diff --git a/core/math/math_2d.h b/core/math/math_2d.h
index 611d47e3ff7..25c39e5d7a6 100644
--- a/core/math/math_2d.h
+++ b/core/math/math_2d.h
@@ -112,6 +112,7 @@ struct Vector2 {
_FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t);
_FORCE_INLINE_ Vector2 linear_interpolate(const Vector2 &p_b, real_t p_t) const;
+ _FORCE_INLINE_ Vector2 slerp(const Vector2 &p_b, real_t p_t) const;
Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_t) const;
Vector2 slide(const Vector2 &p_normal) const;
@@ -263,6 +264,14 @@ Vector2 Vector2::linear_interpolate(const Vector2 &p_b, real_t p_t) const {
return res;
}
+Vector2 Vector2::slerp(const Vector2 &p_b, real_t p_t) const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_normalized() == false, Vector2());
+#endif
+ real_t theta = angle_to(p_b);
+ return rotated(theta * p_t);
+}
+
Vector2 Vector2::linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_t) {
Vector2 res = p_a;
diff --git a/core/math/matrix3.cpp b/core/math/matrix3.cpp
index b0b05d1ec87..8ee8ccb457c 100644
--- a/core/math/matrix3.cpp
+++ b/core/math/matrix3.cpp
@@ -826,3 +826,16 @@ void Basis::set_diagonal(const Vector3 p_diag) {
elements[2][1] = 0;
elements[2][2] = p_diag.z;
}
+
+Basis Basis::slerp(const Basis &target, const real_t &t) const {
+ // TODO: implement this directly without using quaternions to make it more efficient
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_rotation() == false, Basis());
+ ERR_FAIL_COND_V(target.is_rotation() == false, Basis());
+#endif
+
+ Quat from(*this);
+ Quat to(target);
+
+ return Basis(from.slerp(to, t));
+}
diff --git a/core/math/matrix3.h b/core/math/matrix3.h
index fd383fc673c..63d4f5d79dd 100644
--- a/core/math/matrix3.h
+++ b/core/math/matrix3.h
@@ -155,6 +155,8 @@ public:
bool is_diagonal() const;
bool is_rotation() const;
+ Basis slerp(const Basis &target, const real_t &t) const;
+
operator String() const;
/* create / set */
diff --git a/core/math/quat.cpp b/core/math/quat.cpp
index 4f61401ac72..b938fc3cfd3 100644
--- a/core/math/quat.cpp
+++ b/core/math/quat.cpp
@@ -98,6 +98,9 @@ void Quat::set_euler_yxz(const Vector3 &p_euler) {
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
Vector3 Quat::get_euler_yxz() const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_normalized() == false, Vector3(0, 0, 0));
+#endif
Basis m(*this);
return m.get_euler_yxz();
}
@@ -135,11 +138,17 @@ bool Quat::is_normalized() const {
}
Quat Quat::inverse() const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_normalized() == false, Quat(0, 0, 0, 0));
+#endif
return Quat(-x, -y, -z, w);
}
Quat Quat::slerp(const Quat &q, const real_t &t) const {
-
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_normalized() == false, Quat(0, 0, 0, 0));
+ ERR_FAIL_COND_V(q.is_normalized() == false, Quat(0, 0, 0, 0));
+#endif
Quat to1;
real_t omega, cosom, sinom, scale0, scale1;
@@ -215,7 +224,10 @@ Quat::operator String() const {
return String::num(x) + ", " + String::num(y) + ", " + String::num(z) + ", " + String::num(w);
}
-Quat::Quat(const Vector3 &axis, const real_t &angle) {
+void Quat::set_axis_angle(const Vector3 &axis, const real_t &angle) {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND(axis.is_normalized() == false);
+#endif
real_t d = axis.length();
if (d == 0)
set(0, 0, 0, 0);
diff --git a/core/math/quat.h b/core/math/quat.h
index ebc924504ba..3e1344a913b 100644
--- a/core/math/quat.h
+++ b/core/math/quat.h
@@ -64,11 +64,13 @@ public:
Quat slerpni(const Quat &q, const real_t &t) const;
Quat cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) const;
