Use Math_TAU and deg2rad/rad2deg in more places and optimize code

core/math/camera_matrix.cpp

@@ -80,7 +80,7 @@ void CameraMatrix::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_
 	}
 
 	real_t sine, cotangent, deltaZ;
-	real_t radians = p_fovy_degrees / 2.0 * Math_PI / 180.0;
+	real_t radians = Math::deg2rad(p_fovy_degrees / 2.0);
 
 	deltaZ = p_z_far - p_z_near;
 	sine = Math::sin(radians);
@@ -107,7 +107,7 @@ void CameraMatrix::set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_
 
 	real_t left, right, modeltranslation, ymax, xmax, frustumshift;
 
-	ymax = p_z_near * tan(p_fovy_degrees * Math_PI / 360.0f);
+	ymax = p_z_near * tan(Math::deg2rad(p_fovy_degrees / 2.0));
 	xmax = ymax * p_aspect;
 	frustumshift = (p_intraocular_dist / 2.0) * p_z_near / p_convergence_dist;
 

core/math/geometry_3d.cpp

@@ -777,10 +777,11 @@ Vector<Plane> Geometry3D::build_box_planes(const Vector3 &p_extents) {
 Vector<Plane> Geometry3D::build_cylinder_planes(real_t p_radius, real_t p_height, int p_sides, Vector3::Axis p_axis) {
 	Vector<Plane> planes;
 
+	const double sides_step = Math_TAU / p_sides;
 	for (int i = 0; i < p_sides; i++) {
 		Vector3 normal;
-		normal[(p_axis + 1) % 3] = Math::cos(i * (2.0 * Math_PI) / p_sides);
-		normal[(p_axis + 2) % 3] = Math::sin(i * (2.0 * Math_PI) / p_sides);
+		normal[(p_axis + 1) % 3] = Math::cos(i * sides_step);
+		normal[(p_axis + 2) % 3] = Math::sin(i * sides_step);
 
 		planes.push_back(Plane(normal, p_radius));
 	}
@@ -805,10 +806,11 @@ Vector<Plane> Geometry3D::build_sphere_planes(real_t p_radius, int p_lats, int p
 	axis_neg[(p_axis + 2) % 3] = 1.0;
 	axis_neg[p_axis] = -1.0;
 
+	const double lon_step = Math_TAU / p_lons;
 	for (int i = 0; i < p_lons; i++) {
 		Vector3 normal;
-		normal[(p_axis + 1) % 3] = Math::cos(i * (2.0 * Math_PI) / p_lons);
-		normal[(p_axis + 2) % 3] = Math::sin(i * (2.0 * Math_PI) / p_lons);
+		normal[(p_axis + 1) % 3] = Math::cos(i * lon_step);
+		normal[(p_axis + 2) % 3] = Math::sin(i * lon_step);
 
 		planes.push_back(Plane(normal, p_radius));
 
@@ -835,10 +837,11 @@ Vector<Plane> Geometry3D::build_capsule_planes(real_t p_radius, real_t p_height,
 	axis_neg[(p_axis + 2) % 3] = 1.0;
 	axis_neg[p_axis] = -1.0;
 
+	const double sides_step = Math_TAU / p_sides;
 	for (int i = 0; i < p_sides; i++) {
 		Vector3 normal;
-		normal[(p_axis + 1) % 3] = Math::cos(i * (2.0 * Math_PI) / p_sides);
-		normal[(p_axis + 2) % 3] = Math::sin(i * (2.0 * Math_PI) / p_sides);
+		normal[(p_axis + 1) % 3] = Math::cos(i * sides_step);
+		normal[(p_axis + 2) % 3] = Math::sin(i * sides_step);
 
 		planes.push_back(Plane(normal, p_radius));
 

core/math/math_funcs.h

@@ -223,11 +223,11 @@ public:
 		return value;
 	}
 
-	static _ALWAYS_INLINE_ double deg2rad(double p_y) { return p_y * Math_PI / 180.0; }
-	static _ALWAYS_INLINE_ float deg2rad(float p_y) { return p_y * Math_PI / 180.0; }
+	static _ALWAYS_INLINE_ double deg2rad(double p_y) { return p_y * (Math_PI / 180.0); }
+	static _ALWAYS_INLINE_ float deg2rad(float p_y) { return p_y * (Math_PI / 180.0); }
 
-	static _ALWAYS_INLINE_ double rad2deg(double p_y) { return p_y * 180.0 / Math_PI; }
-	static _ALWAYS_INLINE_ float rad2deg(float p_y) { return p_y * 180.0 / Math_PI; }
+	static _ALWAYS_INLINE_ double rad2deg(double p_y) { return p_y * (180.0 / Math_PI); }
+	static _ALWAYS_INLINE_ float rad2deg(float p_y) { return p_y * (180.0 / Math_PI); }
 
 	static _ALWAYS_INLINE_ double lerp(double p_from, double p_to, double p_weight) { return p_from + (p_to - p_from) * p_weight; }
 	static _ALWAYS_INLINE_ float lerp(float p_from, float p_to, float p_weight) { return p_from + (p_to - p_from) * p_weight; }

editor/node_3d_editor_gizmos.cpp

@@ -844,7 +844,7 @@ static float _find_closest_angle_to_half_pi_arc(const Vector3 &p_from, const Vec
 
 	//min_p = p_arc_xform.affine_inverse().xform(min_p);
 	float a = (Math_PI * 0.5) - Vector2(min_p.x, -min_p.z).angle();
-	return a * 180.0 / Math_PI;
+	return Math::rad2deg(a);
 }
 
 void Light3DGizmoPlugin::set_handle(EditorNode3DGizmo *p_gizmo, int p_idx, Camera3D *p_camera, const Point2 &p_point) {
@@ -1033,12 +1033,9 @@ void Light3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		p_gizmo->add_lines(points_primary, material_primary, false, color);
 		p_gizmo->add_lines(points_secondary, material_secondary, false, color);
 
-		const float ra = 16 * Math_PI * 2.0 / 64.0;
-		const Point2 a = Vector2(Math::sin(ra), Math::cos(ra)) * w;
-
 		Vector<Vector3> handles;
 		handles.push_back(Vector3(0, 0, -r));
-		handles.push_back(Vector3(a.x, a.y, -d));
+		handles.push_back(Vector3(w, 0, -d));
 
 		p_gizmo->add_handles(handles, get_material("handles"));
 		p_gizmo->add_unscaled_billboard(icon, 0.05, color);
@@ -1095,8 +1092,8 @@ void AudioStreamPlayer3DGizmoPlugin::set_handle(EditorNode3DGizmo *p_gizmo, int
 	float closest_angle = 1e20;
 
 	for (int i = 0; i < 180; i++) {
-		float a = i * Math_PI / 180.0;
-		float an = (i + 1) * Math_PI / 180.0;
+		float a = Math::deg2rad((float)i);
+		float an = Math::deg2rad((float)(i + 1));
 
