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-// mathlib.cpp
-//
-// Created by Matt Kosarek
-//
-// A file containing some common math functionality that I find
-// useful in my projects. I don't like that I don't know what's happening
-// in glm, so I wrote most of this myself. All mistakes are my own.
-//
-
-#include "mathlib.h"
-#include <cstdlib>
-
-// ***************************************
-// Vector2
-Vector2::Vector2() { }
-
-Vector2::Vector2(float inX, float inY) {
- x = inX;
- y = inY;
-}
-
-Vector2 getRandomNormalVector2() {
- Vector2 retval = {
- static_cast<float>(rand()) / static_cast<float>(RAND_MAX),
- static_cast<float>(rand()) / static_cast<float>(RAND_MAX)
- };
-
- return retval.normalize();
-}
-
-Vector2 Vector2::operator+(Vector2 other) {
- return { x + other.x, y + other.y };
-}
-
-Vector2& Vector2::operator+=(Vector2 other) {
- x += other.x;
- y += other.y;
- return *this;
-}
-
-Vector2 Vector2::operator-(Vector2 other) {
- return { x - other.x, y - other.y };
-}
-
-Vector2 Vector2::operator*(float s) {
- return { x * s, y * s };
-}
-
-Vector2 Vector2::operator/(float s) {
- return { x / s, y / s };
-}
-
-float Vector2::dot(Vector2 other) {
- return x * other.x + y * other.y;
-}
-
-float Vector2::length() {
- return sqrtf(x * x + y * y);
-}
-
-Vector2 Vector2::normalize() {
- float len = length();
- float inverseLength = len == 0 ? 1.0 : 1.0 / len;
-
- return { x * inverseLength, y * inverseLength };
-}
-
-Vector2 Vector2::negate() {
- return { -x, -y };
-}
-
-Vector2 Vector2::getPerp() {
- return { y, -x };
-}
-
-Vector2 Vector2::rotate(float angle) {
- return {
- x * cosf(angle) - y * sinf(angle),
- x * sinf(angle) + y * cosf(angle)
- };
-}
-
-Vector2 Vector2::rotateAround(float angle, const Vector2& other) {
- Vector2 point = { x - other.x, y - other.y };
- point = {
- point.x * cosf(angle) - point.y * sinf(angle),
- point.x * sinf(angle) + point.y * cosf(angle)
- };
- point = point + other;
- return point;
-}
-
-void Vector2::printDebug(const char* name) {
- printf("%s=Vector2(%f, %f)\n", name, x, y);
-}
-
-
-// ***************************************
-// Vector3
-Vector3::Vector3() { };
-
-Vector3::Vector3(float value) {
- x = value;
- y = value;
- z = value;
-}
-
-Vector3::Vector3(float inX, float inY, float inZ) {
- x = inX;
- y = inY;
- z = inZ;
-}
-
-float Vector3::length() {
- return sqrtf(x * x + y * y + z * z);
-}
-
-float Vector3::dot(const Vector3& other) {
- return x * other.x + y * other.y + z * other.z;
-}
-
-Vector3 Vector3::scale(float scalar) {
- return {
- x * scalar,
- y * scalar,
- z * scalar
- };
-}
-
-Vector3 Vector3::add(const Vector3& other) {
- return {
- x + other.x,
- y + other.y,
- z + other.z
- };
-}
-
-Vector3 Vector3::subtract(const Vector3& other) {
- return {
- x - other.x,
- y - other.y,
- z - other.z
- };
-}
-
-Vector3 Vector3::negate() {
- return {
- -x,
- -y,
- -z
- };
-}
-
-Vector3 Vector3::cross(const Vector3& other) {
- return {
- y * other.z - z * other.y,
