (-p.distance - orpn) / nd;
-
- return dist > 0.0f ? dist : -1.0f;
-}
-
-inline bool
-intersection3(Plane p1, Plane p2, Plane p3, Vector3* ip)
-{
- f32 den = -math::dot(math::cross(p1.normal, p2.normal), p3.normal);
-
- if (math::equals(den, 0.0f))
- return false;
-
- Vector3 res = p1.distance * math::cross(p2.normal, p3.normal)
- + p2.distance * math::cross(p3.normal, p1.normal)
- + p3.distance * math::cross(p1.normal, p2.normal);
- *ip = res / den;
-
- return true;
-}
-} // namespace plane
-
-#if !defined(GB_MATH_NO_RANDOM)
-namespace random
-{
-inline Random
-make(s64 seed)
-{
- Random r = {};
- set_seed(&r, seed);
- return r;
-}
-
-void
-set_seed(Random* r, s64 seed)
-{
- r->seed = seed;
- r->mt[0] = seed;
- for (u64 i = 1; i < 312; i++)
- r->mt[i] = 6364136223846793005ull * (r->mt[i-1] ^ r->mt[i-1] >> 62) + i;
-}
-
-s64
-next(Random* r)
-{
- const u64 MAG01[2] = {0ull, 0xb5026f5aa96619e9ull};
-
- u64 x;
- if (r->index > 312)
- {
- u32 i = 0;
- for (; i < 312-156; i++)
- {
- x = (r->mt[i] & 0xffffffff80000000ull) | (r->mt[i+1] & 0x7fffffffull);
- r->mt[i] = r->mt[i+156] ^ (x>>1) ^ MAG01[(u32)(x & 1ull)];
- }
- for (; i < 312-1; i++)
- {
- x = (r->mt[i] & 0xffffffff80000000ull) | (r->mt[i+1] & 0x7fffffffull);
- r->mt[i] = r->mt[i + (312-156)] ^ (x >> 1) ^ MAG01[(u32)(x & 1ull)];
- }
- x = (r->mt[312-1] & 0xffffffff80000000ull) | (r->mt[0] & 0x7fffffffull);
- r->mt[312-1] = r->mt[156-1] ^ (x>>1) ^ MAG01[(u32)(x & 1ull)];
-
- r->index = 0;
- }
-
- x = r->mt[r->index++];
-
- x ^= (x >> 29) & 0x5555555555555555ull;
- x ^= (x << 17) & 0x71d67fffeda60000ull;
- x ^= (x << 37) & 0xfff7eee000000000ull;
- x ^= (x >> 43);
-
- return x;
-}
-
-void
-next_from_device(void* buffer, u32 length_in_bytes)
-{
-#if defined(GB_SYSTEM_WINDOWS)
- HCRYPTPROV prov;
-
- bool ok = CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT);
- GB_ASSERT(ok, "CryptAcquireContext");
- ok = CryptGenRandom(prov, length_in_bytes, reinterpret_cast<u8*>(&buffer));
- GB_ASSERT(ok, "CryptGenRandom");
-
- CryptReleaseContext(prov, 0);
-
-#else
- #error Implement random::next_from_device()
-#endif
-}
-
-inline s32
-next_s32(Random* r)
-{
- return bit_cast<s32>(random::next(r));
-}
-
-inline u32
-next_u32(Random* r)
-{
- return bit_cast<u32>(random::next(r));
-}
-
-inline f32
-next_f32(Random* r)
-{
- return bit_cast<f32>(random::next(r));
-}
-
-inline s64
-next_s64(Random* r)
-{
- return random::next(r);
-}
-
-inline u64
-next_u64(Random* r)
-{
- return bit_cast<u64>(random::next(r));
-}
-
-inline f64
-next_f64(Random* r)
-{
- return bit_cast<f64>(random::next(r));
-}
-
-inline s32
-uniform_s32(Random* r, s32 min_inc, s32 max_inc)
-{
- return (random::next_s32(r) & (max_inc - min_inc + 1)) + min_inc;
-}
-
-inline u32
-uniform_u32(Random* r, u32 min_inc, u32 max_inc)
-{