 		Vector3 from(Math::sin(a), 0, -Math::cos(a));
 		Vector3 to(Math::sin(an), 0, -Math::cos(an));
@@ -1145,9 +1142,10 @@ void AudioStreamPlayer3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		Vector<Vector3> points_primary;
 		points_primary.resize(200);
 
+		real_t step = Math_TAU / 100.0;
 		for (int i = 0; i < 100; i++) {
-			const float a = i * 2.0 * Math_PI / 100.0;
-			const float an = (i + 1) * 2.0 * Math_PI / 100.0;
+			const float a = i * step;
+			const float an = (i + 1) * step;
 
 			const Vector3 from(Math::sin(a) * radius, Math::cos(a) * radius, ofs);
 			const Vector3 to(Math::sin(an) * radius, Math::cos(an) * radius, ofs);
@@ -1163,7 +1161,7 @@ void AudioStreamPlayer3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		points_secondary.resize(16);
 
 		for (int i = 0; i < 8; i++) {
-			const float a = i * 2.0 * Math_PI / 8.0;
+			const float a = i * (Math_TAU / 8.0);
 			const Vector3 from(Math::sin(a) * radius, Math::cos(a) * radius, ofs);
 
 			points_secondary.write[i * 2 + 0] = from;
@@ -2616,8 +2614,8 @@ void GPUParticlesCollision3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		Vector<Vector3> collision_segments;
 
 		for (int i = 0; i < 64; i++) {
-			float ra = i * Math_PI * 2.0 / 64.0;
-			float rb = (i + 1) * Math_PI * 2.0 / 64.0;
+			float ra = i * (Math_TAU / 64.0);
+			float rb = (i + 1) * (Math_TAU / 64.0);
 			Point2 a = Vector2(Math::sin(ra), Math::cos(ra)) * r;
 			Point2 b = Vector2(Math::sin(rb), Math::cos(rb)) * r;
 
@@ -3317,7 +3315,7 @@ void BakedLightmapGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 	int stack_count = 8;
 	int sector_count = 16;
 
-	float sector_step = 2 * Math_PI / sector_count;
+	float sector_step = (Math_PI * 2.0) / sector_count;
 	float stack_step = Math_PI / stack_count;
 
 	Vector<Vector3> vertices;
@@ -3454,7 +3452,7 @@ void LightmapProbeGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 	int stack_count = 8;
 	int sector_count = 16;
 
-	float sector_step = 2 * Math_PI / sector_count;
+	float sector_step = (Math_PI * 2.0) / sector_count;
 	float stack_step = Math_PI / stack_count;
 
 	Vector<Vector3> vertices;
@@ -3854,8 +3852,8 @@ void CollisionShape3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		Vector<Vector3> collision_segments;
 
 		for (int i = 0; i < 64; i++) {
-			float ra = i * Math_PI * 2.0 / 64.0;
-			float rb = (i + 1) * Math_PI * 2.0 / 64.0;
+			float ra = i * (Math_TAU / 64.0);
+			float rb = (i + 1) * (Math_TAU / 64.0);
 			Point2 a = Vector2(Math::sin(ra), Math::cos(ra)) * r;
 			Point2 b = Vector2(Math::sin(rb), Math::cos(rb)) * r;
 
@@ -3939,8 +3937,8 @@ void CollisionShape3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		Vector<Vector3> collision_segments;
 
 		for (int i = 0; i < 64; i++) {
-			float ra = i * Math_PI * 2.0 / 64.0;
-			float rb = (i + 1) * Math_PI * 2.0 / 64.0;
+			float ra = i * (Math_TAU / 64.0);
+			float rb = (i + 1) * (Math_TAU / 64.0);
 			Point2 a = Vector2(Math::sin(ra), Math::cos(ra)) * radius;
 			Point2 b = Vector2(Math::sin(rb), Math::cos(rb)) * radius;
 
@@ -4002,8 +4000,8 @@ void CollisionShape3DGizmoPlugin::redraw(EditorNode3DGizmo *p_gizmo) {
 		Vector<Vector3> collision_segments;
 
 		for (int i = 0; i < 64; i++) {
-			float ra = i * Math_PI * 2.0 / 64.0;
-			float rb = (i + 1) * Math_PI * 2.0 / 64.0;
+			float ra = i * (Math_TAU / 64.0);
+			float rb = (i + 1) * (Math_TAU / 64.0);
 			Point2 a = Vector2(Math::sin(ra), Math::cos(ra)) * radius;
 			Point2 b = Vector2(Math::sin(rb), Math::cos(rb)) * radius;
 

editor/plugins/canvas_item_editor_plugin.cpp

@@ -216,8 +216,8 @@ public:
 		grid_step_x->set_value(p_grid_step.x);
 		grid_step_y->set_value(p_grid_step.y);
 		primary_grid_steps->set_value(p_primary_grid_steps);
-		rotation_offset->set_value(p_rotation_offset * (180 / Math_PI));
-		rotation_step->set_value(p_rotation_step * (180 / Math_PI));
+		rotation_offset->set_value(Math::rad2deg(p_rotation_offset));
+		rotation_step->set_value(Math::rad2deg(p_rotation_step));
 		scale_step->set_value(p_scale_step);
 	}
 
@@ -225,8 +225,8 @@ public:
 		p_grid_offset = Point2(grid_offset_x->get_value(), grid_offset_y->get_value());
 		p_grid_step = Point2(grid_step_x->get_value(), grid_step_y->get_value());
 		p_primary_grid_steps = int(primary_grid_steps->get_value());
-		p_rotation_offset = rotation_offset->get_value() / (180 / Math_PI);
-		p_rotation_step = rotation_step->get_value() / (180 / Math_PI);
+		p_rotation_offset = Math::deg2rad(rotation_offset->get_value());
+		p_rotation_step = Math::deg2rad(rotation_step->get_value());
 		p_scale_step = scale_step->get_value();
 	}
 };
@@ -5638,7 +5638,7 @@ CanvasItemEditor::CanvasItemEditor(EditorNode *p_editor) {
 	primary_grid_steps = 8; // A power-of-two value works better as a default
 	grid_step_multiplier = 0;
 	snap_rotation_offset = 0;
-	snap_rotation_step = 15 / (180 / Math_PI);
+	snap_rotation_step = Math::deg2rad(15.0);
 	snap_scale_step = 0.1f;
 	smart_snap_active = false;
 	grid_snap_active = false;

editor/plugins/editor_preview_plugins.cpp

@@ -382,7 +382,9 @@ EditorMaterialPreviewPlugin::EditorMaterialPreviewPlugin() {
 
 	int lats = 32;
 	int lons = 32;
-	float radius = 1.0;
+	const double lat_step = Math_TAU / lats;
+	const double lon_step = Math_TAU / lons;
+	real_t radius = 1.0;
 
