Merge pull request #451 from Zylann/math

Added Godot's math functions

include/core/Defs.hpp

@@ -73,6 +73,7 @@ typedef float real_t;
 #define CMP_EPSILON 0.00001
 #define CMP_EPSILON2 (CMP_EPSILON * CMP_EPSILON)
 #define Math_PI 3.14159265358979323846
+#define Math_TAU 6.2831853071795864769252867666
 
 #define _PLANE_EQ_DOT_EPSILON 0.999
 #define _PLANE_EQ_D_EPSILON 0.0001

include/core/Math.hpp

@@ -0,0 +1,250 @@
+#ifndef GODOT_MATH_H
+#define GODOT_MATH_H
+
+#include "Defs.hpp"
+#include <cmath>
+
+namespace godot {
+namespace Math {
+
+// Functions reproduced as in Godot's source code `math_funcs.h`.
+// Some are overloads to automatically support changing real_t into either double or float in the way Godot does.
+
+inline double fmod(double p_x, double p_y) {
+	return ::fmod(p_x, p_y);
+}
+inline float fmod(float p_x, float p_y) {
+	return ::fmodf(p_x, p_y);
+}
+
+inline double floor(double p_x) {
+	return ::floor(p_x);
+}
+inline float floor(float p_x) {
+	return ::floorf(p_x);
+}
+
+inline double exp(double p_x) {
+	return ::exp(p_x);
+}
+inline float exp(float p_x) {
+	return ::expf(p_x);
+}
+
+inline double sin(double p_x) {
+	return ::sin(p_x);
+}
+inline float sin(float p_x) {
+	return ::sinf(p_x);
+}
+
+inline double cos(double p_x) {
+	return ::cos(p_x);
+}
+inline float cos(float p_x) {
+	return ::cosf(p_x);
+}
+
+inline double tan(double p_x) {
+	return ::tan(p_x);
+}
+inline float tan(float p_x) {
+	return ::tanf(p_x);
+}
+
+inline double atan2(double p_y, double p_x) {
+	return ::atan2(p_y, p_x);
+}
+inline float atan2(float p_y, float p_x) {
+	return ::atan2f(p_y, p_x);
+}
+
+inline double sqrt(double p_x) {
+	return ::sqrt(p_x);
+}
+inline float sqrt(float p_x) {
+	return ::sqrtf(p_x);
+}
+
+inline float lerp(float minv, float maxv, float t) {
+	return minv + t * (maxv - minv);
+}
+inline double lerp(double minv, double maxv, double t) {
+	return minv + t * (maxv - minv);
+}
+
+inline double lerp_angle(double p_from, double p_to, double p_weight) {
+	double difference = fmod(p_to - p_from, Math_TAU);
+	double distance = fmod(2.0 * difference, Math_TAU) - difference;
+	return p_from + distance * p_weight;
+}
+inline float lerp_angle(float p_from, float p_to, float p_weight) {
+	float difference = fmod(p_to - p_from, (float)Math_TAU);
+	float distance = fmod(2.0f * difference, (float)Math_TAU) - difference;
+	return p_from + distance * p_weight;
+}
+
+template <typename T>
+inline T clamp(T x, T minv, T maxv) {
+	if (x < minv) {
+		return minv;
+	}
+	if (x > maxv) {
+		return maxv;
+	}
+	return x;
+}
+
+template <typename T>
+inline T min(T a, T b) {
+	return a < b ? a : b;
+}
+
+template <typename T>
+inline T max(T a, T b) {
+	return a > b ? a : b;
+}
+
+template <typename T>
+inline T sign(T x) {
+	return x < 0 ? -1 : 1;
+}
+
+inline double deg2rad(double p_y) {
+	return p_y * Math_PI / 180.0;
+}
+inline float deg2rad(float p_y) {
+	return p_y * Math_PI / 180.0;
+}
+
+inline double rad2deg(double p_y) {
+	return p_y * 180.0 / Math_PI;
+}
+inline float rad2deg(float p_y) {
+	return p_y * 180.0 / Math_PI;
+}
+
+inline double inverse_lerp(double p_from, double p_to, double p_value) {
+	return (p_value - p_from) / (p_to - p_from);
+}
+inline float inverse_lerp(float p_from, float p_to, float p_value) {
+	return (p_value - p_from) / (p_to - p_from);
+}
+
+inline double range_lerp(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) {
+	return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
+}
+inline float range_lerp(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) {
+	return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
+}
+
+inline bool is_equal_approx(real_t a, real_t b) {
+	// Check for exact equality first, required to handle "infinity" values.
+	if (a == b) {
+		return true;
+	}
+	// Then check for approximate equality.
+	real_t tolerance = CMP_EPSILON * std::abs(a);
+	if (tolerance < CMP_EPSILON) {
+		tolerance = CMP_EPSILON;
+	}
+	return std::abs(a - b) < tolerance;
+}
+
+inline bool is_equal_approx(real_t a, real_t b, real_t tolerance) {
+	// Check for exact equality first, required to handle "infinity" values.
+	if (a == b) {
+		return true;
+	}
+	// Then check for approximate equality.
+	return std::abs(a - b) < tolerance;
+}
+
+inline bool is_zero_approx(real_t s) {
+	return std::abs(s) < CMP_EPSILON;
+}
+
+inline double smoothstep(double p_from, double p_to, double p_weight) {
+	if (is_equal_approx(p_from, p_to)) {
+		return p_from;
+	}
+	double x = clamp((p_weight - p_from) / (p_to - p_from), 0.0, 1.0);
+	return x * x * (3.0 - 2.0 * x);
+}
+inline float smoothstep(float p_from, float p_to, float p_weight) {
+	if (is_equal_approx(p_from, p_to)) {
+		return p_from;
+	}
+	float x = clamp((p_weight - p_from) / (p_to - p_from), 0.0f, 1.0f);
+	return x * x * (3.0f - 2.0f * x);
+}
+
+inline double move_toward(double p_from, double p_to, double p_delta) {
+	return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta;
+}
+
+inline float move_toward(float p_from, float p_to, float p_delta) {
+	return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta;
+}
+
+inline double linear2db(double p_linear) {
+	return log(p_linear) * 8.6858896380650365530225783783321;
+}
+inline float linear2db(float p_linear) {
+	return log(p_linear) * 8.6858896380650365530225783783321f;
+}
+
+inline double db2linear(double p_db) {
+	return exp(p_db * 0.11512925464970228420089957273422);
+}
+inline float db2linear(float p_db) {
+	return exp(p_db * 0.11512925464970228420089957273422f);
+}
+
+inline double round(double p_val) {
+	return (p_val >= 0) ? floor(p_val + 0.5) : -floor(-p_val + 0.5);
+}
+inline float round(float p_val) {
+	return (p_val >= 0) ? floor(p_val + 0.5) : -floor(-p_val + 0.5);
+}
+
+inline int64_t wrapi(int64_t value, int64_t min, int64_t max) {
+	int64_t range = max - min;
+	return range == 0 ? min : min + ((((value - min) % range) + range) % range);
+}
+
+inline double wrapf(double value, double min, double max) {
+	double range = max - min;
+	return is_zero_approx(range) ? min : value - (range * floor((value - min) / range));
+}
+inline float wrapf(float value, float min, float max) {
+	float range = max - min;
+	return is_zero_approx(range) ? min : value - (range * floor((value - min) / range));
+}
+
+inline real_t stepify(real_t p_value, real_t p_step) {
+	if (p_step != 0) {
+		p_value = floor(p_value / p_step + 0.5) * p_step;
+	}
+	return p_value;
+}
+
+inline unsigned int next_power_of_2(unsigned int x) {
+
+	if (x == 0)
+		return 0;
+
+	--x;
+	x |= x >> 1;
+	x |= x >> 2;
+	x |= x >> 4;
+	x |= x >> 8;
+	x |= x >> 16;
+
+	return ++x;
+}
+
+} // namespace Math
+} // namespace godot
+
+#endif // GODOT_MATH_H

