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Added various functions basic math classes. Also enabled math checks only for debug builds.

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Added set_scale, set_rotation_euler, set_rotation_axis_angle. Addresses #2565 directly.
Added an euler angle constructor for Basis in GDScript and also exposed is_normalized for vectors and quaternions.
Various other changes mostly cosmetic in nature.
This commit is contained in:
Ferenc Arn 2017-04-05 17:47:13 -05:00
parent 454f53c776
commit 9a37ff1e34
13 changed files with 217 additions and 50 deletions
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9
core/math/math_2d.cpp
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@ -62,7 +62,8 @@ Vector2 Vector2::normalized() const {
}
bool Vector2::is_normalized() const {
return Math::isequal_approx(length(), (real_t)1.0);
// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
return Math::is_equal_approx(length_squared(), 1.0);
}
real_t Vector2::distance_to(const Vector2 &p_vector2) const {
@ -280,7 +281,7 @@ Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, c
// slide returns the component of the vector along the given plane, specified by its normal vector.
Vector2 Vector2::slide(const Vector2 &p_n) const {
#ifdef DEBUG_ENABLED
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(p_n.is_normalized() == false, Vector2());
#endif
return *this - p_n * this->dot(p_n);
@ -291,7 +292,7 @@ Vector2 Vector2::bounce(const Vector2 &p_n) const {
}
Vector2 Vector2::reflect(const Vector2 &p_n) const {
#ifdef DEBUG_ENABLED
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(p_n.is_normalized() == false, Vector2());
#endif
return 2.0 * p_n * this->dot(p_n) - *this;
@ -438,7 +439,9 @@ Transform2D Transform2D::inverse() const {
void Transform2D::affine_invert() {
real_t det = basis_determinant();
#ifdef MATH_CHECKS
ERR_FAIL_COND(det == 0);
#endif
real_t idet = 1.0 / det;
SWAP(elements[0][0], elements[1][1]);

4
core/math/math_defs.h
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@ -34,6 +34,10 @@
#define CMP_NORMALIZE_TOLERANCE 0.000001
#define CMP_POINT_IN_PLANE_EPSILON 0.00001
#ifdef DEBUG_ENABLED
#define MATH_CHECKS
#endif
#define USEC_TO_SEC(m_usec) ((m_usec) / 1000000.0)
/**
* "Real" is a type that will be translated to either floats or fixed depending

2
core/math/math_funcs.h
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@ -167,7 +167,7 @@ public:
static float random(float from, float to);
static real_t random(int from, int to) { return (real_t)random((real_t)from, (real_t)to); }
static _ALWAYS_INLINE_ bool isequal_approx(real_t a, real_t b) {
static _ALWAYS_INLINE_ bool is_equal_approx(real_t a, real_t b) {
// TODO: Comparing floats for approximate-equality is non-trivial.
// Using epsilon should cover the typical cases in Godot (where a == b is used to compare two reals), such as matrix and vector comparison operators.
// A proper implementation in terms of ULPs should eventually replace the contents of this function.

