diff options
Diffstat (limited to 'core/math/basis.cpp')
| -rw-r--r-- | core/math/basis.cpp | 61 |
1 files changed, 33 insertions, 28 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp index 0eb6320ac6..9b8188eed8 100644 --- a/core/math/basis.cpp +++ b/core/math/basis.cpp @@ -31,7 +31,7 @@ #include "basis.h" #include "core/math/math_funcs.h" -#include "core/string/print_string.h" +#include "core/string/ustring.h" #define cofac(row1, col1, row2, col2) \ (rows[row1][col1] * rows[row2][col2] - rows[row1][col2] * rows[row2][col1]) @@ -142,8 +142,8 @@ bool Basis::is_symmetric() const { #endif Basis Basis::diagonalize() { -//NOTE: only implemented for symmetric matrices -//with the Jacobi iterative method +// NOTE: only implemented for symmetric matrices +// with the Jacobi iterative method #ifdef MATH_CHECKS ERR_FAIL_COND_V(!is_symmetric(), Basis()); #endif @@ -691,6 +691,10 @@ bool Basis::is_equal_approx(const Basis &p_basis) const { return rows[0].is_equal_approx(p_basis.rows[0]) && rows[1].is_equal_approx(p_basis.rows[1]) && rows[2].is_equal_approx(p_basis.rows[2]); } +bool Basis::is_finite() const { + return rows[0].is_finite() && rows[1].is_finite() && rows[2].is_finite(); +} + bool Basis::operator==(const Basis &p_matrix) const { for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { @@ -754,29 +758,28 @@ 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; @@ -786,7 +789,7 @@ 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; @@ -796,7 +799,7 @@ 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; @@ -808,22 +811,24 @@ 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) { |