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Merge pull request #63428 from fabriceci/fix-basis-get-axis-angle
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Test, refactor and fix a bug in Basis.get_axis_angle
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@akien-mga
akien-mga committed Sep 15, 2022
2 parents d39d462 + 9f1a57d commit f2ba73f
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Showing 2 changed files with 81 additions and 27 deletions.
51 changes: 26 additions & 25 deletions core/math/basis.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -754,29 +754,28 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND(!is_rotation());
#endif
*/
real_t angle, x, y, z; // variables for result
real_t angle_epsilon = 0.1; // margin to distinguish between 0 and 180 degrees

if ((Math::abs(rows[1][0] - rows[0][1]) < CMP_EPSILON) && (Math::abs(rows[2][0] - rows[0][2]) < CMP_EPSILON) && (Math::abs(rows[2][1] - rows[1][2]) < CMP_EPSILON)) {
// singularity found
// first check for identity matrix which must have +1 for all terms
// in leading diagonal and zero in other terms
if ((Math::abs(rows[1][0] + rows[0][1]) < angle_epsilon) && (Math::abs(rows[2][0] + rows[0][2]) < angle_epsilon) && (Math::abs(rows[2][1] + rows[1][2]) < angle_epsilon) && (Math::abs(rows[0][0] + rows[1][1] + rows[2][2] - 3) < angle_epsilon)) {
// this singularity is identity matrix so angle = 0
*/

// https://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
real_t x, y, z; // Variables for result.
if (Math::is_zero_approx(rows[0][1] - rows[1][0]) && Math::is_zero_approx(rows[0][2] - rows[2][0]) && Math::is_zero_approx(rows[1][2] - rows[2][1])) {
// Singularity found.
// First check for identity matrix which must have +1 for all terms in leading diagonal and zero in other terms.
if (is_diagonal() && (Math::abs(rows[0][0] + rows[1][1] + rows[2][2] - 3) < 3 * CMP_EPSILON)) {
// This singularity is identity matrix so angle = 0.
r_axis = Vector3(0, 1, 0);
r_angle = 0;
return;
}
// otherwise this singularity is angle = 180
angle = Math_PI;
// Otherwise this singularity is angle = 180.
real_t xx = (rows[0][0] + 1) / 2;
real_t yy = (rows[1][1] + 1) / 2;
real_t zz = (rows[2][2] + 1) / 2;
real_t xy = (rows[1][0] + rows[0][1]) / 4;
real_t xz = (rows[2][0] + rows[0][2]) / 4;
real_t yz = (rows[2][1] + rows[1][2]) / 4;
if ((xx > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term
real_t xy = (rows[0][1] + rows[1][0]) / 4;
real_t xz = (rows[0][2] + rows[2][0]) / 4;
real_t yz = (rows[1][2] + rows[2][1]) / 4;

if ((xx > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term.
if (xx < CMP_EPSILON) {
x = 0;
y = Math_SQRT12;
Expand All @@ -786,7 +785,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
y = xy / x;
z = xz / x;
}
} else if (yy > zz) { // rows[1][1] is the largest diagonal term
} else if (yy > zz) { // rows[1][1] is the largest diagonal term.
if (yy < CMP_EPSILON) {
x = Math_SQRT12;
y = 0;
Expand All @@ -796,7 +795,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
x = xy / y;
z = yz / y;
}
} else { // rows[2][2] is the largest diagonal term so base result on this
} else { // rows[2][2] is the largest diagonal term so base result on this.
if (zz < CMP_EPSILON) {
x = Math_SQRT12;
y = Math_SQRT12;
Expand All @@ -808,22 +807,24 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
}
}
r_axis = Vector3(x, y, z);
r_angle = angle;
r_angle = Math_PI;
return;
}
// as we have reached here there are no singularities so we can handle normally
real_t s = Math::sqrt((rows[1][2] - rows[2][1]) * (rows[1][2] - rows[2][1]) + (rows[2][0] - rows[0][2]) * (rows[2][0] - rows[0][2]) + (rows[0][1] - rows[1][0]) * (rows[0][1] - rows[1][0])); // s=|axis||sin(angle)|, used to normalise
// As we have reached here there are no singularities so we can handle normally.
double s = Math::sqrt((rows[2][1] - rows[1][2]) * (rows[2][1] - rows[1][2]) + (rows[0][2] - rows[2][0]) * (rows[0][2] - rows[2][0]) + (rows[1][0] - rows[0][1]) * (rows[1][0] - rows[0][1])); // Used to normalise.