- z * other.x - x * other.z,
- x * other.y - y * other.x
- };
-}
-
-Vector3 Vector3::normalize() {
- float len = 1.f / length();
- return {
- x * len,
- y * len,
- z * len
- };
-}
-
-Vector3 Vector3::operator+(const Vector3& v2) {
- return add(v2);
-}
-
-Vector3& Vector3::operator+=(Vector3 other) {
- x += other.x;
- y += other.y;
- z += other.z;
- return *this;
-}
-
-Vector3 Vector3::operator-(const Vector3& v2) {
- return subtract(v2);
-}
-
-Vector3 Vector3::operator-() {
- return negate();
-}
-
-Vector3 Vector3::operator*(float value) {
- return scale(value);
-}
-
-Vector3 Vector3::operator/(const Vector3& v2) {
- return {
- x / v2.x,
- y / v2.y,
- z / v2.z
- };
-}
-
-Vector3 Vector3::operator*(const Vector3& v2) {
- return {
- x * v2.x,
- y * v2.y,
- z * v2.z
- };
-}
-
-float Vector3::operator [](int index) {
- switch (index) {
- case 0:
- return x;
- case 1:
- return y;
- case 2:
- return z;
- default:
- return 0;
- }
-}
-
-void Vector2::operator=(const Vector4& other) {
- x = other.x;
- y = other.y;
-}
-
-void Vector3::printDebug(const char* name) {
- printf("%s=Vector3(%f, %f, %f)\n", name, x, y, z);
-}
-
-
-// ***************************************
-// Vector4
-Vector4::Vector4() { }
-
-Vector4::Vector4(float value) {
- x = value;
- y = value;
- z = value;
- w = value;
-}
-
-Vector4::Vector4(float inX, float inY, float inZ, float inW) {
- x = inX;
- y = inY;
- z = inZ;
- w = inW;
-}
-
-Vector4::Vector4(Vector2& v) {
- x = v.x;
- y = v.y;
- z = 0;
- w = 1;
-}
-
-Vector4::Vector4(Vector3& v) {
- x = v.x;
- y = v.y;
- z = v.z;
- w = 1;
-}
-
-Vector4 Vector4::fromColor(float r, float g, float b, float a) {
- float scale = 1.f / 255.f;
- return { r * scale, g * scale, b * scale, a * scale };
-}
-
-Vector4 Vector4::toNormalizedColor() {
- return fromColor(x, y, z, w);
-}
-
-
-Vector3 Vector4::toVector3() {
- return { x, y, z };
-}
-
-float Vector4::length() {
- return sqrtf(x * x + y * y + z * z + w * w);
-}
-
-Vector4 Vector4::normalize() {
- float len = length();
- float inverseLength = len == 0 ? 1.0 : 1.0 / len;
-
- return { x * inverseLength, y * inverseLength, z * inverseLength, w * inverseLength };
-}
-
-float Vector4::dot(const Vector4& other) {
- return x * other.x + y * other.y + z * other.z + w * other.w;
-}
-
-Vector4 Vector4::scale(float scalar) {
- return {
- x * scalar,
- y * scalar,
- z * scalar,
- w * scalar
- };
-}
-
-Vector4 Vector4::add(const Vector4& other) {
- return {
- x + other.x,
- y + other.y,
- z + other.z,
- w + other.w
- };
-}
-
-Vector4 Vector4::subtract(const Vector4& other) {
- return {
- x - other.x,
- y - other.y,
- z - other.z,
- w - other.w
- };
-}
-
-Vector4 Vector4::negate() {
- return { -x, -y, -z, -w };
-}
-
-Vector4 Vector4::cross(const Vector4& other) {
- return {
- y * other.z - z * other.y,
- z * other.x - x * other.z,
- x * other.y - y * other.x,
- 1.f
- };
-}
-
-Vector4 lerp(Vector4 start, Vector4 end, float t) {
- return (end - start) * t + start;
-}
-