 	Vector<Vector3> vertices;
 	Vector<Vector3> normals;
@@ -391,20 +393,20 @@ EditorMaterialPreviewPlugin::EditorMaterialPreviewPlugin() {
 	Basis tt = Basis(Vector3(0, 1, 0), Math_PI * 0.5);
 
 	for (int i = 1; i <= lats; i++) {
-		double lat0 = Math_PI * (-0.5 + (double)(i - 1) / lats);
+		double lat0 = lat_step * (i - 1) - Math_TAU / 4;
 		double z0 = Math::sin(lat0);
 		double zr0 = Math::cos(lat0);
 
-		double lat1 = Math_PI * (-0.5 + (double)i / lats);
+		double lat1 = lat_step * i - Math_TAU / 4;
 		double z1 = Math::sin(lat1);
 		double zr1 = Math::cos(lat1);
 
 		for (int j = lons; j >= 1; j--) {
-			double lng0 = 2 * Math_PI * (double)(j - 1) / lons;
+			double lng0 = lon_step * (j - 1);
 			double x0 = Math::cos(lng0);
 			double y0 = Math::sin(lng0);
 
-			double lng1 = 2 * Math_PI * (double)(j) / lons;
+			double lng1 = lon_step * j;
 			double x1 = Math::cos(lng1);
 			double y1 = Math::sin(lng1);
 

editor/plugins/node_3d_editor_plugin.cpp

@@ -5314,9 +5314,10 @@ void Node3DEditor::_init_indicators() {
 
 				int arrow_sides = 16;
 
+				const real_t arrow_sides_step = Math_TAU / arrow_sides;
 				for (int k = 0; k < arrow_sides; k++) {
-					Basis ma(ivec, Math_PI * 2 * float(k) / arrow_sides);
-					Basis mb(ivec, Math_PI * 2 * float(k + 1) / arrow_sides);
+					Basis ma(ivec, k * arrow_sides_step);
+					Basis mb(ivec, (k + 1) * arrow_sides_step);
 
 					for (int j = 0; j < arrow_points - 1; j++) {
 						Vector3 points[4] = {
@@ -5391,13 +5392,14 @@ void Node3DEditor::_init_indicators() {
 				int n = 128; // number of circle segments
 				int m = 6; // number of thickness segments
 
+				real_t step = Math_TAU / n;
 				for (int j = 0; j < n; ++j) {
-					Basis basis = Basis(ivec, (Math_PI * 2.0f * j) / n);
+					Basis basis = Basis(ivec, j * step);
 
 					Vector3 vertex = basis.xform(ivec2 * GIZMO_CIRCLE_SIZE);
 
 					for (int k = 0; k < m; ++k) {
-						Vector2 ofs = Vector2(Math::cos((Math_PI * 2.0 * k) / m), Math::sin((Math_PI * 2.0 * k) / m));
+						Vector2 ofs = Vector2(Math::cos((Math_TAU * k) / m), Math::sin((Math_TAU * k) / m));
 						Vector3 normal = ivec * ofs.x + ivec2 * ofs.y;
 
 						surftool->set_normal(basis.xform(normal));
@@ -5524,9 +5526,10 @@ void Node3DEditor::_init_indicators() {
 
 				int arrow_sides = 4;
 
+				const real_t arrow_sides_step = Math_TAU / arrow_sides;
 				for (int k = 0; k < 4; k++) {
-					Basis ma(ivec, Math_PI * 2 * float(k) / arrow_sides);
-					Basis mb(ivec, Math_PI * 2 * float(k + 1) / arrow_sides);
+					Basis ma(ivec, k * arrow_sides_step);
+					Basis mb(ivec, (k + 1) * arrow_sides_step);
 
 					for (int j = 0; j < arrow_points - 1; j++) {
 						Vector3 points[4] = {

modules/csg/csg_shape.cpp

@@ -927,25 +927,27 @@ CSGBrush *CSGSphere3D::_build_brush() {
 		bool *invertw = invert.ptrw();
 
 		int face = 0;
+		const double lat_step = Math_TAU / rings;
+		const double lon_step = Math_TAU / radial_segments;
 
 		for (int i = 1; i <= rings; i++) {
-			double lat0 = Math_PI * (-0.5 + (double)(i - 1) / rings);
+			double lat0 = lat_step * (i - 1) - Math_TAU / 4;
 			double z0 = Math::sin(lat0);
 			double zr0 = Math::cos(lat0);
 			double u0 = double(i - 1) / rings;
 
-			double lat1 = Math_PI * (-0.5 + (double)i / rings);
+			double lat1 = lat_step * i - Math_TAU / 4;
 			double z1 = Math::sin(lat1);
 			double zr1 = Math::cos(lat1);
 			double u1 = double(i) / rings;
 
 			for (int j = radial_segments; j >= 1; j--) {
-				double lng0 = 2 * Math_PI * (double)(j - 1) / radial_segments;
+				double lng0 = lon_step * (j - 1);
 				double x0 = Math::cos(lng0);
 				double y0 = Math::sin(lng0);
 				double v0 = double(i - 1) / radial_segments;
 
-				double lng1 = 2 * Math_PI * (double)(j) / radial_segments;
+				double lng1 = lon_step * j;
 				double x1 = Math::cos(lng1);
 				double y1 = Math::sin(lng1);
 				double v1 = double(i) / radial_segments;
@@ -1266,8 +1268,8 @@ CSGBrush *CSGCylinder3D::_build_brush() {
 				float inc = float(i) / sides;
 				float inc_n = float((i + 1)) / sides;
 
-				float ang = inc * Math_PI * 2.0;
-				float ang_n = inc_n * Math_PI * 2.0;
+				float ang = inc * Math_TAU;
+				float ang_n = inc_n * Math_TAU;
 
 				Vector3 base(Math::cos(ang), 0, Math::sin(ang));
 				Vector3 base_n(Math::cos(ang_n), 0, Math::sin(ang_n));
@@ -1508,8 +1510,8 @@ CSGBrush *CSGTorus3D::_build_brush() {
 				float inci = float(i) / sides;
 				float inci_n = float((i + 1)) / sides;
 
-				float angi = inci * Math_PI * 2.0;
-				float angi_n = inci_n * Math_PI * 2.0;
+				float angi = inci * Math_TAU;
+				float angi_n = inci_n * Math_TAU;
 
 				Vector3 normali = Vector3(Math::cos(angi), 0, Math::sin(angi));
 				Vector3 normali_n = Vector3(Math::cos(angi_n), 0, Math::sin(angi_n));
@@ -1518,8 +1520,8 @@ CSGBrush *CSGTorus3D::_build_brush() {
 					float incj = float(j) / ring_sides;
 					float incj_n = float((j + 1)) / ring_sides;
 