126
core/math/matrix3.cpp
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@ -61,8 +61,9 @@ void Basis::invert() {
real_t det = elements[0][0] * co[0] +
elements[0][1] * co[1] +
elements[0][2] * co[2];
#ifdef MATH_CHECKS
ERR_FAIL_COND(det == 0);
#endif
real_t s = 1.0 / det;
set(co[0] * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
@ -71,8 +72,9 @@ void Basis::invert() {
}
void Basis::orthonormalize() {
#ifdef MATH_CHECKS
ERR_FAIL_COND(determinant() == 0);
#endif
// Gram-Schmidt Process
Vector3 x = get_axis(0);
@ -101,20 +103,20 @@ bool Basis::is_orthogonal() const {
Basis id;
Basis m = (*this) * transposed();
return isequal_approx(id, m);
return is_equal_approx(id, m);
}
bool Basis::is_rotation() const {
return Math::isequal_approx(determinant(), 1) && is_orthogonal();
return Math::is_equal_approx(determinant(), 1) && is_orthogonal();
}
bool Basis::is_symmetric() const {
if (Math::abs(elements[0][1] - elements[1][0]) > CMP_EPSILON)
if (!Math::is_equal_approx(elements[0][1], elements[1][0]))
return false;
if (Math::abs(elements[0][2] - elements[2][0]) > CMP_EPSILON)
if (!Math::is_equal_approx(elements[0][2], elements[2][0]))
return false;
if (Math::abs(elements[1][2] - elements[2][1]) > CMP_EPSILON)
if (!Math::is_equal_approx(elements[1][2], elements[2][1]))
return false;
return true;
@ -122,11 +124,11 @@ bool Basis::is_symmetric() const {
Basis Basis::diagonalize() {
//NOTE: only implemented for symmetric matrices
//with the Jacobi iterative method method
//NOTE: only implemented for symmetric matrices
//with the Jacobi iterative method method
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_symmetric(), Basis());
#endif
const int ite_max = 1024;
real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];
@ -159,7 +161,7 @@ Basis Basis::diagonalize() {
// Compute the rotation angle
real_t angle;
if (Math::abs(elements[j][j] - elements[i][i]) < CMP_EPSILON) {
if (Math::is_equal_approx(elements[j][j], elements[i][i])) {
angle = Math_PI / 4;
} else {
angle = 0.5 * Math::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
@ -225,11 +227,25 @@ Basis Basis::scaled(const Vector3 &p_scale) const {
}
Vector3 Basis::get_scale() const {
// We are assuming M = R.S, and performing a polar decomposition to extract R and S.
// FIXME: We eventually need a proper polar decomposition.
// As a cheap workaround until then, to ensure that R is a proper rotation matrix with determinant +1
// (such that it can be represented by a Quat or Euler angles), we absorb the sign flip into the scaling matrix.
// As such, it works in conjunction with get_rotation().
// FIXME: We are assuming M = R.S (R is rotation and S is scaling), and use polar decomposition to extract R and S.
// A polar decomposition is M = O.P, where O is an orthogonal matrix (meaning rotation and reflection) and
// P is a positive semi-definite matrix (meaning it contains absolute values of scaling along its diagonal).
//
// Despite being different from what we want to achieve, we can nevertheless make use of polar decomposition
// here as follows. We can split O into a rotation and a reflection as O = R.Q, and obtain M = R.S where
// we defined S = Q.P. Now, R is a proper rotation matrix and S is a (signed) scaling matrix,
// which can involve negative scalings. However, there is a catch: unlike the polar decomposition of M = O.P,
// the decomposition of O into a rotation and reflection matrix as O = R.Q is not unique.
// Therefore, we are going to do this decomposition by sticking to a particular convention.
// This may lead to confusion for some users though.
//
// The convention we use here is to absorb the sign flip into the scaling matrix.
// The same convention is also used in other similar functions such as set_scale,
// get_rotation_axis_angle, get_rotation, set_rotation_axis_angle, set_rotation_euler, ...
//
// A proper way to get rid of this issue would be to store the scaling values (or at least their signs)
// as a part of Basis. However, if we go that path, we need to disable direct (write) access to the
// matrix elements.
real_t det_sign = determinant() > 0 ? 1 : -1;
return det_sign * Vector3(
Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
@ -237,6 +253,17 @@ Vector3 Basis::get_scale() const {
Vector3(elements[0][2], elements[1][2], elements[2][2]).length());
}
// Sets scaling while preserving rotation.
// This requires some care when working with matrices with negative determinant,
// since we're using a particular convention for "polar" decomposition in get_scale and get_rotation.