-void Vector4::operator=(const Vector2& v2) {
- x = v2.x;
- y = v2.y;
- z = 0;
- w = 1;
-}
-
-void Vector4::operator=(const Vector3& v2) {
- x = v2.x;
- y = v2.y;
- z = v2.z;
- w = 1;
-}
-
-Vector4 Vector4::operator+(const Vector4& v2) {
- return add(v2);
-}
-
-Vector4 Vector4::operator-(const Vector4& v2) {
- return subtract(v2);
-}
-
-Vector4 Vector4::operator-() {
- return negate();
-}
-
-Vector4 Vector4::operator*(float value) {
- return scale(value);
-}
-
-Vector4 Vector4::operator*(const Vector4& v2) {
- return {
- x * v2.x,
- y * v2.y,
- z * v2.z,
- w * v2.w
- };
-}
-
-float Vector4::operator[](int index) {
- switch (index) {
- case 0:
- return x;
- case 1:
- return y;
- case 2:
- return z;
- case 3:
- return w;
- default:
- return 0;
- }
-}
-
-void Vector4::printDebug(const char* name) {
- printf("%s=Vector4(%f, %f, %f, %f)\n", name, x, y, z, w);
-}
-
-
-// ***************************************
-// Mat4x4
-Mat4x4 Mat4x4::copy() {
- Mat4x4 result;
- memcpy(result.m, m, sizeof(float) * 16);
- return result;
-}
-
-Mat4x4 Mat4x4::scale(Vector3 v) {
- Mat4x4 result = copy();
- result.m[0] = result.m[0] * v.x;
- result.m[5] = result.m[5] *v.y;
- result.m[10] = result.m[10] * v.z;
- return result;
-}
-
-Mat4x4 Mat4x4::translate(Vector3 v) {
- Mat4x4 result = copy();
- result.m[12] += v.x;
- result.m[13] += v.y;
- result.m[14] += v.z;
- return result;
-}
-
-Mat4x4 Mat4x4::translateByVec2(Vector2 v) {
- Mat4x4 result = copy();
- result.m[12] += v.x;
- result.m[13] += v.y;
- return result;
-}
-
-Mat4x4 Mat4x4::rotate2D(float angle) {
- Mat4x4 result = copy();
- result.m[0] = cos(angle);
- result.m[1] = -sin(angle);
- result.m[4] = sin(angle);
- result.m[5] = cos(angle);
- return result;
-}
-
-Mat4x4 Mat4x4::getXRotationMatrix(float angleRadians) {
- return {
- { 1, 0, 0, 0,
- 0, cos(angleRadians), -sin(angleRadians), 0,
- 0, sin(angleRadians), cos(angleRadians), 0,
- 0, 0, 0, 1 }
- };
-}
-
-Mat4x4 Mat4x4::getYRotationMatrix(float angleRadians) {
- return {
- { cos(angleRadians), 0, sin(angleRadians), 0,
- 0, 1, 0, 0,
- -sin(angleRadians), 0, cos(angleRadians), 0,
- 0, 0, 0, 1 }
- };
-}
-
-Mat4x4 Mat4x4::getZRotationMatrix(float angleRadians) {
- return {
- { cos(angleRadians), -sin(angleRadians), 0, 0,
- sin(angleRadians), cos(angleRadians), 0, 0,
- 0, 0, 1, 0,
- 0, 0, 0, 1 }
- };
-}
-
-Mat4x4 Mat4x4::rotate(float xRadians, float yRadians, float zRadians) {
- Mat4x4 result = copy();
-
- Mat4x4 rotationMatrix;
- if (xRadians != 0) {
- rotationMatrix = getXRotationMatrix(xRadians);
- result = result * rotationMatrix;
- }
-
- if (yRadians != 0) {
- rotationMatrix = getYRotationMatrix(yRadians);
- result = result * rotationMatrix;
- }
-
- if (zRadians != 0) {
- rotationMatrix = getZRotationMatrix(zRadians);
- result = result * rotationMatrix;
- }
-
- return result;
-}
-
-Vector2 Mat4x4::multByVec2(Vector2 v) {
- Vector4 vec4 = { v.x, v.y, 0.0, 1.0 };
- return {
- vec4.x * m[0] + vec4.y * m[4] + vec4.z * m[8] + vec4.w * m[12],