-					float angj = incj * Math_PI * 2.0;
-					float angj_n = incj_n * Math_PI * 2.0;
+					float angj = incj * Math_TAU;
+					float angj_n = incj_n * Math_TAU;
 
 					Vector2 normalj = Vector2(Math::cos(angj), Math::sin(angj)) * radius + Vector2(min_radius + radius, 0);
 					Vector2 normalj_n = Vector2(Math::cos(angj_n), Math::sin(angj_n)) * radius + Vector2(min_radius + radius, 0);
@@ -1891,8 +1893,8 @@ CSGBrush *CSGPolygon3D::_build_brush() {
 					float inci = float(i) / spin_sides;
 					float inci_n = float((i + 1)) / spin_sides;
 
-					float angi = -(inci * spin_degrees / 360.0) * Math_PI * 2.0;
-					float angi_n = -(inci_n * spin_degrees / 360.0) * Math_PI * 2.0;
+					float angi = -Math::deg2rad(inci * spin_degrees);
+					float angi_n = -Math::deg2rad(inci_n * spin_degrees);
 
 					Vector3 normali = Vector3(Math::cos(angi), 0, Math::sin(angi));
 					Vector3 normali_n = Vector3(Math::cos(angi_n), 0, Math::sin(angi_n));

modules/opensimplex/open_simplex_noise.cpp

@@ -131,10 +131,10 @@ Ref<Image> OpenSimplexNoise::get_seamless_image(int p_size) const {
 			float ii = (float)i / (float)p_size;
 			float jj = (float)j / (float)p_size;
 
-			ii *= 2.0 * Math_PI;
-			jj *= 2.0 * Math_PI;
+			ii *= Math_TAU;
+			jj *= Math_TAU;
 
-			float radius = p_size / (2.0 * Math_PI);
+			float radius = p_size / Math_TAU;
 
 			float x = radius * Math::sin(jj);
 			float y = radius * Math::cos(jj);

scene/2d/cpu_particles_2d.cpp

@@ -700,7 +700,7 @@ void CPUParticles2D::_particles_process(float p_delta) {
 			p.hue_rot_rand = Math::randf();
 			p.anim_offset_rand = Math::randf();
 
-			float angle1_rad = Math::atan2(direction.y, direction.x) + (Math::randf() * 2.0 - 1.0) * Math_PI * spread / 180.0;
+			float angle1_rad = Math::atan2(direction.y, direction.x) + Math::deg2rad((Math::randf() * 2.0 - 1.0) * spread);
 			Vector2 rot = Vector2(Math::cos(angle1_rad), Math::sin(angle1_rad));
 			p.velocity = rot * parameters[PARAM_INITIAL_LINEAR_VELOCITY] * Math::lerp(1.0f, float(Math::randf()), randomness[PARAM_INITIAL_LINEAR_VELOCITY]);
 
@@ -721,7 +721,7 @@ void CPUParticles2D::_particles_process(float p_delta) {
 					//do none
 				} break;
 				case EMISSION_SHAPE_SPHERE: {
-					float s = Math::randf(), t = 2.0 * Math_PI * Math::randf();
+					float s = Math::randf(), t = Math_TAU * Math::randf();
 					float radius = emission_sphere_radius * Math::sqrt(1.0 - s * s);
 					p.transform[2] = Vector2(Math::cos(t), Math::sin(t)) * radius;
 				} break;
@@ -837,7 +837,7 @@ void CPUParticles2D::_particles_process(float p_delta) {
 			//orbit velocity
 			float orbit_amount = (parameters[PARAM_ORBIT_VELOCITY] + tex_orbit_velocity) * Math::lerp(1.0f, rand_from_seed(alt_seed), randomness[PARAM_ORBIT_VELOCITY]);
 			if (orbit_amount != 0.0) {
-				float ang = orbit_amount * local_delta * Math_PI * 2.0;
+				float ang = orbit_amount * local_delta * Math_TAU;
 				// Not sure why the ParticlesMaterial code uses a clockwise rotation matrix,
 				// but we use -ang here to reproduce its behavior.
 				Transform2D rot = Transform2D(-ang, Vector2());
@@ -877,7 +877,7 @@ void CPUParticles2D::_particles_process(float p_delta) {
 			tex_hue_variation = curve_parameters[PARAM_HUE_VARIATION]->interpolate(p.custom[1]);
 		}
 
-		float hue_rot_angle = (parameters[PARAM_HUE_VARIATION] + tex_hue_variation) * Math_PI * 2.0 * Math::lerp(1.0f, p.hue_rot_rand * 2.0f - 1.0f, randomness[PARAM_HUE_VARIATION]);
+		float hue_rot_angle = (parameters[PARAM_HUE_VARIATION] + tex_hue_variation) * Math_TAU * Math::lerp(1.0f, p.hue_rot_rand * 2.0f - 1.0f, randomness[PARAM_HUE_VARIATION]);
 		float hue_rot_c = Math::cos(hue_rot_angle);
 		float hue_rot_s = Math::sin(hue_rot_angle);
 

scene/2d/line_builder.cpp

@@ -554,7 +554,7 @@ void LineBuilder::new_arc(Vector2 center, Vector2 vbegin, float angle_delta, Col
 	float t = Vector2(1, 0).angle_to(vbegin);
 	float end_angle = t + angle_delta;
 	Vector2 rpos(0, 0);
-	float tt_begin = -Math_PI / 2.f;
+	float tt_begin = -Math_PI / 2.0f;
 	float tt = tt_begin;
 
 	// Center vertice

scene/3d/cpu_particles_3d.cpp

@@ -676,13 +676,13 @@ void CPUParticles3D::_particles_process(float p_delta) {
 			p.anim_offset_rand = Math::randf();
 
 			if (particle_flags[PARTICLE_FLAG_DISABLE_Z]) {
-				float angle1_rad = Math::atan2(direction.y, direction.x) + (Math::randf() * 2.0 - 1.0) * Math_PI * spread / 180.0;
+				float angle1_rad = Math::atan2(direction.y, direction.x) + Math::deg2rad((Math::randf() * 2.0 - 1.0) * spread);
 				Vector3 rot = Vector3(Math::cos(angle1_rad), Math::sin(angle1_rad), 0.0);
 				p.velocity = rot * parameters[PARAM_INITIAL_LINEAR_VELOCITY] * Math::lerp(1.0f, float(Math::randf()), randomness[PARAM_INITIAL_LINEAR_VELOCITY]);
 			} else {
 				//initiate velocity spread in 3D
-				float angle1_rad = Math::atan2(direction.x, direction.z) + (Math::randf() * 2.0 - 1.0) * Math_PI * spread / 180.0;
-				float angle2_rad = Math::atan2(direction.y, Math::abs(direction.z)) + (Math::randf() * 2.0 - 1.0) * (1.0 - flatness) * Math_PI * spread / 180.0;
+				float angle1_rad = Math::atan2(direction.x, direction.z) + Math::deg2rad((Math::randf() * 2.0 - 1.0) * spread);
+				float angle2_rad = Math::atan2(direction.y, Math::abs(direction.z)) + Math::deg2rad((Math::randf() * 2.0 - 1.0) * (1.0 - flatness) * spread);
 
