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Test, refactor and fix a bug in Basis.get_axis_angle

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This commit is contained in:
fabriceci 2022-07-25 11:01:26 +02:00
parent d9e974cdb0
commit 9f1a57d48b
2 changed files with 80 additions and 26 deletions
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49
core/math/basis.cpp
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@ -754,29 +754,28 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
#ifdef MATH_CHECKS #ifdef MATH_CHECKS
ERR_FAIL_COND(!is_rotation()); ERR_FAIL_COND(!is_rotation());
#endif #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)) { // https://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
// singularity found real_t x, y, z; // Variables for result.
// first check for identity matrix which must have +1 for all terms 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])) {
// in leading diagonal and zero in other terms // Singularity found.
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)) { // First check for identity matrix which must have +1 for all terms in leading diagonal and zero in other terms.
// this singularity is identity matrix so angle = 0 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_axis = Vector3(0, 1, 0);
r_angle = 0; r_angle = 0;
return; return;
} }
// otherwise this singularity is angle = 180 // Otherwise this singularity is angle = 180.
angle = Math_PI;
real_t xx = (rows[0][0] + 1) / 2; real_t xx = (rows[0][0] + 1) / 2;
real_t yy = (rows[1][1] + 1) / 2; real_t yy = (rows[1][1] + 1) / 2;
real_t zz = (rows[2][2] + 1) / 2; real_t zz = (rows[2][2] + 1) / 2;
real_t xy = (rows[1][0] + rows[0][1]) / 4; real_t xy = (rows[0][1] + rows[1][0]) / 4;
real_t xz = (rows[2][0] + rows[0][2]) / 4; real_t xz = (rows[0][2] + rows[2][0]) / 4;
real_t yz = (rows[2][1] + rows[1][2]) / 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 > yy) && (xx > zz)) { // rows[0][0] is the largest diagonal term.
if (xx < CMP_EPSILON) { if (xx < CMP_EPSILON) {
x = 0; x = 0;
y = Math_SQRT12; y = Math_SQRT12;
@ -786,7 +785,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
y = xy / x; y = xy / x;
z = xz / 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) { if (yy < CMP_EPSILON) {
x = Math_SQRT12; x = Math_SQRT12;
y = 0; y = 0;
@ -796,7 +795,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
x = xy / y; x = xy / y;
z = yz / 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) { if (zz < CMP_EPSILON) {
x = Math_SQRT12; x = Math_SQRT12;
y = Math_SQRT12; y = Math_SQRT12;
@ -808,22 +807,24 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
} }
} }
r_axis = Vector3(x, y, z); r_axis = Vector3(x, y, z);
r_angle = angle; r_angle = Math_PI;
return; return;
} }
// as we have reached here there are no singularities so we can handle normally // 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 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 (Math::abs(s) < CMP_EPSILON) {
if (angle < 0) { // Prevent divide by zero, should not happen if matrix is orthogonal and should be caught by singularity test above.
s = -s; s = 1;
} }
x = (rows[2][1] - rows[1][2]) / s; x = (rows[2][1] - rows[1][2]) / s;
y = (rows[0][2] - rows[2][0]) / s; y = (rows[0][2] - rows[2][0]) / s;
z = (rows[1][0] - rows[0][1]) / s; z = (rows[1][0] - rows[0][1]) / s;
r_axis = Vector3(x, y, z); 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) { void Basis::set_quaternion(const Quaternion &p_quaternion) {

57
tests/core/math/test_basis.h
View File

@ -47,7 +47,7 @@ enum RotOrder {
EulerZYX EulerZYX
}; };
Vector3 deg2rad(const Vector3 &p_rotation) { Vector3 deg_to_rad(const Vector3 &p_rotation) {
return p_rotation / 180.0 * Math_PI; return p_rotation / 180.0 * Math_PI;
} }
@ -155,7 +155,7 @@ void test_rotation(Vector3 deg_original_euler, RotOrder rot_order) {
// are correct. // are correct.
// Euler to rotation // 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); const Basis to_rotation = EulerToBasis(rot_order, original_euler);
// Euler from rotation // Euler from rotation
@ -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 } // namespace TestBasis
#endif // TEST_BASIS_H #endif // TEST_BASIS_H