// For details, see the explanation in get_scale.
void Basis::set_scale(const Vector3 &p_scale) {
Vector3 e = get_euler();
Basis(); // reset to identity
scale(p_scale);
rotate(e);
}
// Multiplies the matrix from left by the rotation matrix: M -> R.M
// Note that this does *not* rotate the matrix itself.
//
@ -259,6 +286,7 @@ void Basis::rotate(const Vector3 &p_euler) {
*this = rotated(p_euler);
}
// TODO: rename this to get_rotation_euler
Vector3 Basis::get_rotation() const {
// Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S,
// and returns the Euler angles corresponding to the rotation part, complementing get_scale().
@ -273,6 +301,42 @@ Vector3 Basis::get_rotation() const {
return m.get_euler();
}
void Basis::get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const {
// Assumes that the matrix can be decomposed into a proper rotation and scaling matrix as M = R.S,
// and returns the Euler angles corresponding to the rotation part, complementing get_scale().
// See the comment in get_scale() for further information.
Basis m = orthonormalized();
real_t det = m.determinant();
if (det < 0) {
// Ensure that the determinant is 1, such that result is a proper rotation matrix which can be represented by Euler angles.
m.scale(Vector3(-1, -1, -1));
}
m.get_axis_angle(p_axis, p_angle);
}
// Sets rotation while preserving scaling.
// This requires some care when working with matrices with negative determinant,
// since we're using a particular convention for "polar" decomposition in get_scale and get_rotation.
// For details, see the explanation in get_scale.
void Basis::set_rotation_euler(const Vector3 &p_euler) {
Vector3 s = get_scale();
Basis(); // reset to identity
scale(s);
rotate(p_euler);
}
// Sets rotation while preserving scaling.
// This requires some care when working with matrices with negative determinant,
// since we're using a particular convention for "polar" decomposition in get_scale and get_rotation.
// For details, see the explanation in get_scale.
void Basis::set_rotation_axis_angle(const Vector3 &p_axis, real_t p_angle) {
Vector3 s = get_scale();
Basis(); // reset to identity
scale(s);
rotate(p_axis, p_angle);
}
// get_euler returns a vector containing the Euler angles in the format
// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last
// (following the convention they are commonly defined in the literature).
@ -293,9 +357,9 @@ Vector3 Basis::get_euler() const {
// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
Vector3 euler;
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(is_rotation() == false, euler);
#endif
euler.y = Math::asin(elements[0][2]);
if (euler.y < Math_PI * 0.5) {
if (euler.y > -Math_PI * 0.5) {
@ -339,11 +403,11 @@ void Basis::set_euler(const Vector3 &p_euler) {
*this = xmat * (ymat * zmat);
}
bool Basis::isequal_approx(const Basis &a, const Basis &b) const {
bool Basis::is_equal_approx(const Basis &a, const Basis &b) const {
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
if (Math::isequal_approx(a.elements[i][j], b.elements[i][j]) == false)
if (Math::is_equal_approx(a.elements[i][j], b.elements[i][j]) == false)
return false;
}
}
@ -386,8 +450,9 @@ Basis::operator String() const {
}
Basis::operator Quat() const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(is_rotation() == false, Quat());
#endif
real_t trace = elements[0][0] + elements[1][1] + elements[2][2];
real_t temp[4];
@ -481,9 +546,10 @@ void Basis::set_orthogonal_index(int p_index) {
*this = _ortho_bases[p_index];
}
void Basis::get_axis_and_angle(Vector3 &r_axis, real_t &r_angle) const {
void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND(is_rotation() == false);
#endif
real_t angle, x, y, z; // variables for result
real_t epsilon = 0.01; // margin to allow for rounding errors
real_t epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
@ -572,11 +638,11 @@ Basis::Basis(const Quat &p_quat) {
xz - wy, yz + wx, 1.0 - (xx + yy));
}
Basis::Basis(const Vector3 &p_axis, real_t p_phi) {
// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_phi) {
// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_angle
#ifdef MATH_CHECKS
ERR_FAIL_COND(p_axis.is_normalized() == false);
#endif
Vector3 axis_sq(p_axis.x * p_axis.x, p_axis.y * p_axis.y, p_axis.z * p_axis.z);
real_t cosine = Math::cos(p_phi);
@ -594,3 +660,7 @@ Basis::Basis(const Vector3 &p_axis, real_t p_phi) {
elements[2][1] = p_axis.y * p_axis.z * (1.0 - cosine) + p_axis.x * sine;
elements[2][2] = axis_sq.z + cosine * (1.0 - axis_sq.z);
}
Basis::Basis(const Vector3 &p_axis, real_t p_phi) {
set_axis_angle(p_axis, p_phi);
}