- vec4.x * m[1] + vec4.y * m[5] + vec4.z * m[9] + vec4.w * m[13]
- };
-}
-
-Vector2 Mat4x4::operator*(Vector2 v) {
- return multByVec2(v);
-}
-
-Mat4x4 Mat4x4::multMat4x4(const Mat4x4& other) {
- Mat4x4 result;
- for (int i = 0; i < 4; ++i) {
- for (int j = 0; j < 4; ++j) {
- int row = i * 4;
- result.m[row + j] = m[row + 0] * other.m[0 + j] + m[row + 1] * other.m[4 + j] + m[row + 2] * other.m[8 + j] + m[row + 3] * other.m[12 + j];
- }
- }
-
- return result;
-}
-
-Mat4x4 Mat4x4::operator*(const Mat4x4& other) {
- return multMat4x4(other);
-}
-
-Mat4x4 Mat4x4::getOrthographicMatrix(float left, float right, float bottom, float top) {
- Mat4x4 result;
- result.m[0] = 2.0 / (right - left);
- result.m[5] = 2.0 / (top - bottom);
- result.m[10] = 1.0;
- result.m[12] = -(right + left) / (right - left);
- result.m[13] = -(top + bottom) / (top - bottom);
- return result;
-}
-
-Mat4x4 Mat4x4::inverse() {
- Mat4x4 inv;
-
- inv.m[0] = m[5] * m[10] * m[15] - m[5] * m[11] * m[14] - m[9] * m[6] * m[15] + m[9] * m[7] * m[14] + m[13] * m[6] * m[11] - m[13] * m[7] * m[10];
- inv.m[4] = -m[4] * m[10] * m[15] + m[4] * m[11] * m[14] + m[8] * m[6] * m[15] - m[8] * m[7] * m[14] - m[12] * m[6] * m[11] + m[12] * m[7] * m[10];
- inv.m[8] = m[4] * m[9] * m[15] - m[4] * m[11] * m[13] - m[8] * m[5] * m[15] + m[8] * m[7] * m[13] + m[12] * m[5] * m[11] - m[12] * m[7] * m[9];
- inv.m[12] = -m[4] * m[9] * m[14] + m[4] * m[10] * m[13] + m[8] * m[5] * m[14] - m[8] * m[6] * m[13] - m[12] * m[5] * m[10] + m[12] * m[6] * m[9];
- inv.m[1] = -m[1] * m[10] * m[15] + m[1] * m[11] * m[14] + m[9] * m[2] * m[15] - m[9] * m[3] * m[14] - m[13] * m[2] * m[11] + m[13] * m[3] * m[10];
- inv.m[5] = m[0] * m[10] * m[15] - m[0] * m[11] * m[14] - m[8] * m[2] * m[15] + m[8] * m[3] * m[14] + m[12] * m[2] * m[11] - m[12] * m[3] * m[10];
- inv.m[9] = -m[0] * m[9] * m[15] + m[0] * m[11] * m[13] + m[8] * m[1] * m[15] - m[8] * m[3] * m[13] - m[12] * m[1] * m[11] + m[12] * m[3] * m[9];
- inv.m[13] = m[0] * m[9] * m[14] - m[0] * m[10] * m[13] - m[8] * m[1] * m[14] + m[8] * m[2] * m[13] + m[12] * m[1] * m[10] - m[12] * m[2] * m[9];
- inv.m[2] = m[1] * m[6] * m[15] - m[1] * m[7] * m[14] - m[5] * m[2] * m[15] + m[5] * m[3] * m[14] + m[13] * m[2] * m[7] - m[13] * m[3] * m[6];
- inv.m[6] = -m[0] * m[6] * m[15] + m[0] * m[7] * m[14] + m[4] * m[2] * m[15] - m[4] * m[3] * m[14] - m[12] * m[2] * m[7] + m[12] * m[3] * m[6];
- inv.m[10] = m[0] * m[5] * m[15] - m[0] * m[7] * m[13] - m[4] * m[1] * m[15] + m[4] * m[3] * m[13] + m[12] * m[1] * m[7] - m[12] * m[3] * m[5];
- inv.m[14] = -m[0] * m[5] * m[14] + m[0] * m[6] * m[13] + m[4] * m[1] * m[14] - m[4] * m[2] * m[13] - m[12] * m[1] * m[6] + m[12] * m[2] * m[5];
- inv.m[3] = -m[1] * m[6] * m[11] + m[1] * m[7] * m[10] + m[5] * m[2] * m[11] - m[5] * m[3] * m[10] - m[9] * m[2] * m[7] + m[9] * m[3] * m[6];
- inv.m[7] = m[0] * m[6] * m[11] - m[0] * m[7] * m[10] - m[4] * m[2] * m[11] + m[4] * m[3] * m[10] + m[8] * m[2] * m[7] - m[8] * m[3] * m[6];
