From a32b26dfa26f2a039bf9c84b90d10666bcf785c9 Mon Sep 17 00:00:00 2001 From: Juan Linietsky Date: Mon, 25 Feb 2019 21:46:24 -0300 Subject: Several fixes to make GLES2 on HTML5 work much better. Changed math class error reporting to be a bit less paranoid. --- core/math/basis.cpp | 74 +++++++++++++++++++++++++++++++------------------- core/math/math_defs.h | 9 ++++++ core/math/math_funcs.h | 16 +++++++++-- core/math/quat.cpp | 2 +- core/math/vector2.cpp | 2 +- core/math/vector3.h | 2 +- 6 files changed, 72 insertions(+), 33 deletions(-) (limited to 'core/math') diff --git a/core/math/basis.cpp b/core/math/basis.cpp index 7f60b7962c..c293e753a6 100644 --- a/core/math/basis.cpp +++ b/core/math/basis.cpp @@ -76,15 +76,23 @@ void Basis::invert() { } void Basis::orthonormalize() { + /* this check is undesired, the matrix could be wrong but we still may want to generate a valid one + * for practical purposes #ifdef MATH_CHECKS ERR_FAIL_COND(determinant() == 0); #endif +*/ // Gram-Schmidt Process Vector3 x = get_axis(0); Vector3 y = get_axis(1); Vector3 z = get_axis(2); +#ifdef MATH_CHECKS + ERR_FAIL_COND(x.length_squared() == 0); + ERR_FAIL_COND(y.length_squared() == 0); + ERR_FAIL_COND(z.length_squared() == 0); +#endif x.normalize(); y = (y - x * (x.dot(y))); y.normalize(); @@ -118,16 +126,16 @@ bool Basis::is_diagonal() const { } bool Basis::is_rotation() const { - return Math::is_equal_approx(determinant(), 1) && is_orthogonal(); + return Math::is_equal_approx(determinant(), 1, UNIT_EPSILON) && is_orthogonal(); } bool Basis::is_symmetric() const { - if (!Math::is_equal_approx(elements[0][1], elements[1][0])) + if (!Math::is_equal_approx_ratio(elements[0][1], elements[1][0], UNIT_EPSILON)) return false; - if (!Math::is_equal_approx(elements[0][2], elements[2][0])) + if (!Math::is_equal_approx_ratio(elements[0][2], elements[2][0], UNIT_EPSILON)) return false; - if (!Math::is_equal_approx(elements[1][2], elements[2][1])) + if (!Math::is_equal_approx_ratio(elements[1][2], elements[2][1], UNIT_EPSILON)) return false; return true; @@ -488,6 +496,11 @@ void Basis::set_euler_xyz(const Vector3 &p_euler) { // as the x, y, and z components of a Vector3 respectively. Vector3 Basis::get_euler_yxz() const { + /* checking this is a bad idea, because obtaining from scaled transform is a valid use case +#ifdef MATH_CHECKS + ERR_FAIL_COND(!is_rotation()); +#endif +*/ // Euler angles in YXZ convention. // See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix // @@ -496,9 +509,7 @@ Vector3 Basis::get_euler_yxz() const { // cy*sx*sz-cz*sy cy*cz*sx+sy*sz cy*cx Vector3 euler; -#ifdef MATH_CHECKS - ERR_FAIL_COND_V(!is_rotation(), euler); -#endif + real_t m12 = elements[1][2]; if (m12 < 1) { @@ -556,7 +567,7 @@ 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::is_equal_approx(a.elements[i][j], b.elements[i][j])) + if (!Math::is_equal_approx_ratio(a.elements[i][j], b.elements[i][j], UNIT_EPSILON)) return false; } } @@ -599,10 +610,14 @@ Basis::operator String() const { } Quat Basis::get_quat() const { -#ifdef MATH_CHECKS - ERR_FAIL_COND_V(!is_rotation(), Quat()); -#endif - real_t trace = elements[0][0] + elements[1][1] + elements[2][2]; + + /* Allow getting a quaternion from an unnormalized transform */ + Basis m = *this; + m.elements[0].normalize(); + m.elements[1].normalize(); + m.elements[2].normalize(); + + real_t trace = m.elements[0][0] + m.elements[1][1] + m.elements[2][2]; real_t temp[4]; if (trace > 0.0) { @@ -610,23 +625,23 @@ Quat Basis::get_quat() const { temp[3] = (s * 0.5); s = 0.5 / s; - temp[0] = ((elements[2][1] - elements[1][2]) * s); - temp[1] = ((elements[0][2] - elements[2][0]) * s); - temp[2] = ((elements[1][0] - elements[0][1]) * s); + temp[0] = ((m.elements[2][1] - m.elements[1][2]) * s); + temp[1] = ((m.elements[0][2] - m.elements[2][0]) * s); + temp[2] = ((m.elements[1][0] - m.elements[0][1]) * s); } else { - int i = elements[0][0] < elements[1][1] ? - (elements[1][1] < elements[2][2] ? 2 : 1) : - (elements[0][0] < elements[2][2] ? 2 : 0); + int i = m.elements[0][0] < m.elements[1][1] ? + (m.elements[1][1] < m.elements[2][2] ? 2 : 1) : + (m.elements[0][0] < m.elements[2][2] ? 