22
core/math/matrix3.h
View File

@ -76,15 +76,25 @@ public:
void rotate(const Vector3 &p_euler);
Basis rotated(const Vector3 &p_euler) const;
Vector3 get_rotation() const;
void scale(const Vector3 &p_scale);
Basis scaled(const Vector3 &p_scale) const;
Vector3 get_scale() const;
Vector3 get_rotation() const;
void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
void set_rotation_euler(const Vector3 &p_euler);
void set_rotation_axis_angle(const Vector3 &p_axis, real_t p_angle);
Vector3 get_euler() const;
void set_euler(const Vector3 &p_euler);
void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const;
void set_axis_angle(const Vector3 &p_axis, real_t p_phi);
void scale(const Vector3 &p_scale);
Basis scaled(const Vector3 &p_scale) const;
Vector3 get_scale() const;
void set_scale(const Vector3 &p_scale);
// transposed dot products
_FORCE_INLINE_ real_t tdotx(const Vector3 &v) const {
return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
@ -96,7 +106,7 @@ public:
return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
}
bool isequal_approx(const Basis &a, const Basis &b) const;
bool is_equal_approx(const Basis &a, const Basis &b) const;
bool operator==(const Basis &p_matrix) const;
bool operator!=(const Basis &p_matrix) const;
@ -120,8 +130,6 @@ public:
operator String() const;
void get_axis_and_angle(Vector3 &r_axis, real_t &r_angle) const;
/* create / set */
_FORCE_INLINE_ void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {

4
core/math/quat.cpp
View File

@ -91,6 +91,10 @@ Quat Quat::normalized() const {
return *this / length();
}
bool Quat::is_normalized() const {
return Math::is_equal_approx(length(), 1.0);
}
Quat Quat::inverse() const {
return Quat(-x, -y, -z, w);
}

3
core/math/quat.h
View File

@ -47,6 +47,7 @@ public:
real_t length() const;
void normalize();
Quat normalized() const;
bool is_normalized() const;
Quat inverse() const;
_FORCE_INLINE_ real_t dot(const Quat &q) const;
void set_euler(const Vector3 &p_euler);
@ -55,7 +56,7 @@ 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;
_FORCE_INLINE_ void get_axis_and_angle(Vector3 &r_axis, real_t &r_angle) const {
_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);

7
core/math/vector3.h
View File

@ -388,7 +388,8 @@ Vector3 Vector3::normalized() const {
}
bool Vector3::is_normalized() const {
return Math::isequal_approx(length(), (real_t)1.0);
// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
return Math::is_equal_approx(length_squared(), 1.0);
}
Vector3 Vector3::inverse() const {
@ -403,7 +404,7 @@ void Vector3::zero() {
// slide returns the component of the vector along the given plane, specified by its normal vector.
Vector3 Vector3::slide(const Vector3 &p_n) const {
#ifdef DEBUG_ENABLED
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(p_n.is_normalized() == false, Vector3());
#endif
return *this - p_n * this->dot(p_n);
@ -414,7 +415,7 @@ Vector3 Vector3::bounce(const Vector3 &p_n) const {
}
Vector3 Vector3::reflect(const Vector3 &p_n) const {
#ifdef DEBUG_ENABLED
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(p_n.is_normalized() == false, Vector3());
#endif
return 2.0 * p_n * this->dot(p_n) - *this;

