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-rw-r--r--shared_cpp/mathlib.cpp396
1 files changed, 396 insertions, 0 deletions
diff --git a/shared_cpp/mathlib.cpp b/shared_cpp/mathlib.cpp
index 8222d00..4dd3dd0 100644
--- a/shared_cpp/mathlib.cpp
+++ b/shared_cpp/mathlib.cpp
@@ -1,6 +1,8 @@
#include "mathlib.h"
#include <cstdlib>
+// ***************************************
+// Vector2
Vector2 getRandomNormalVector2() {
Vector2 retval = {
static_cast<float>(rand()) / static_cast<float>(RAND_MAX),
@@ -9,3 +11,397 @@ Vector2 getRandomNormalVector2() {
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)
+ };
+}
+
+void Vector2::printDebug(const char* name) {
+ printf("%s=Vector2(%f, %f)\n", name, x, y);
+}
+
+
+// ***************************************
+// Vector3
+float Vector3::length() {
+ return sqrtf(x * x + y * y + z * z);
+}
+
+Vector3 Vector3::operator+(const Vector3& other) {
+ return { x + other.x, y + other.y, z + other.z };
+}
+
+
+// ***************************************
+// Vector4
+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 };
+}
+
+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);
+}
+
+
+// ***************************************
+// 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");
+}
+
+// ***************************************
+// Quaternion
+
+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 - 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& second) const {
+ return w * second.w + x * second.x + y * second.y + z * second.z;
+}
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