+ void set_axis_angle(const Vector3 &axis, const real_t &angle);
_FORCE_INLINE_ void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
r_angle = 2 * Math::acos(w);
- r_axis.x = x / Math::sqrt(1 - w * w);
- r_axis.y = y / Math::sqrt(1 - w * w);
- r_axis.z = z / Math::sqrt(1 - w * w);
+ real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
+ r_axis.x = x * r;
+ r_axis.y = y * r;
+ r_axis.z = z * r;
}
void operator*=(const Quat &q);
@@ -83,9 +85,9 @@ public:
_FORCE_INLINE_ Vector3 xform(const Vector3 &v) const {
- Quat q = *this * v;
- q *= this->inverse();
- return Vector3(q.x, q.y, q.z);
+ Vector3 u(x, y, z);
+ Vector3 uv = u.cross(v);
+ return v + ((uv * w) + u.cross(uv)) * ((real_t)2);
}
_FORCE_INLINE_ void operator+=(const Quat &q);
@@ -115,7 +117,15 @@ public:
z = p_z;
w = p_w;
}
- Quat(const Vector3 &axis, const real_t &angle);
+ Quat(const Vector3 &axis, const real_t &angle) { set_axis_angle(axis, angle); }
+
+ Quat(const Vector3 &euler) { set_euler(euler); }
+ Quat(const Quat &q) {
+ x = q.x;
+ y = q.y;
+ z = q.z;
+ w = q.w;
+ }
Quat(const Vector3 &v0, const Vector3 &v1) // shortest arc
{
diff --git a/core/math/vector3.h b/core/math/vector3.h
index 3bbfd7627c4..433adf09ee8 100644
--- a/core/math/vector3.h
+++ b/core/math/vector3.h
@@ -91,6 +91,7 @@ struct Vector3 {
/* Static Methods between 2 vector3s */
_FORCE_INLINE_ Vector3 linear_interpolate(const Vector3 &p_b, real_t p_t) const;
+ _FORCE_INLINE_ Vector3 slerp(const Vector3 &p_b, real_t p_t) const;
Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_t) const;
Vector3 cubic_interpolaten(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_t) const;
@@ -218,6 +219,15 @@ Vector3 Vector3::linear_interpolate(const Vector3 &p_b, real_t p_t) const {
z + (p_t * (p_b.z - z)));
}
+Vector3 Vector3::slerp(const Vector3 &p_b, real_t p_t) const {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_V(is_normalized() == false, Vector3());
+#endif
+
+ real_t theta = angle_to(p_b);
+ return rotated(cross(p_b), theta * p_t);
+}
+
real_t Vector3::distance_to(const Vector3 &p_b) const {
return (p_b - *this).length();
diff --git a/core/variant_call.cpp b/core/variant_call.cpp
index bd1cde5a82d..4e883d496fc 100644
--- a/core/variant_call.cpp
+++ b/core/variant_call.cpp
@@ -340,6 +340,7 @@ struct _VariantCall {
VCALL_LOCALMEM1R(Vector2, angle_to);
VCALL_LOCALMEM1R(Vector2, angle_to_point);
VCALL_LOCALMEM2R(Vector2, linear_interpolate);
+ VCALL_LOCALMEM2R(Vector2, slerp);
VCALL_LOCALMEM4R(Vector2, cubic_interpolate);
VCALL_LOCALMEM1R(Vector2, rotated);
VCALL_LOCALMEM0R(Vector2, tangent);
@@ -380,6 +381,7 @@ struct _VariantCall {
VCALL_LOCALMEM1R(Vector3, snapped);
VCALL_LOCALMEM2R(Vector3, rotated);
VCALL_LOCALMEM2R(Vector3, linear_interpolate);
+ VCALL_LOCALMEM2R(Vector3, slerp);
VCALL_LOCALMEM4R(Vector3, cubic_interpolate);
VCALL_LOCALMEM1R(Vector3, dot);
VCALL_LOCALMEM1R(Vector3, cross);
@@ -439,6 +441,9 @@ struct _VariantCall {
VCALL_LOCALMEM2R(Quat, slerp);
VCALL_LOCALMEM2R(Quat, slerpni);
VCALL_LOCALMEM4R(Quat, cubic_slerp);
+ VCALL_LOCALMEM0R(Quat, get_euler);
+ VCALL_LOCALMEM1(Quat, set_euler);
+ VCALL_LOCALMEM2(Quat, set_axis_angle);
VCALL_LOCALMEM0R(Color, to_rgba32);
VCALL_LOCALMEM0R(Color, to_argb32);
@@ -876,6 +881,11 @@ struct _VariantCall {
r_ret = Quat(((Vector3)(*p_args[0])), ((float)(*p_args[1])));
}
+ static void Quat_init3(Variant &r_ret, const Variant **p_args) {
+
+ r_ret = Quat(((Vector3)(*p_args[0])));
+ }
+
static void Color_init1(Variant &r_ret, const Variant **p_args) {
r_ret = Color(*p_args[0], *p_args[1], *p_args[2], *p_args[3]);