18
core/variant_call.cpp
View File

@ -327,6 +327,7 @@ struct _VariantCall {
VCALL_LOCALMEM0R(Vector2, normalized);
VCALL_LOCALMEM0R(Vector2, length);
VCALL_LOCALMEM0R(Vector2, length_squared);
VCALL_LOCALMEM0R(Vector2, is_normalized);
VCALL_LOCALMEM1R(Vector2, distance_to);
VCALL_LOCALMEM1R(Vector2, distance_squared_to);
VCALL_LOCALMEM1R(Vector2, angle_to);
@ -361,6 +362,7 @@ struct _VariantCall {
VCALL_LOCALMEM0R(Vector3, max_axis);
VCALL_LOCALMEM0R(Vector3, length);
VCALL_LOCALMEM0R(Vector3, length_squared);
VCALL_LOCALMEM0R(Vector3, is_normalized);
VCALL_LOCALMEM0R(Vector3, normalized);
VCALL_LOCALMEM0R(Vector3, inverse);
VCALL_LOCALMEM1R(Vector3, snapped);
@ -417,6 +419,7 @@ struct _VariantCall {
VCALL_LOCALMEM0R(Quat, length);
VCALL_LOCALMEM0R(Quat, length_squared);
VCALL_LOCALMEM0R(Quat, normalized);
VCALL_LOCALMEM0R(Quat, is_normalized);
VCALL_LOCALMEM0R(Quat, inverse);
VCALL_LOCALMEM1R(Quat, dot);
VCALL_LOCALMEM1R(Quat, xform);
@ -703,6 +706,9 @@ struct _VariantCall {
VCALL_PTR1R(Basis, scaled);
VCALL_PTR0R(Basis, get_scale);
VCALL_PTR0R(Basis, get_euler);
VCALL_PTR1(Basis, set_scale);
VCALL_PTR1(Basis, set_rotation_euler);
VCALL_PTR2(Basis, set_rotation_axis_angle);
VCALL_PTR1R(Basis, tdotx);
VCALL_PTR1R(Basis, tdoty);
VCALL_PTR1R(Basis, tdotz);
@ -874,6 +880,11 @@ struct _VariantCall {
r_ret = Basis(p_args[0]->operator Vector3(), p_args[1]->operator real_t());
}
static void Basis_init3(Variant &r_ret, const Variant **p_args) {
r_ret = Basis(p_args[0]->operator Vector3());
}
static void Transform_init1(Variant &r_ret, const Variant **p_args) {
Transform t;
@ -1428,6 +1439,7 @@ void register_variant_methods() {
ADDFUNC0(VECTOR2, REAL, Vector2, length, varray());
ADDFUNC0(VECTOR2, REAL, Vector2, angle, varray());
ADDFUNC0(VECTOR2, REAL, Vector2, length_squared, varray());
ADDFUNC0(VECTOR2, BOOL, Vector2, is_normalized, varray());
ADDFUNC1(VECTOR2, REAL, Vector2, distance_to, VECTOR2, "to", varray());
ADDFUNC1(VECTOR2, REAL, Vector2, distance_squared_to, VECTOR2, "to", varray());
ADDFUNC1(VECTOR2, REAL, Vector2, angle_to, VECTOR2, "to", varray());
@ -1461,6 +1473,7 @@ void register_variant_methods() {
ADDFUNC0(VECTOR3, INT, Vector3, max_axis, varray());