- inv.m[11] = -m[0] * m[5] * m[11] + m[0] * m[7] * m[9] + m[4] * m[1] * m[11] - m[4] * m[3] * m[9] - m[8] * m[1] * m[7] + m[8] * m[3] * m[5];
- inv.m[15] = m[0] * m[5] * m[10] - m[0] * m[6] * m[9] - m[4] * m[1] * m[10] + m[4] * m[2] * m[9] + m[8] * m[1] * m[6] - m[8] * m[2] * m[5];
-
- float det = m[0] * inv.m[0] + m[1] * inv.m[4] + m[2] * inv.m[8] + m[3] * inv.m[12];
-
- if (det == 0)
- return Mat4x4();
-
- det = 1.f / det;
-
- for (int i = 0; i < 16; i++)
- inv.m[i] = inv.m[i] * det;
-
- return inv;
-}
-
-Mat4x4 Mat4x4::getPerspectiveProjection(float near, float far, float fieldOfViewRadians, float aspectRatio) {
- float halfFieldOfView = fieldOfViewRadians * 0.5f;
- float top = tan(halfFieldOfView) * near;
- float bottom = -top;
- float right = top * aspectRatio;
- float left = -right;
-
- return {
- { (2 * near) / (right - left), 0, 0, 0,
- 0, (2 * near) / (top - bottom), 0, 0,
- (right + left) / (right - left), (top + bottom) / (top - bottom), -(far + near) / (far - near), -1,
- 0, 0, (-2 * far * near) / (far - near), 0 }
- };
-}
-
-void Mat4x4::print() {
- printf("[ ");
- for (int idx = 0; idx < 16; idx++) {
- printf("%f, ", m[idx]);
- }
- printf(" ]\n");
-}
-
-// See https://stackoverflow.com/questions/349050/calculating-a-lookat-matrix for why the dot product is in the bottom
-Mat4x4 Mat4x4::getLookAt(Vector3 eye,Vector3 pointToLookAt, Vector3 up) {
- Vector3 zAxis = (pointToLookAt - eye).normalize();
- Vector3 xAxis = zAxis.cross(up).normalize();
- Vector3 yAxis = xAxis.cross(zAxis).normalize();
-
- return {
- { xAxis.x, yAxis.x, -zAxis.x, 0,
- xAxis.y, yAxis.y, -zAxis.y, 0,
- xAxis.z, yAxis.z, -zAxis.z, 0,
- -xAxis.dot(eye), -yAxis.dot(eye), zAxis.dot(eye), 1 }
- };
-}
-
-// ***************************************
-// Quaternion
-Quaternion::Quaternion() { };
-
-Quaternion::Quaternion(float inW, float inX, float inY, float inZ) {
- w = inW;
- x = inX;
- y = inY;
- z = inZ;
-}
-
-float Quaternion::operator [](int index) {
- switch (index) {
- case 0:
- return x;
- case 1:
- return y;
- case 2:
- return z;
- case 3:
- return w;
- default:
- return 0;
- }
-}
-
-Quaternion Quaternion::operator*(const Quaternion& other) const {
- return {
- w * other.w - x * other.x - y * other.y - z * other.z, // w
- w * other.x + x * other.w + y * other.z - z * other.y, // i
- w * other.y - x * other.z + y * other.w + z * other.x, // j
- w * other.z + x * other.y - y * other.x + z * other.w // k
- };
-}
-
-Quaternion Quaternion::operator*(const float& scale) const {
- return {
- w * scale,
- x * scale,
- y * scale,
- z * scale
- };
-}
-
-Quaternion Quaternion::operator+(const Quaternion& other) const {
- return {
- w + other.w,
- x + other.x,
- y + other.y,
- z + other.z
- };
-}
-
-Quaternion Quaternion::operator-(const Quaternion& other) const {
- return {
- w - other.w,
- x - other.x,
- y - other.y,
- z - other.z
- };
-}
-
-const float DOT_THRESHOLD = 0.9999f;
-
-// Using a slerp here, mostly taken from here: http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/.