angle = Math::acos((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2);
if (angle < 0) {
s = -s;
if (Math::abs(s) < CMP_EPSILON) {
// Prevent divide by zero, should not happen if matrix is orthogonal and should be caught by singularity test above.
s = 1;
}

x = (rows[2][1] - rows[1][2]) / s;
y = (rows[0][2] - rows[2][0]) / s;
z = (rows[1][0] - rows[0][1]) / s;

r_axis = Vector3(x, y, z);
r_angle = angle;
// CLAMP to avoid NaN if the value passed to acos is not in [0,1].
r_angle = Math::acos(CLAMP((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2, (real_t)0.0, (real_t)1.0));
}

void Basis::set_quaternion(const Quaternion &p_quaternion) {
Expand Down
57 changes: 55 additions & 2 deletions tests/core/math/test_basis.h
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ enum RotOrder {
EulerZYX
};

Vector3 deg2rad(const Vector3 &p_rotation) {
Vector3 deg_to_rad(const Vector3 &p_rotation) {
return p_rotation / 180.0 * Math_PI;
}

Expand Down Expand Up @@ -155,7 +155,7 @@ void test_rotation(Vector3 deg_original_euler, RotOrder rot_order) {
// are correct.

// Euler to rotation
const Vector3 original_euler = deg2rad(deg_original_euler);
const Vector3 original_euler = deg_to_rad(deg_original_euler);
const Basis to_rotation = EulerToBasis(rot_order, original_euler);

// Euler from rotation
Expand Down Expand Up @@ -281,6 +281,59 @@ TEST_CASE("[Stress][Basis] Euler conversions") {
}
}
}

TEST_CASE("[Basis] Set axis angle") {
Vector3 axis;
real_t angle;
real_t pi = (real_t)Math_PI;

// Testing the singularity when the angle is 0°.
Basis identity(1, 0, 0, 0, 1, 0, 0, 0, 1);
identity.get_axis_angle(axis, angle);
CHECK(angle == 0);

// Testing the singularity when the angle is 180°.
Basis singularityPi(-1, 0, 0, 0, 1, 0, 0, 0, -1);
singularityPi.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, pi));

// Testing reversing the an axis (of an 30° angle).
float cos30deg = Math::cos(Math::deg_to_rad((real_t)30.0));
Basis z_positive(cos30deg, -0.5, 0, 0.5, cos30deg, 0, 0, 0, 1);
Basis z_negative(cos30deg, 0.5, 0, -0.5, cos30deg, 0, 0, 0, 1);

z_positive.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, Math::deg_to_rad((real_t)30.0)));
CHECK(axis == Vector3(0, 0, 1));

z_negative.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, Math::deg_to_rad((real_t)30.0)));
CHECK(axis == Vector3(0, 0, -1));

// Testing a rotation of 90° on x-y-z.
Basis x90deg(1, 0, 0, 0, 0, -1, 0, 1, 0);
x90deg.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, pi / (real_t)2));
CHECK(axis == Vector3(1, 0, 0));

Basis y90deg(0, 0, 1, 0, 1, 0, -1, 0, 0);
y90deg.get_axis_angle(axis, angle);
CHECK(axis == Vector3(0, 1, 0));

Basis z90deg(0, -1, 0, 1, 0, 0, 0, 0, 1);
z90deg.get_axis_angle(axis, angle);
CHECK(axis == Vector3(0, 0, 1));

// Regression test: checks that the method returns a small angle (not 0).
Basis tiny(1, 0, 0, 0, 0.9999995, -0.001, 0, 001, 0.9999995); // The min angle possible with float is 0.001rad.
tiny.get_axis_angle(axis, angle);
CHECK(Math::is_equal_approx(angle, (real_t)0.001, (real_t)0.0001));

// Regression test: checks that the method returns an angle which is a number (not NaN)
Basis bugNan(1.00000024, 0, 0.000100001693, 0, 1, 0, -0.000100009143, 0, 1.00000024);
bugNan.get_axis_angle(axis, angle);
CHECK(!Math::is_nan(angle));
}
} // namespace TestBasis

#endif // TEST_BASIS_H

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