ADDFUNC0(VECTOR3, REAL, Vector3, length, varray());
ADDFUNC0(VECTOR3, REAL, Vector3, length_squared, varray());
ADDFUNC0(VECTOR3, BOOL, Vector3, is_normalized, varray());
ADDFUNC0(VECTOR3, VECTOR3, Vector3, normalized, varray());
ADDFUNC0(VECTOR3, VECTOR3, Vector3, inverse, varray());
ADDFUNC1(VECTOR3, VECTOR3, Vector3, snapped, REAL, "by", varray());
@ -1496,6 +1509,7 @@ void register_variant_methods() {
ADDFUNC0(QUAT, REAL, Quat, length, varray());
ADDFUNC0(QUAT, REAL, Quat, length_squared, varray());
ADDFUNC0(QUAT, QUAT, Quat, normalized, varray());
ADDFUNC0(QUAT, BOOL, Quat, is_normalized, varray());
ADDFUNC0(QUAT, QUAT, Quat, inverse, varray());
ADDFUNC1(QUAT, REAL, Quat, dot, QUAT, "b", varray());
ADDFUNC1(QUAT, VECTOR3, Quat, xform, VECTOR3, "v", varray());
@ -1691,6 +1705,9 @@ void register_variant_methods() {
ADDFUNC0(BASIS, REAL, Basis, determinant, varray());
ADDFUNC2(BASIS, BASIS, Basis, rotated, VECTOR3, "axis", REAL, "phi", varray());
ADDFUNC1(BASIS, BASIS, Basis, scaled, VECTOR3, "scale", varray());
ADDFUNC1(BASIS, NIL, Basis, set_scale, VECTOR3, "scale", varray());
ADDFUNC1(BASIS, NIL, Basis, set_rotation_euler, VECTOR3, "euler", varray());
ADDFUNC2(BASIS, NIL, Basis, set_rotation_axis_angle, VECTOR3, "axis", REAL, "angle", varray());
ADDFUNC0(BASIS, VECTOR3, Basis, get_scale, varray());
ADDFUNC0(BASIS, VECTOR3, Basis, get_euler, varray());
ADDFUNC1(BASIS, REAL, Basis, tdotx, VECTOR3, "with", varray());
@ -1748,6 +1765,7 @@ void register_variant_methods() {
_VariantCall::add_constructor(_VariantCall::Basis_init1, Variant::BASIS, "x_axis", Variant::VECTOR3, "y_axis", Variant::VECTOR3, "z_axis", Variant::VECTOR3);
_VariantCall::add_constructor(_VariantCall::Basis_init2, Variant::BASIS, "axis", Variant::VECTOR3, "phi", Variant::REAL);
_VariantCall::add_constructor(_VariantCall::Basis_init3, Variant::BASIS, "euler", Variant::VECTOR3);
_VariantCall::add_constructor(_VariantCall::Transform_init1, Variant::TRANSFORM, "x_axis", Variant::VECTOR3, "y_axis", Variant::VECTOR3, "z_axis", Variant::VECTOR3, "origin", Variant::VECTOR3);
_VariantCall::add_constructor(_VariantCall::Transform_init2, Variant::TRANSFORM, "basis", Variant::BASIS, "origin", Variant::VECTOR3);