- return (random::next_u32(r) & (max_inc - min_inc + 1)) + min_inc;
-}
-
-inline f32
-uniform_f32(Random* r, f32 min_inc, f32 max_inc)
-{
- f64 n = (random::next_s64(r) >> 11) * (1.0/4503599627370495.0);
- return static_cast<f32>(n * (max_inc - min_inc + 1.0) + min_inc);
-}
-
-inline s64
-uniform_s64(Random* r, s64 min_inc, s64 max_inc)
-{
- return (random::next_s32(r) & (max_inc - min_inc + 1)) + min_inc;
-}
-
-inline u64
-uniform_u64(Random* r, u64 min_inc, u64 max_inc)
-{
- return (random::next_u64(r) & (max_inc - min_inc + 1)) + min_inc;
-}
-
-inline f64
-uniform_f64(Random* r, f64 min_inc, f64 max_inc)
-{
- f64 n = (random::next_s64(r) >> 11) * (1.0/4503599627370495.0);
- return (n * (max_inc - min_inc + 1.0) + min_inc);
-}
-
-
-global_variable const s32 g_perlin_randtab[512] =
-{
- 23, 125, 161, 52, 103, 117, 70, 37, 247, 101, 203, 169, 124, 126, 44, 123,
- 152, 238, 145, 45, 171, 114, 253, 10, 192, 136, 4, 157, 249, 30, 35, 72,
- 175, 63, 77, 90, 181, 16, 96, 111, 133, 104, 75, 162, 93, 56, 66, 240,
- 8, 50, 84, 229, 49, 210, 173, 239, 141, 1, 87, 18, 2, 198, 143, 57,
- 225, 160, 58, 217, 168, 206, 245, 204, 199, 6, 73, 60, 20, 230, 211, 233,
- 94, 200, 88, 9, 74, 155, 33, 15, 219, 130, 226, 202, 83, 236, 42, 172,
- 165, 218, 55, 222, 46, 107, 98, 154, 109, 67, 196, 178, 127, 158, 13, 243,
- 65, 79, 166, 248, 25, 224, 115, 80, 68, 51, 184, 128, 232, 208, 151, 122,
- 26, 212, 105, 43, 179, 213, 235, 148, 146, 89, 14, 195, 28, 78, 112, 76,
- 250, 47, 24, 251, 140, 108, 186, 190, 228, 170, 183, 139, 39, 188, 244, 246,
- 132, 48, 119, 144, 180, 138, 134, 193, 82, 182, 120, 121, 86, 220, 209, 3,
- 91, 241, 149, 85, 205, 150, 113, 216, 31, 100, 41, 164, 177, 214, 153, 231,
- 38, 71, 185, 174, 97, 201, 29, 95, 7, 92, 54, 254, 191, 118, 34, 221,
- 131, 11, 163, 99, 234, 81, 227, 147, 156, 176, 17, 142, 69, 12, 110, 62,
- 27, 255, 0, 194, 59, 116, 242, 252, 19, 21, 187, 53, 207, 129, 64, 135,
- 61, 40, 167, 237, 102, 223, 106, 159, 197, 189, 215, 137, 36, 32, 22, 5,
-
-// Copy
- 23, 125, 161, 52, 103, 117, 70, 37, 247, 101, 203, 169, 124, 126, 44, 123,
- 152, 238, 145, 45, 171, 114, 253, 10, 192, 136, 4, 157, 249, 30, 35, 72,
- 175, 63, 77, 90, 181, 16, 96, 111, 133, 104, 75, 162, 93, 56, 66, 240,
- 8, 50, 84, 229, 49, 210, 173, 239, 141, 1, 87, 18, 2, 198, 143, 57,
- 225, 160, 58, 217, 168, 206, 245, 204, 199, 6, 73, 60, 20, 230, 211, 233,
- 94, 200, 88, 9, 74, 155, 33, 15, 219, 130, 226, 202, 83, 236, 42, 172,
- 165, 218, 55, 222, 46, 107, 98, 154, 109, 67, 196, 178, 127, 158, 13, 243,
- 65, 79, 166, 248, 25, 224, 115, 80, 68, 51, 184, 128, 232, 208, 151, 122,
- 26, 212, 105, 43, 179, 213, 235, 148, 146, 89, 14, 195, 28, 78, 112, 76,
- 250, 47, 24, 251, 140, 108, 186, 190, 228, 170, 183, 139, 39, 188, 244, 246,
- 132, 48, 119, 144, 180, 138, 134, 193, 82, 182, 120, 121, 86, 220, 209, 3,