 				Vector3 direction_xz = Vector3(Math::sin(angle1_rad), 0, Math::cos(angle1_rad));
 				Vector3 direction_yz = Vector3(0, Math::sin(angle2_rad), Math::cos(angle2_rad));
@@ -706,8 +706,9 @@ void CPUParticles3D::_particles_process(float p_delta) {
 					//do none
 				} break;
 				case EMISSION_SHAPE_SPHERE: {
-					float s = 2.0 * Math::randf() - 1.0, t = 2.0 * Math_PI * Math::randf();
-					float radius = emission_sphere_radius * Math::sqrt(1.0 - s * s);
+					real_t s = 2.0 * Math::randf() - 1.0;
+					real_t t = Math_TAU * Math::randf();
+					real_t radius = emission_sphere_radius * Math::sqrt(1.0 - s * s);
 					p.transform.origin = Vector3(radius * Math::cos(t), radius * Math::sin(t), emission_sphere_radius * s);
 				} break;
 				case EMISSION_SHAPE_BOX: {
@@ -855,7 +856,7 @@ void CPUParticles3D::_particles_process(float p_delta) {
 			if (particle_flags[PARTICLE_FLAG_DISABLE_Z]) {
 				float orbit_amount = (parameters[PARAM_ORBIT_VELOCITY] + tex_orbit_velocity) * Math::lerp(1.0f, rand_from_seed(alt_seed), randomness[PARAM_ORBIT_VELOCITY]);
 				if (orbit_amount != 0.0) {
-					float ang = orbit_amount * local_delta * Math_PI * 2.0;
+					float ang = orbit_amount * local_delta * Math_TAU;
 					// Not sure why the ParticlesMaterial code uses a clockwise rotation matrix,
 					// but we use -ang here to reproduce its behavior.
 					Transform2D rot = Transform2D(-ang, Vector2());
@@ -895,7 +896,7 @@ void CPUParticles3D::_particles_process(float p_delta) {
 			tex_hue_variation = curve_parameters[PARAM_HUE_VARIATION]->interpolate(p.custom[1]);
 		}
 
-		float hue_rot_angle = (parameters[PARAM_HUE_VARIATION] + tex_hue_variation) * Math_PI * 2.0 * Math::lerp(1.0f, p.hue_rot_rand * 2.0f - 1.0f, randomness[PARAM_HUE_VARIATION]);
+		float hue_rot_angle = (parameters[PARAM_HUE_VARIATION] + tex_hue_variation) * Math_TAU * Math::lerp(1.0f, p.hue_rot_rand * 2.0f - 1.0f, randomness[PARAM_HUE_VARIATION]);
 		float hue_rot_c = Math::cos(hue_rot_angle);
 		float hue_rot_s = Math::sin(hue_rot_angle);
 

scene/3d/immediate_geometry_3d.cpp

@@ -87,21 +87,24 @@ Vector<Face3> ImmediateGeometry3D::get_faces(uint32_t p_usage_flags) const {
 }
 
 void ImmediateGeometry3D::add_sphere(int p_lats, int p_lons, float p_radius, bool p_add_uv) {
+	const double lat_step = Math_TAU / p_lats;
+	const double lon_step = Math_TAU / p_lons;
+
 	for (int i = 1; i <= p_lats; i++) {
-		double lat0 = Math_PI * (-0.5 + (double)(i - 1) / p_lats);
+		double lat0 = lat_step * (i - 1) - Math_TAU / 4;
 		double z0 = Math::sin(lat0);
 		double zr0 = Math::cos(lat0);
 
-		double lat1 = Math_PI * (-0.5 + (double)i / p_lats);
+		double lat1 = lat_step * i - Math_TAU / 4;
 		double z1 = Math::sin(lat1);
 		double zr1 = Math::cos(lat1);
 
 		for (int j = p_lons; j >= 1; j--) {
-			double lng0 = 2 * Math_PI * (double)(j - 1) / p_lons;
+			double lng0 = lon_step * (j - 1);
 			double x0 = Math::cos(lng0);
 			double y0 = Math::sin(lng0);
 
-			double lng1 = 2 * Math_PI * (double)(j) / p_lons;
+			double lng1 = lon_step * j;
 			double x1 = Math::cos(lng1);
 			double y1 = Math::sin(lng1);
 

scene/3d/node_3d.cpp

@@ -330,7 +330,7 @@ void Node3D::set_rotation(const Vector3 &p_euler_rad) {
 }
 
 void Node3D::set_rotation_degrees(const Vector3 &p_euler_deg) {
-	set_rotation(p_euler_deg * Math_PI / 180.0);
+	set_rotation(p_euler_deg * (Math_PI / 180.0));
 }
 
 void Node3D::set_scale(const Vector3 &p_scale) {
@@ -364,7 +364,7 @@ Vector3 Node3D::get_rotation() const {
 }
 
 Vector3 Node3D::get_rotation_degrees() const {
-	return get_rotation() * 180.0 / Math_PI;
+	return get_rotation() * (180.0 / Math_PI);
 }
 
 Vector3 Node3D::get_scale() const {

scene/3d/physics_body_3d.cpp

@@ -2381,11 +2381,11 @@ Vector3 PhysicalBone3D::get_joint_rotation() const {
 }
 
 void PhysicalBone3D::set_joint_rotation_degrees(const Vector3 &p_euler_deg) {
-	set_joint_rotation(p_euler_deg * Math_PI / 180.0);
+	set_joint_rotation(p_euler_deg * (Math_PI / 180.0));
 }
 
 Vector3 PhysicalBone3D::get_joint_rotation_degrees() const {
-	return get_joint_rotation() * 180.0 / Math_PI;
+	return get_joint_rotation() * (180.0 / Math_PI);
 }
 
 const Transform &PhysicalBone3D::get_body_offset() const {

scene/resources/capsule_shape_2d.cpp

@@ -36,12 +36,13 @@
 
 Vector<Vector2> CapsuleShape2D::_get_points() const {
 	Vector<Vector2> points;
+	const real_t turn_step = Math_TAU / 24.0;
 	for (int i = 0; i < 24; i++) {
 		Vector2 ofs = Vector2(0, (i > 6 && i <= 18) ? -get_height() * 0.5 : get_height() * 0.5);
 
