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Add a new decomposition to Basis.

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This new decomposition splits the basis into a rotation-reflection matrix and a positive scaling matrix, which is required for physics calculations.
This commit is contained in:
Ferenc Arn 2017-08-25 15:45:21 -04:00
parent a1d7c496b9
commit 5ad8d310f2
2 changed files with 38 additions and 4 deletions
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39
core/math/matrix3.cpp
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@ -107,6 +107,13 @@ bool Basis::is_orthogonal() const {
return is_equal_approx(id, m);
}
bool Basis::is_diagonal() const {
return (
Math::is_equal_approx(elements[0][1], 0) && Math::is_equal_approx(elements[0][2], 0) &&
Math::is_equal_approx(elements[1][0], 0) && Math::is_equal_approx(elements[1][2], 0) &&
Math::is_equal_approx(elements[2][0], 0) && Math::is_equal_approx(elements[2][1], 0));
}
bool Basis::is_rotation() const {
return Math::is_equal_approx(determinant(), 1) && is_orthogonal();
}
@ -241,12 +248,13 @@ Vector3 Basis::get_scale() const {
// 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, ...
// The same convention is also used in other similar functions such as get_rotation_axis_angle, get_rotation, ...
//
// 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.
//
// The rotation part of this decomposition is returned by get_rotation* functions.
real_t det_sign = determinant() > 0 ? 1 : -1;
return det_sign * Vector3(
Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
@ -254,6 +262,26 @@ Vector3 Basis::get_scale() const {
Vector3(elements[0][2], elements[1][2], elements[2][2]).length());
}
// Decomposes a Basis into a rotation-reflection matrix (an element of the group O(3)) and a positive scaling matrix as B = O.S.
// Returns the rotation-reflection matrix via reference argument, and scaling information is returned as a Vector3.
// This (internal) function is too specıfıc and named too ugly to expose to users, and probably there's no need to do so.
Vector3 Basis::rotref_posscale_decomposition(Basis &rotref) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(determinant() == 0, Vector3());
Basis m = transposed() * (*this);
ERR_FAIL_COND_V(m.is_diagonal() == false, Vector3());
#endif
Vector3 scale = get_scale();
Basis inv_scale = Basis().scaled(scale.inverse()); // this will also absorb the sign of scale
rotref = (*this) * inv_scale;
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(rotref.is_orthogonal() == false, Vector3());
#endif
return scale.abs();
}
// Multiplies the matrix from left by the rotation matrix: M -> R.M
// Note that this does *not* rotate the matrix itself.
//
@ -331,8 +359,9 @@ Vector3 Basis::get_euler_xyz() const {
euler.y = Math::asin(elements[0][2]);
if (euler.y < Math_PI * 0.5) {
if (euler.y > -Math_PI * 0.5) {
//if rotation is Y-only, return a proper -pi,pi range like in x or z for the same case.
// is this a pure Y rotation?
if (elements[1][0] == 0.0 && elements[0][1] == 0.0 && elements[1][2] == 0 && elements[2][1] == 0 && elements[1][1] == 1) {
// return the simplest form
euler.x = 0;
euler.y = atan2(elements[0][2], elements[0][0]);
euler.z = 0;
@ -399,7 +428,9 @@ Vector3 Basis::get_euler_yxz() const {
if (m12 < 1) {
if (m12 > -1) {
if (elements[1][0] == 0 && elements[0][1] == 0 && elements[0][2] == 0 && elements[2][0] == 0 && elements[0][0] == 1) { // use pure x rotation
// is this a pure X rotation?
if (elements[1][0] == 0 && elements[0][1] == 0 && elements[0][2] == 0 && elements[2][0] == 0 && elements[0][0] == 1) {
// return the simplest form
euler.x = atan2(-m12, elements[1][1]);
euler.y = 0;
euler.z = 0;

3
core/math/matrix3.h
View file

@ -81,6 +81,8 @@ public:
Vector3 get_rotation() const;
void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
Vector3 rotref_posscale_decomposition(Basis &rotref) const;
Vector3 get_euler_xyz() const;
void set_euler_xyz(const Vector3 &p_euler);
Vector3 get_euler_yxz() const;
@ -128,6 +130,7 @@ public:
void set_orthogonal_index(int p_index);
bool is_orthogonal() const;
bool is_diagonal() const;
bool is_rotation() const;
operator String() const;