- 91, 241, 149, 85, 205, 150, 113, 216, 31, 100, 41, 164, 177, 214, 153, 231,
- 38, 71, 185, 174, 97, 201, 29, 95, 7, 92, 54, 254, 191, 118, 34, 221,
- 131, 11, 163, 99, 234, 81, 227, 147, 156, 176, 17, 142, 69, 12, 110, 62,
- 27, 255, 0, 194, 59, 116, 242, 252, 19, 21, 187, 53, 207, 129, 64, 135,
- 61, 40, 167, 237, 102, 223, 106, 159, 197, 189, 215, 137, 36, 32, 22, 5,
-};
-
-
-internal_linkage f32
-perlin_grad(s32 hash, f32 x, f32 y, f32 z)
-{
- local_persist const f32 basis[12][4] =
- {
- { 1, 1, 0},
- {-1, 1, 0},
- { 1,-1, 0},
- {-1,-1, 0},
- { 1, 0, 1},
- {-1, 0, 1},
- { 1, 0,-1},
- {-1, 0,-1},
- { 0, 1, 1},
- { 0,-1, 1},
- { 0, 1,-1},
- { 0,-1,-1},
- };
-
- local_persist const u8 indices[64] =
- {
- 0,1,2,3,4,5,6,7,8,9,10,11,
- 0,9,1,11,
- 0,1,2,3,4,5,6,7,8,9,10,11,
- 0,1,2,3,4,5,6,7,8,9,10,11,
- 0,1,2,3,4,5,6,7,8,9,10,11,
- 0,1,2,3,4,5,6,7,8,9,10,11,
- };
-
- const f32* grad = basis[indices[hash & 63]];
- return grad[0]*x + grad[1]*y + grad[2]*z;
-}
-
-
-inline f32
-perlin_3d(f32 x, f32 y, f32 z, s32 x_wrap, s32 y_wrap, s32 z_wrap)
-{
- u32 x_mask = (x_wrap-1) & 255;
- u32 y_mask = (y_wrap-1) & 255;
- u32 z_mask = (z_wrap-1) & 255;
-
- s32 px = static_cast<s32>(math::floor(x));
- s32 py = static_cast<s32>(math::floor(y));
- s32 pz = static_cast<s32>(math::floor(z));
-
- s32 x0 = (px) & x_mask;
- s32 x1 = (px+1) & x_mask;
- s32 y0 = (py) & y_mask;
- s32 y1 = (py+1) & y_mask;
- s32 z0 = (pz) & z_mask;
- s32 z1 = (pz+1) & z_mask;
-
- x -= px;
- y -= py;
- z -= pz;
-
-#define GB__PERLIN_EASE(t) (((6*t - 15)*t + 10)*t*t*t)
- f32 u = GB__PERLIN_EASE(x);
- f32 v = GB__PERLIN_EASE(y);
- f32 w = GB__PERLIN_EASE(z);
-#undef GB__PERLIN_EASE
-
- s32 r0 = g_perlin_randtab[x0];
- s32 r1 = g_perlin_randtab[x1];
-
- s32 r00 = g_perlin_randtab[r0 + y0];
- s32 r01 = g_perlin_randtab[r0 + y1];
- s32 r10 = g_perlin_randtab[r1 + y0];
- s32 r11 = g_perlin_randtab[r1 + y1];
-
- f32 n000 = perlin_grad(g_perlin_randtab[r00 + z0], x, y, z );
- f32 n001 = perlin_grad(g_perlin_randtab[r00 + z1], x, y, z - 1);
- f32 n010 = perlin_grad(g_perlin_randtab[r01 + z0], x, y - 1, z );
- f32 n011 = perlin_grad(g_perlin_randtab[r01 + z1], x, y - 1, z - 1);
- f32 n100 = perlin_grad(g_perlin_randtab[r10 + z0], x - 1, y, z );
- f32 n101 = perlin_grad(g_perlin_randtab[r10 + z1], x - 1, y, z - 1);
- f32 n110 = perlin_grad(g_perlin_randtab[r11 + z0], x - 1, y - 1, z );
- f32 n111 = perlin_grad(g_perlin_randtab[r11 + z1], x - 1, y - 1, z - 1);
-
- f32 n00 = math::lerp(n000, n001, w);
- f32 n01 = math::lerp(n010, n011, w);
- f32 n10 = math::lerp(n100, n101, w);
- f32 n11 = math::lerp(n110, n111, w);
-
- f32 n0 = math::lerp(n00, n01, v);
- f32 n1 = math::lerp(n10, n11, v);
-
- return math::lerp(n0, n1, u);
-}
-
-} // namespace random
-#endif
-
-__GB_NAMESPACE_END
-
-#endif // GB_MATH_IMPLEMENTATION