-		points.push_back(Vector2(Math::sin(i * Math_PI * 2 / 24.0), Math::cos(i * Math_PI * 2 / 24.0)) * get_radius() + ofs);
+		points.push_back(Vector2(Math::sin(i * turn_step), Math::cos(i * turn_step)) * get_radius() + ofs);
 		if (i == 6 || i == 18) {
-			points.push_back(Vector2(Math::sin(i * Math_PI * 2 / 24.0), Math::cos(i * Math_PI * 2 / 24.0)) * get_radius() - ofs);
+			points.push_back(Vector2(Math::sin(i * turn_step), Math::cos(i * turn_step)) * get_radius() - ofs);
 		}
 	}
 

scene/resources/circle_shape_2d.cpp

@@ -71,8 +71,9 @@ real_t CircleShape2D::get_enclosing_radius() const {
 
 void CircleShape2D::draw(const RID &p_to_rid, const Color &p_color) {
 	Vector<Vector2> points;
+	const real_t turn_step = Math_TAU / 24.0;
 	for (int i = 0; i < 24; i++) {
-		points.push_back(Vector2(Math::cos(i * Math_PI * 2 / 24.0), Math::sin(i * Math_PI * 2 / 24.0)) * get_radius());
+		points.push_back(Vector2(Math::cos(i * turn_step), Math::sin(i * turn_step)) * get_radius());
 	}
 
 	Vector<Color> col;

scene/resources/primitive_meshes.cpp

@@ -304,8 +304,8 @@ void CapsuleMesh::_create_mesh_array(Array &p_arr) const {
 			u = i;
 			u /= radial_segments;
 
-			x = -sin(u * (Math_PI * 2.0));
-			z = cos(u * (Math_PI * 2.0));
+			x = -sin(u * Math_TAU);
+			z = cos(u * Math_TAU);
 
 			Vector3 p = Vector3(x * radius * w, y, -z * radius * w);
 			points.push_back(p + Vector3(0.0, 0.5 * mid_height, 0.0));
@@ -343,8 +343,8 @@ void CapsuleMesh::_create_mesh_array(Array &p_arr) const {
 			u = i;
 			u /= radial_segments;
 
-			x = -sin(u * (Math_PI * 2.0));
-			z = cos(u * (Math_PI * 2.0));
+			x = -sin(u * Math_TAU);
+			z = cos(u * Math_TAU);
 
 			Vector3 p = Vector3(x * radius, y, -z * radius);
 			points.push_back(p);
@@ -383,8 +383,8 @@ void CapsuleMesh::_create_mesh_array(Array &p_arr) const {
 			float u2 = i;
 			u2 /= radial_segments;
 
-			x = -sin(u2 * (Math_PI * 2.0));
-			z = cos(u2 * (Math_PI * 2.0));
+			x = -sin(u2 * Math_TAU);
+			z = cos(u2 * Math_TAU);
 
 			Vector3 p = Vector3(x * radius * w, y, -z * radius * w);
 			points.push_back(p + Vector3(0.0, -0.5 * mid_height, 0.0));
@@ -769,8 +769,8 @@ void CylinderMesh::_create_mesh_array(Array &p_arr) const {
 			u = i;
 			u /= radial_segments;
 
-			x = sin(u * (Math_PI * 2.0));
-			z = cos(u * (Math_PI * 2.0));
+			x = sin(u * Math_TAU);
+			z = cos(u * Math_TAU);
 
 			Vector3 p = Vector3(x * radius, y, z * radius);
 			points.push_back(p);
@@ -809,8 +809,8 @@ void CylinderMesh::_create_mesh_array(Array &p_arr) const {
 			float r = i;
 			r /= radial_segments;
 
-			x = sin(r * (Math_PI * 2.0));
-			z = cos(r * (Math_PI * 2.0));
+			x = sin(r * Math_TAU);
+			z = cos(r * Math_TAU);
 
 			u = ((x + 1.0) * 0.25);
 			v = 0.5 + ((z + 1.0) * 0.25);
@@ -845,8 +845,8 @@ void CylinderMesh::_create_mesh_array(Array &p_arr) const {
 			float r = i;
 			r /= radial_segments;
 
-			x = sin(r * (Math_PI * 2.0));
-			z = cos(r * (Math_PI * 2.0));
+			x = sin(r * Math_TAU);
+			z = cos(r * Math_TAU);
 
 			u = 0.5 + ((x + 1.0) * 0.25);
 			v = 1.0 - ((z + 1.0) * 0.25);
@@ -1458,8 +1458,8 @@ void SphereMesh::_create_mesh_array(Array &p_arr) const {
 			float u = i;
 			u /= radial_segments;
 
-			x = sin(u * (Math_PI * 2.0));
-			z = cos(u * (Math_PI * 2.0));
+			x = sin(u * Math_TAU);
+			z = cos(u * Math_TAU);
 
 			if (is_hemisphere && y < 0.0) {
 				points.push_back(Vector3(x * radius * w, 0.0, z * radius * w));

scene/resources/style_box.cpp

@@ -576,8 +576,8 @@ inline void draw_ring(Vector<Vector2> &verts, Vector<int> &indices, Vector<Color
 					color = outer_color;
 					corner_point = outer_points[corner_index];
 				}
-				float x = radius * (float)cos((double)corner_index * Math_PI / 2.0 + (double)detail / (double)adapted_corner_detail * Math_PI / 2.0 + Math_PI) + corner_point.x;
-				float y = radius * (float)sin((double)corner_index * Math_PI / 2.0 + (double)detail / (double)adapted_corner_detail * Math_PI / 2.0 + Math_PI) + corner_point.y;
+				real_t x = radius * (real_t)cos((corner_index + detail / (double)adapted_corner_detail) * (Math_TAU / 4.0) + Math_PI) + corner_point.x;
+				real_t y = radius * (real_t)sin((corner_index + detail / (double)adapted_corner_detail) * (Math_TAU / 4.0) + Math_PI) + corner_point.y;
 				verts.push_back(Vector2(x, y));
 				colors.push_back(color);
 			}

servers/audio/audio_filter_sw.cpp

@@ -58,7 +58,7 @@ void AudioFilterSW::prepare_coefficients(Coeffs *p_coeffs) {
 		final_cutoff = 1; //don't allow less than this
 	}
 
-	double omega = 2.0 * Math_PI * final_cutoff / sampling_rate;
+	double omega = Math_TAU * final_cutoff / sampling_rate;
 
 	double sin_v = Math::sin(omega);
 	double cos_v = Math::cos(omega);
@@ -132,7 +132,7 @@ void AudioFilterSW::prepare_coefficients(Coeffs *p_coeffs) {
 			double hicutoff = resonance;
 			double centercutoff = (cutoff + resonance) / 2.0;
 			double bandwidth = (Math::log(centercutoff) - Math::log(hicutoff)) / Math::log((double)2);
-			omega = 2.0 * Math_PI * centercutoff / sampling_rate;
+			omega = Math_TAU * centercutoff / sampling_rate;
 			alpha = Math::sin(omega) * Math::sinh(Math::log((double)2) / 2 * bandwidth * omega / Math::sin(omega));
 			a0 = 1 + alpha;
 