-// As JBlow says, it's expensive as heck. I will address this if it becomes a problem.
-Quaternion Quaternion::interpolate(const Quaternion& other, const float factor) {
- Quaternion newOther = other;
- float dotProduct = dot(other);
-
- if (dotProduct < 0) {
- newOther = other * -1;
- dotProduct *= -1;
- }
-
- if (dotProduct > DOT_THRESHOLD) {
- return (*this + ((newOther - *this) * factor)).normalize();
- }
-
- float thetaZero = acos(dotProduct); // angle between input vectors
- float theta = thetaZero * factor;
-
- Quaternion v2 = (newOther - (*this * dotProduct)).normalize();
-
- return (*this * cos(theta)) + (v2 * sin(theta));
-}
-
-float Quaternion::length() const {
- return sqrtf(x * x + y * y + z * z + w * w);
-}
-
-Quaternion Quaternion::normalize() const {
- float l = length();
- return {
- w / l,
- x / l,
- y / l,
- z / l,
- };
-}
-
-/*Mat4x4 Quaternion::toMatrix() const {
- return {
- {
- 1 - 2 * (y * y - z * z),
- 2 * (x * y - z * w),
- 2 * (x * z + w * y),
- 0,
-
- 2 * (x * y + w * z),
- 1 - 2 * (x * x - z * z),
- 2 * (y * z - w * x),
- 0,
-
- 2 * (x * z - w * y),
- 2 * (y * z + w * x),
- 1 - 2 * (x * x - y * y),
- 0,
-
- 0,
- 0,
- 0,
- 1
- }
- };
-}*/
-
-Mat4x4 Quaternion::toMatrix() const {
- return {
- {
- 1 - 2 * (y * y + z * z),
- 2 * (x * y + z * w),
- 2 * (x * z - y * w),
- 0,
- 2 * (x * y - w * z),
- 1 - 2 * (x * x + z * z),
- 2 * (y * z + w * x),
- 0,
- 2 * (x * z + w * y),
- 2 * (y * z - w * x),
- 1 - 2 * (x * x + y * y),
- 0,
- 0,
- 0,
- 0,
- 1
- }
- };
-}
-
-float Quaternion::dot(const Quaternion& other) const {
- return w * other.w + x * other.x + y * other.y + z * other.z;
-}
-
-Quaternion quaternionFromRotation(Vector3 axis, float angleRadians) {
- float halfAngleRadians = angleRadians / 2.f;
- float cosHalfAngRad = cosf(halfAngleRadians);
- float sinHalfAngRad = sinf(halfAngleRadians);
-
- return {
- cosHalfAngRad,
- axis.x * sinHalfAngRad,
- axis.y * sinHalfAngRad,
- axis.z * sinHalfAngRad
- };
-}
-
-Quaternion quaternionFromEulerAngle(float yaw, float pitch, float roll) {
- float cy = cosf(yaw * 0.5f);
- float sy = sinf(yaw * 0.5f);
- float cp = cosf(pitch * 0.5f);
- float sp = sinf(pitch * 0.5f);
- float cr = cosf(roll * 0.5f);
- float sr = sinf(roll * 0.5f);
-
- return {
- cr * cp * cy + sr * sp * sy,
- sr * cp * cy - cr * sp * sy,
- cr * sp * cy + sr * cp * sy,
- cr * cp * sy - sr * sp * cy
- };
-}
-
-void Quaternion::printDebug(const char* name) {
- printf("%s=Quaternion(%f, %f, %f, %f)\n", name, x, y, z, w);
-}
generated by cgit v1.2.1 (git 2.18.0) at 2024-09-20 02:50:51 +0000