@@ -1150,7 +1160,7 @@ Variant Variant::construct(const Variant::Type p_type, const Variant **p_args, i
case RECT2: return (Rect2(*p_args[0]));
case VECTOR3: return (Vector3(*p_args[0]));
case PLANE: return (Plane(*p_args[0]));
- case QUAT: return (Quat(*p_args[0]));
+ case QUAT: return (p_args[0]->operator Quat());
case AABB:
return (::AABB(*p_args[0])); // 10
case BASIS: return (Basis(p_args[0]->operator Basis()));
@@ -1518,6 +1528,7 @@ void register_variant_methods() {
ADDFUNC1R(VECTOR2, REAL, Vector2, angle_to, VECTOR2, "to", varray());
ADDFUNC1R(VECTOR2, REAL, Vector2, angle_to_point, VECTOR2, "to", varray());
ADDFUNC2R(VECTOR2, VECTOR2, Vector2, linear_interpolate, VECTOR2, "b", REAL, "t", varray());
+ ADDFUNC2R(VECTOR2, VECTOR2, Vector2, slerp, VECTOR2, "b", REAL, "t", varray());
ADDFUNC4R(VECTOR2, VECTOR2, Vector2, cubic_interpolate, VECTOR2, "b", VECTOR2, "pre_a", VECTOR2, "post_b", REAL, "t", varray());
ADDFUNC1R(VECTOR2, VECTOR2, Vector2, rotated, REAL, "phi", varray());
ADDFUNC0R(VECTOR2, VECTOR2, Vector2, tangent, varray());
@@ -1557,6 +1568,7 @@ void register_variant_methods() {
ADDFUNC1R(VECTOR3, VECTOR3, Vector3, snapped, VECTOR3, "by", varray());
ADDFUNC2R(VECTOR3, VECTOR3, Vector3, rotated, VECTOR3, "axis", REAL, "phi", varray());
ADDFUNC2R(VECTOR3, VECTOR3, Vector3, linear_interpolate, VECTOR3, "b", REAL, "t", varray());
+ ADDFUNC2R(VECTOR3, VECTOR3, Vector3, slerp, VECTOR3, "b", REAL, "t", varray());
ADDFUNC4R(VECTOR3, VECTOR3, Vector3, cubic_interpolate, VECTOR3, "b", VECTOR3, "pre_a", VECTOR3, "post_b", REAL, "t", varray());
ADDFUNC1R(VECTOR3, REAL, Vector3, dot, VECTOR3, "b", varray());
ADDFUNC1R(VECTOR3, VECTOR3, Vector3, cross, VECTOR3, "b", varray());
@@ -1594,6 +1606,9 @@ void register_variant_methods() {
ADDFUNC2R(QUAT, QUAT, Quat, slerp, QUAT, "b", REAL, "t", varray());
ADDFUNC2R(QUAT, QUAT, Quat, slerpni, QUAT, "b", REAL, "t", varray());
ADDFUNC4R(QUAT, QUAT, Quat, cubic_slerp, QUAT, "b", QUAT, "pre_a", QUAT, "post_b", REAL, "t", varray());
+ ADDFUNC0R(QUAT, VECTOR3, Quat, get_euler, varray());
+ ADDFUNC1(QUAT, NIL, Quat, set_euler, VECTOR3, "euler", varray());
+ ADDFUNC2(QUAT, NIL, Quat, set_axis_angle, VECTOR3, "axis", REAL, "angle", varray());
ADDFUNC0R(COLOR, INT, Color, to_rgba32, varray());
ADDFUNC0R(COLOR, INT, Color, to_argb32, varray());
@@ -1816,6 +1831,7 @@ void register_variant_methods() {
_VariantCall::add_constructor(_VariantCall::Quat_init1, Variant::QUAT, "x", Variant::REAL, "y", Variant::REAL, "z", Variant::REAL, "w", Variant::REAL);
_VariantCall::add_constructor(_VariantCall::Quat_init2, Variant::QUAT, "axis", Variant::VECTOR3, "angle", Variant::REAL);
+ _VariantCall::add_constructor(_VariantCall::Quat_init3, Variant::QUAT, "euler", Variant::VECTOR3);
_VariantCall::add_constructor(_VariantCall::Color_init1, Variant::COLOR, "r", Variant::REAL, "g", Variant::REAL, "b", Variant::REAL, "a", Variant::REAL);
_VariantCall::add_constructor(_VariantCall::Color_init2, Variant::COLOR, "r", Variant::REAL, "g", Variant::REAL, "b", Variant::REAL);
diff --git a/doc/classes/Basis.xml b/doc/classes/Basis.xml
index 554ed999644..b9dc763820b 100644
--- a/doc/classes/Basis.xml
+++ b/doc/classes/Basis.xml
@@ -4,11 +4,12 @@
3x3 matrix datatype.
- 3x3 matrix used for 3D rotation and scale. Contains 3 vector fields x,y and z as its columns, which can be interpreted as the local basis vectors of a transformation. Can also be accessed as array of 3D vectors. These vectors are orthogonal to each other, but are not necessarily normalized. Almost always used as orthogonal basis for a [Transform].