@@ -197,7 +197,7 @@ void AudioFilterSW::set_stages(int p_stages) { //adjust for multiple stages
 /* Fouriertransform kernel to obtain response */
 
 float AudioFilterSW::get_response(float p_freq, Coeffs *p_coeffs) {
-	float freq = p_freq / sampling_rate * Math_PI * 2.0f;
+	float freq = p_freq / sampling_rate * Math_TAU;
 
 	float cx = p_coeffs->b0, cy = 0.0;
 

servers/audio/effects/audio_effect_chorus.cpp

@@ -84,7 +84,7 @@ void AudioEffectChorusInstance::_process_chunk(const AudioFrame *p_src_frames, A
 		if (v.cutoff == 0) {
 			continue;
 		}
-		float auxlp = expf(-2.0 * Math_PI * v.cutoff / mix_rate);
+		float auxlp = expf(-Math_TAU * v.cutoff / mix_rate);
 		float c1 = 1.0 - auxlp;
 		float c2 = auxlp;
 		AudioFrame h = filter_h[vc];
@@ -104,7 +104,7 @@ void AudioEffectChorusInstance::_process_chunk(const AudioFrame *p_src_frames, A
 
 			float phase = (float)(local_cycles & AudioEffectChorus::CYCLES_MASK) / (float)(1 << AudioEffectChorus::CYCLES_FRAC);
 
-			float wave_delay = sinf(phase * 2.0 * Math_PI) * max_depth_frames;
+			float wave_delay = sinf(phase * Math_TAU) * max_depth_frames;
 
 			int wave_delay_frames = lrint(floor(wave_delay));
 			float wave_delay_frac = wave_delay - (float)wave_delay_frames;

servers/audio/effects/audio_effect_delay.cpp

@@ -75,7 +75,7 @@ void AudioEffectDelayInstance::_process_chunk(const AudioFrame *p_src_frames, Au
 	tap2_vol.r *= CLAMP(1.0 + base->tap_2_pan, 0, 1);
 
 	// feedback lowpass here
-	float lpf_c = expf(-2.0 * Math_PI * base->feedback_lowpass / mix_rate); // 0 .. 10khz
+	float lpf_c = expf(-Math_TAU * base->feedback_lowpass / mix_rate); // 0 .. 10khz
 	float lpf_ic = 1.0 - lpf_c;
 
 	const AudioFrame *src = p_src_frames;

servers/audio/effects/audio_effect_distortion.cpp

@@ -36,8 +36,8 @@ void AudioEffectDistortionInstance::process(const AudioFrame *p_src_frames, Audi
 	const float *src = (const float *)p_src_frames;
 	float *dst = (float *)p_dst_frames;
 
-	//float lpf_c=expf(-2.0*Math_PI*keep_hf_hz.get()/(mix_rate*(float)OVERSAMPLE));
-	float lpf_c = expf(-2.0 * Math_PI * base->keep_hf_hz / (AudioServer::get_singleton()->get_mix_rate()));
+	//float lpf_c=expf(-Math_TAU*keep_hf_hz.get()/(mix_rate*(float)OVERSAMPLE));
+	float lpf_c = expf(-Math_TAU * base->keep_hf_hz / (AudioServer::get_singleton()->get_mix_rate()));
 	float lpf_ic = 1.0 - lpf_c;
 
 	float drive_f = base->drive;

servers/audio/effects/audio_effect_phaser.cpp

@@ -38,13 +38,13 @@ void AudioEffectPhaserInstance::process(const AudioFrame *p_src_frames, AudioFra
 	float dmin = base->range_min / (sampling_rate / 2.0);
 	float dmax = base->range_max / (sampling_rate / 2.0);
 
-	float increment = 2.f * Math_PI * (base->rate / sampling_rate);
+	float increment = Math_TAU * (base->rate / sampling_rate);
 
 	for (int i = 0; i < p_frame_count; i++) {
 		phase += increment;
 
-		while (phase >= Math_PI * 2.f) {
-			phase -= Math_PI * 2.f;
+		while (phase >= Math_TAU) {
+			phase -= Math_TAU;
 		}
 
 		float d = dmin + (dmax - dmin) * ((sin(phase) + 1.f) / 2.f);

servers/audio/effects/audio_effect_spectrum_analyzer.cpp

@@ -110,10 +110,11 @@ void AudioEffectSpectrumAnalyzerInstance::process(const AudioFrame *p_src_frames
 	while (p_frame_count) {
 		int to_fill = fft_size * 2 - temporal_fft_pos;
 		to_fill = MIN(to_fill, p_frame_count);
+		const double to_fill_step = Math_TAU / (double)fft_size;
 
 		float *fftw = temporal_fft.ptrw();
 		for (int i = 0; i < to_fill; i++) { //left and right buffers
-			float window = -0.5 * Math::cos(2.0 * Math_PI * (double)temporal_fft_pos / (double)fft_size) + 0.5;
+			float window = -0.5 * Math::cos(to_fill_step * (double)temporal_fft_pos) + 0.5;
 			fftw[temporal_fft_pos * 2] = window * p_src_frames->l;
 			fftw[temporal_fft_pos * 2 + 1] = 0;
 			fftw[(temporal_fft_pos + fft_size * 2) * 2] = window * p_src_frames->r;

servers/audio/effects/eq.cpp

@@ -89,8 +89,8 @@ void EQ::recalculate_band_coefficients() {
 		double frq_l = round(frq / pow(2.0, octave_size / 2.0));
 
 		double side_gain2 = POW2(Math_SQRT12);
-		double th = 2.0 * Math_PI * frq / mix_rate;
-		double th_l = 2.0 * Math_PI * frq_l / mix_rate;
+		double th = Math_TAU * frq / mix_rate;
+		double th_l = Math_TAU * frq_l / mix_rate;
 
 		double c2a = side_gain2 * POW2(cos(th)) - 2.0 * side_gain2 * cos(th_l) * cos(th) + side_gain2 - POW2(sin(th_l));
 

servers/audio/effects/reverb.cpp

@@ -91,7 +91,7 @@ void Reverb::process(float *p_src, float *p_dst, int p_frames) {
 	}
 
 	if (params.hpf > 0) {
-		float hpaux = expf(-2.0 * Math_PI * params.hpf * 6000 / params.mix_rate);
+		float hpaux = expf(-Math_TAU * params.hpf * 6000 / params.mix_rate);
 		float hp_a1 = (1.0 + hpaux) / 2.0;
 		float hp_a2 = -(1.0 + hpaux) / 2.0;
 		float hp_b1 = hpaux;
@@ -293,7 +293,7 @@ void Reverb::update_parameters() {
 		float auxdmp = params.damp / 2.0 + 0.5; //only half the range (0.5 .. 1.0  is enough)
 		auxdmp *= auxdmp;
 