62
doc/base/classes.xml
View File

@ -6839,6 +6839,15 @@
Create a rotation matrix which rotates around the given axis by the specified angle. The axis must be a normalized vector.
</description>
</method>
<method name="Basis">
<return type="Basis">
</return>
<argument index="0" name="euler" type="Vector3">
</argument>
<description>
Create a rotation matrix (in the XYZ convention: first Z, then Y, and X last) from the specified Euler angles, given in the vector format as (third,second,first).
</description>
</method>
<method name="Basis">
<return type="Basis">
</return>
@ -6863,8 +6872,7 @@
<return type="Vector3">
</return>
<description>
Return Euler angles (in the XYZ convention: first Z, then Y, and X last) from the matrix. Returned vector contains the rotation angles in the format (third,second,first).
This function only works if the matrix represents a proper rotation.
Assuming that the matrix is a proper rotation matrix (orthonormal matrix with determinant +1), return Euler angles (in the XYZ convention: first Z, then Y, and X last). Returned vector contains the rotation angles in the format (third,second,first).
</description>
</method>
<method name="get_orthogonal_index">
@ -6906,6 +6914,26 @@
Introduce an additional rotation around the given axis by phi. Only relevant when the matrix is being used as a part of [Transform]. The axis must be a normalized vector.
</description>
</method>
<method name="set_rotation_euler">
<return type="Basis">
</return>
<argument index="0" name="euler" type="Vector3">
</argument>
<description>
Changes only the rotation part of the [Basis] to a rotation corresponding to given Euler angles, while preserving the scaling part (as determined by get_scale).
</description>
</method>
<method name="set_rotation_axis_angle">
<return type="Basis">
</return>
<argument index="0" name="axis" type="Vector3">
</argument>
<argument index="1" name="phi" type="float">
</argument>
<description>
Changes only the rotation part of the [Basis] to a rotation around given axis by phi, while preserving the scaling part (as determined by get_scale).
</description>
</method>
<method name="scaled">
<return type="Basis">
</return>
@ -6915,6 +6943,15 @@
Introduce an additional scaling specified by the given 3D scaling factor. Only relevant when the matrix is being used as a part of [Transform].
</description>
</method>
<method name="set_scale">
<return type="Basis">
</return>
<argument index="0" name="scale" type="Vector3">
</argument>
<description>
Changes only the scaling part of the Basis to the specified scaling, while preserving the rotation part (as determined by get_rotation).
</description>
</method>
<method name="tdotx">
<return type="float">
</return>
@ -34942,6 +34979,13 @@
Returns a copy of the quaternion, normalized to unit length.
</description>
</method>
<method name="is_normalized">
<return type="bool">
</return>
<description>
Returns whether the quaternion is normalized or not.
</description>
</method>
<method name="slerp">
<return type="Quat">
</return>
@ -47093,6 +47137,13 @@ do_property].
Returns a normalized vector to unit length.
</description>
</method>
<method name="is_normalized">
<return type="bool">
</return>
<description>
Returns whether the vector is normalized or not.
</description>
</method>
<method name="reflect">
<return type="Vector2">
</return>
@ -47317,6 +47368,13 @@ do_property].
Return a copy of the normalized vector to unit length. This is the same as v / v.length().
</description>
</method>
<method name="is_normalized">
<return type="bool">
</return>
<description>
Returns whether the vector is normalized or not.
</description>
</method>
<method name="outer">
<return type="Basis">
</return>

2
main/tests/test_math.cpp
View File

@ -601,7 +601,7 @@ MainLoop *test() {
print_line(q3);
print_line("before v: " + v + " a: " + rtos(a));
q.get_axis_and_angle(v, a);
q.get_axis_angle(v, a);
print_line("after v: " + v + " a: " + rtos(a));
}

4
scene/resources/animation.cpp
View File

@ -1760,8 +1760,8 @@ bool Animation::_transform_track_optimize_key(const TKey<TransformKey> &t0, cons
Vector3 v02, v01;
real_t a02, a01;
r02.get_axis_and_angle(v02, a02);
r01.get_axis_and_angle(v01, a01);
r02.get_axis_angle(v02, a02);
r01.get_axis_angle(v01, a01);
if (Math::abs(a02) > p_max_optimizable_angle)
return false;

4
servers/physics/body_sw.cpp
View File

@ -494,7 +494,7 @@ void BodySW::integrate_forces(real_t p_step) {
Vector3 axis;
real_t angle;
rot.get_axis_and_angle(axis, angle);
rot.get_axis_angle(axis, angle);
axis.normalize();
angular_velocity = axis.normalized() * (angle / p_step);
@ -637,7 +637,7 @@ void BodySW::simulate_motion(const Transform& p_xform,real_t p_step) {
Vector3 axis;
real_t angle;
rot.get_axis_and_angle(axis,angle);
rot.get_axis_angle(axis,angle);
axis.normalize();
angular_velocity=axis.normalized() * (angle/p_step);
linear_velocity = (p_xform.origin - get_transform().origin)/p_step;