+ 3x3 matrix used for 3D rotation and scale. Contains 3 vector fields x,y and z as its columns, which can be interpreted as the local basis vectors of a transformation. Can also be accessed as array of 3D vectors. These vectors are orthogonal to each other, but are not necessarily normalized (due to scaling). Almost always used as orthogonal basis for a [Transform].
For such use, it is composed of a scaling and a rotation matrix, in that order (M = R.S).
http://docs.godotengine.org/en/latest/tutorials/3d/using_transforms.html
+ http://docs.godotengine.org/en/latest/tutorials/math/rotations.html
@@ -105,7 +106,7 @@
- Introduce an additional rotation around the given axis by phi (radians). Only relevant when the matrix is being used as a part of [Transform]. The axis must be a normalized vector.
+ Introduce an additional rotation around the given axis by phi (radians). The axis must be a normalized vector.
@@ -114,7 +115,18 @@
- Introduce an additional scaling specified by the given 3D scaling factor. Only relevant when the matrix is being used as a part of [Transform].
+ Introduce an additional scaling specified by the given 3D scaling factor.
+
+
+
+
+
+
+
+
+
+
+ Assuming that the matrix is a proper rotation matrix, slerp performs a spherical-linear interpolation with another rotation matrix.
diff --git a/doc/classes/Quat.xml b/doc/classes/Quat.xml
index 33f2b9758b0..41217908817 100644
--- a/doc/classes/Quat.xml
+++ b/doc/classes/Quat.xml
@@ -4,13 +4,14 @@
Quaternion.
- A 4-dimensional vector representing a rotation.
- The vector represents a 4 dimensional complex number where multiplication of the basis elements is not commutative (multiplying i with j gives a different result than multiplying j with i).
- Multiplying quaternions reproduces rotation sequences. However quaternions need to be often renormalized, or else they suffer from precision issues.
- It can be used to perform SLERP (spherical-linear interpolation) between two rotations.
+ A unit quaternion used for representing 3D rotations.
+ It is similar to [Basis], which implements matrix representation of rotations, and can be parametrized using both an axis-angle pair or Euler angles. But due to its compactness and the way it is stored in memory, certain operations (obtaining axis-angle and performing SLERP, in particular) are more efficient and robust against floating point errors.
+
+ Quaternions need to be (re)normalized.
http://docs.godotengine.org/en/latest/tutorials/3d/using_transforms.html#interpolating-with-quaternions
+ http://docs.godotengine.org/en/latest/tutorials/math/rotations.html
@@ -41,6 +42,15 @@
Returns a quaternion that will rotate around the given axis by the specified angle. The axis must be a normalized vector.
+
+
+
+
+
+
+ Returns a quaternion that will perform a rotation specified by Euler angles (in the YXZ convention: first Z, then X, and Y last), given in the vector format as (X-angle, Y-angle, Z-angle).
+
+
@@ -74,6 +84,13 @@
Returns the dot product of two quaternions.
+
+
+
+
+ Return Euler angles (in the YXZ convention: first Z, then X, and Y last) corresponding to the rotation represented by the unit quaternion. Returned vector contains the rotation angles in the format (X-angle, Y-angle, Z-angle).
+
+
@@ -109,6 +126,22 @@
Returns a copy of the quaternion, normalized to unit length.
+
+
+
+
+
+
+ Set the quaternion to a rotation which rotates around axis by the specified angle, in radians. The axis must be a normalized vector.
+
+
+
+
+
+
+ Set the quaternion to a rotation specified by Euler angles (in the YXZ convention: first Z, then X, and Y last), given in the vector format as (X-angle, Y-angle, Z-angle).
+
+
diff --git a/doc/classes/Vector2.xml b/doc/classes/Vector2.xml
index 66563dc5a48..cee80281eef 100644
--- a/doc/classes/Vector2.xml
+++ b/doc/classes/Vector2.xml
@@ -208,6 +208,18 @@
+
+
+
+
+
+
+
+
+ Returns the result of SLERP between this vector and "b", by amount "t". "t" should be a float of 0.0-1.0, a percentage of how far along the interpolation is.
+ Both vectors need to be normalized.
+
+
diff --git a/doc/classes/Vector3.xml b/doc/classes/Vector3.xml
index 0ffb5603c70..827033e4816 100644
--- a/doc/classes/Vector3.xml
+++ b/doc/classes/Vector3.xml
@@ -210,6 +210,18 @@
+
+
+
+
+
+
+
+
+ Returns the result of SLERP between this vector and "b", by amount "t". "t" should be a float of 0.0-1.0, a percentage of how far along the interpolation is.
+ Both vectors need to be normalized.
+
+