-		c.damp = expf(-2.0 * Math_PI * auxdmp * 10000 / params.mix_rate); // 0 .. 10khz
+		c.damp = expf(-Math_TAU * auxdmp * 10000 / params.mix_rate); // 0 .. 10khz
 	}
 }
 

servers/physics_2d/space_2d_sw.cpp

@@ -1328,7 +1328,7 @@ Space2DSW::Space2DSW() {
 
 	constraint_bias = 0.2;
 	body_linear_velocity_sleep_threshold = GLOBAL_DEF("physics/2d/sleep_threshold_linear", 2.0);
-	body_angular_velocity_sleep_threshold = GLOBAL_DEF("physics/2d/sleep_threshold_angular", (8.0 / 180.0 * Math_PI));
+	body_angular_velocity_sleep_threshold = GLOBAL_DEF("physics/2d/sleep_threshold_angular", Math::deg2rad(8.0));
 	body_time_to_sleep = GLOBAL_DEF("physics/2d/time_before_sleep", 0.5);
 	ProjectSettings::get_singleton()->set_custom_property_info("physics/2d/time_before_sleep", PropertyInfo(Variant::FLOAT, "physics/2d/time_before_sleep", PROPERTY_HINT_RANGE, "0,5,0.01,or_greater"));
 

servers/physics_3d/joints/cone_twist_joint_3d_sw.cpp

@@ -92,9 +92,9 @@ ConeTwistJoint3DSW::ConeTwistJoint3DSW(Body3DSW *rbA, Body3DSW *rbB, const Trans
 	m_rbAFrame = rbAFrame;
 	m_rbBFrame = rbBFrame;
 
-	m_swingSpan1 = Math_PI / 4.0;
-	m_swingSpan2 = Math_PI / 4.0;
-	m_twistSpan = Math_PI * 2;
+	m_swingSpan1 = Math_TAU / 8.0;
+	m_swingSpan2 = Math_TAU / 8.0;
+	m_twistSpan = Math_TAU;
 	m_biasFactor = 0.3f;
 	m_relaxationFactor = 1.0f;
 

servers/physics_3d/space_3d_sw.cpp

@@ -1211,7 +1211,7 @@ Space3DSW::Space3DSW() {
 
 	constraint_bias = 0.01;
 	body_linear_velocity_sleep_threshold = GLOBAL_DEF("physics/3d/sleep_threshold_linear", 0.1);
-	body_angular_velocity_sleep_threshold = GLOBAL_DEF("physics/3d/sleep_threshold_angular", (8.0 / 180.0 * Math_PI));
+	body_angular_velocity_sleep_threshold = GLOBAL_DEF("physics/3d/sleep_threshold_angular", Math::deg2rad(8.0));
 	body_time_to_sleep = GLOBAL_DEF("physics/3d/time_before_sleep", 0.5);
 	ProjectSettings::get_singleton()->set_custom_property_info("physics/3d/time_before_sleep", PropertyInfo(Variant::FLOAT, "physics/3d/time_before_sleep", PROPERTY_HINT_RANGE, "0,5,0.01,or_greater"));
 	body_angular_velocity_damp_ratio = 10;

servers/rendering/renderer_canvas_cull.cpp

@@ -721,8 +721,10 @@ void RendererCanvasCull::canvas_item_add_circle(RID p_item, const Point2 &p_pos,
 	static const int circle_points = 64;
 
 	points.resize(circle_points);
+	const real_t circle_point_step = Math_TAU / circle_points;
+
 	for (int i = 0; i < circle_points; i++) {
-		float angle = (i / float(circle_points)) * 2 * Math_PI;
+		float angle = i * circle_point_step;
 		points.write[i].x = Math::cos(angle) * p_radius;
 		points.write[i].y = Math::sin(angle) * p_radius;
 		points.write[i] += p_pos;

servers/rendering/renderer_rd/renderer_canvas_render_rd.cpp

@@ -1622,7 +1622,7 @@ void RendererCanvasRenderRD::light_update_shadow(RID p_rid, int p_shadow_index,
 			projection.set_frustum(xmin, xmax, ymin, ymax, nearp, farp);
 		}
 
-		Vector3 cam_target = Basis(Vector3(0, 0, Math_PI * 2 * ((i + 3) / 4.0))).xform(Vector3(0, 1, 0));
+		Vector3 cam_target = Basis(Vector3(0, 0, Math_TAU * ((i + 3) / 4.0))).xform(Vector3(0, 1, 0));
 		projection = projection * CameraMatrix(Transform().looking_at(cam_target, Vector3(0, 0, -1)).affine_inverse());
 
 		ShadowRenderPushConstant push_constant;

servers/rendering/renderer_rd/renderer_scene_render_rd.cpp

@@ -4877,7 +4877,7 @@ void RendererSceneRenderRD::_debug_sdfgi_probes(RID p_render_buffers, RD::DrawLi
 	push_constant.band_power = 4;
 	push_constant.sections_in_band = ((band_points / 2) - 1);
 	push_constant.band_mask = band_points - 2;
-	push_constant.section_arc = (Math_PI * 2.0) / float(push_constant.sections_in_band);
+	push_constant.section_arc = Math_TAU / float(push_constant.sections_in_band);
 	push_constant.y_mult = rb->sdfgi->y_mult;
 
 	uint32_t total_points = push_constant.sections_in_band * band_points;

servers/rendering_server.cpp

@@ -242,22 +242,24 @@ RID RenderingServer::_make_test_cube() {
 RID RenderingServer::make_sphere_mesh(int p_lats, int p_lons, float p_radius) {
 	Vector<Vector3> vertices;
 	Vector<Vector3> normals;
+	const double lat_step = Math_TAU / p_lats;
+	const double lon_step = Math_TAU / p_lons;
 
 	for (int i = 1; i <= p_lats; i++) {
-		double lat0 = Math_PI * (-0.5 + (double)(i - 1) / p_lats);
+		double lat0 = lat_step * (i - 1) - Math_TAU / 4;
 		double z0 = Math::sin(lat0);
 		double zr0 = Math::cos(lat0);
 
-		double lat1 = Math_PI * (-0.5 + (double)i / p_lats);
+		double lat1 = lat_step * i - Math_TAU / 4;
 		double z1 = Math::sin(lat1);
 		double zr1 = Math::cos(lat1);
 
 		for (int j = p_lons; j >= 1; j--) {
-			double lng0 = 2 * Math_PI * (double)(j - 1) / p_lons;
+			double lng0 = lon_step * (j - 1);
 			double x0 = Math::cos(lng0);
 			double y0 = Math::sin(lng0);
 
-			double lng1 = 2 * Math_PI * (double)(j) / p_lons;
+			double lng1 = lon_step * j;
 			double x1 = Math::cos(lng1);
 			double y1 = Math::sin(lng1);