include/core/Vector2.hpp

@@ -5,7 +5,7 @@
 
 #include "Defs.hpp"
 
-#include <cmath>
+#include <Math.hpp>
 
 namespace godot {
 
@@ -222,13 +222,13 @@ struct Vector2 {
 	}
 
 	inline Vector2 floor() const {
-		return Vector2(::floor(x), ::floor(y));
+		return Vector2(Math::floor(x), Math::floor(y));
 	}
 
 	inline Vector2 snapped(const Vector2 &p_by) const {
 		return Vector2(
-				p_by.x != 0 ? ::floor(x / p_by.x + 0.5) * p_by.x : x,
-				p_by.y != 0 ? ::floor(y / p_by.y + 0.5) * p_by.y : y);
+				Math::stepify(x, p_by.x),
+				Math::stepify(y, p_by.y));
 	}
 
 	inline real_t aspect() const { return width / height; }
@@ -240,6 +240,22 @@ inline Vector2 operator*(real_t p_scalar, const Vector2 &p_vec) {
 	return p_vec * p_scalar;
 }
 
+namespace Math {
+
+// Convenience, since they exist in GDScript
+
+inline Vector2 cartesian2polar(Vector2 v) {
+	return Vector2(Math::sqrt(v.x * v.x + v.y * v.y), Math::atan2(v.y, v.x));
+}
+
+inline Vector2 polar2cartesian(Vector2 v) {
+	// x == radius
+	// y == angle
+	return Vector2(v.x * Math::cos(v.y), v.x * Math::sin(v.y));
+}
+
+} // namespace Math
+
 } // namespace godot
 
 #endif // VECTOR2_H

include/core/Vector3.hpp

@@ -7,7 +7,7 @@
 
 #include "String.hpp"
 
-#include <cmath>
+#include <Math.hpp>
 
 namespace godot {
 

src/core/Vector3.cpp

@@ -67,17 +67,12 @@ void Vector3::rotate(const Vector3 &p_axis, real_t p_phi) {
 	*this = Basis(p_axis, p_phi).xform(*this);
 }
 
-// this is ugly as well, but hey, I'm a simple man
-#define _ugly_stepify(val, step) (step != 0 ? ::floor(val / step + 0.5) * step : val)
-
 void Vector3::snap(real_t p_val) {
-	x = _ugly_stepify(x, p_val);
-	y = _ugly_stepify(y, p_val);
-	z = _ugly_stepify(z, p_val);
+	x = Math::stepify(x, p_val);
+	y = Math::stepify(y, p_val);
+	z = Math::stepify(z, p_val);
 }
 
-#undef _ugly_stepify
-
 Vector3::operator String() const {
 	return String::num(x) + ", " + String::num(y) + ", " + String::num(z);
 }