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

4 files changed, 19 insertions, 15 deletions

diff --git a/scene/3d/cpu_particles_3d.cpp b/scene/3d/cpu_particles_3d.cpp
index 3562f7b778..c36c135fe6 100644
--- a/scene/3d/cpu_particles_3d.cpp
+++ b/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);
 
diff --git a/scene/3d/immediate_geometry_3d.cpp b/scene/3d/immediate_geometry_3d.cpp
index 17410d5870..47242cf196 100644
--- a/scene/3d/immediate_geometry_3d.cpp
+++ b/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);
 
diff --git a/scene/3d/node_3d.cpp b/scene/3d/node_3d.cpp
index 503dd5735b..55eaeed9b8 100644
--- a/scene/3d/node_3d.cpp
+++ b/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 {
diff --git a/scene/3d/physics_body_3d.cpp b/scene/3d/physics_body_3d.cpp
index 5645923f22..cf5fd21e79 100644
--- a/scene/3d/physics_body_3d.cpp
+++ b/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 {