2 : 0); int j = (i + 1) % 3; int k = (i + 2) % 3; - real_t s = Math::sqrt(elements[i][i] - elements[j][j] - elements[k][k] + 1.0); + real_t s = Math::sqrt(m.elements[i][i] - m.elements[j][j] - m.elements[k][k] + 1.0); temp[i] = s * 0.5; s = 0.5 / s; - temp[3] = (elements[k][j] - elements[j][k]) * s; - temp[j] = (elements[j][i] + elements[i][j]) * s; - temp[k] = (elements[k][i] + elements[i][k]) * s; + temp[3] = (m.elements[k][j] - m.elements[j][k]) * s; + temp[j] = (m.elements[j][i] + m.elements[i][j]) * s; + temp[k] = (m.elements[k][i] + m.elements[i][k]) * s; } return Quat(temp[0], temp[1], temp[2], temp[3]); @@ -696,9 +711,11 @@ void Basis::set_orthogonal_index(int p_index) { } void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const { + /* checking this is a bad idea, because obtaining from scaled transform is a valid use case #ifdef MATH_CHECKS ERR_FAIL_COND(!is_rotation()); #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 @@ -835,14 +852,15 @@ void Basis::set_diagonal(const Vector3 p_diag) { } Basis Basis::slerp(const Basis &target, const real_t &t) const { -// TODO: implement this directly without using quaternions to make it more efficient -#ifdef MATH_CHECKS - ERR_FAIL_COND_V(!is_rotation(), Basis()); - ERR_FAIL_COND_V(!target.is_rotation(), Basis()); -#endif + //consider scale Quat from(*this); Quat to(target); - return Basis(from.slerp(to, t)); + Basis b(from.slerp(to, t)); + b.elements[0] *= Math::lerp(elements[0].length(), target.elements[0].length(), t); + b.elements[1] *= Math::lerp(elements[1].length(), target.elements[1].length(), t); + b.elements[2] *= Math::lerp(elements[2].length(), target.elements[2].length(), t); + + return b; } diff --git a/core/math/math_defs.h b/core/math/math_defs.h index 48533ba659..c54d3cc96f 100644 --- a/core/math/math_defs.h +++ b/core/math/math_defs.h @@ -33,6 +33,7 @@ #define CMP_EPSILON 0.00001 #define CMP_EPSILON2 (CMP_EPSILON * CMP_EPSILON) + #define CMP_NORMALIZE_TOLERANCE 0.000001 #define CMP_POINT_IN_PLANE_EPSILON 0.00001 @@ -49,6 +50,14 @@ #define MATH_CHECKS #endif +//this epsilon is for values related to a unit size (scalar or vector len) +#ifdef PRECISE_MATH_CHECKS +#define UNIT_EPSILON 0.00001 +#else +//tolerate some more floating point error normally +#define UNIT_EPSILON 0.001 +#endif + #define USEC_TO_SEC(m_usec) ((m_usec) / 1000000.0) enum ClockDirection { diff --git a/core/math/math_funcs.h b/core/math/math_funcs.h index f2234d5dd6..17112d8940 100644 --- a/core/math/math_funcs.h +++ b/core/math/math_funcs.h @@ -249,13 +249,25 @@ 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 is_equal_approx(real_t a, real_t b) { + static _ALWAYS_INLINE_ bool is_equal_approx_ratio(real_t a, real_t b, real_t epsilon = CMP_EPSILON) { + // this is an approximate way to check that numbers are close, as a ratio of their average size + // helps compare approximate numbers that may be very big or very small + real_t diff = abs(a - b); + if (diff == 0.0) { + return true; + } + real_t avg_size = (abs(a) + abs(b)) / 2.0; + diff /= avg_size; + return diff < epsilon; + } + + static _ALWAYS_INLINE_ bool is_equal_approx(real_t a, real_t b, real_t epsilon = CMP_EPSILON) { // 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. // See https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ for details. - return abs(a - b) < CMP_EPSILON; + return abs(a - b) < epsilon; } static _ALWAYS_INLINE_ float absf(float g) { diff --git a/core/math/quat.cpp b/core/math/quat.cpp index 6833d5de55..1a67be7384 100644 --- a/core/math/quat.cpp +++ b/core/math/quat.cpp @@ -135,7 +135,7 @@ Quat Quat::normalized() const { } bool Quat::is_normalized() const { - return Math::is_equal_approx(length_squared(), 1.0); + return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); //use less epsilon } Quat Quat::inverse() const { diff --git a/core/math/vector2.cpp b/core/math/vector2.cpp index e580057950..5c1ea5943d 100644 --- a/core/math/vector2.cpp +++ b/core/math/vector2.cpp @@ -65,7 +65,7 @@ Vector2 Vector2::normalized() const { bool Vector2::is_normalized() const { // use length_squared() instead of length() to avoid sqrt(), makes it more stringent. - return Math::is_equal_approx(length_squared(), 1.0); + return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); } real_t Vector2::distance_to(const Vector2 &p_vector2) const { diff --git a/core/math/vector3.h b/core/math/vector3.h index 8d6e093c4c..b11838d16e 100644 --- a/core/math/vector3.h +++ b/core/math/vector3.h @@ -414,7 +414,7 @@ Vector3 Vector3::normalized() const { bool Vector3::is_normalized() const { // use length_squared() instead of length() to avoid sqrt(), makes it more stringent. - return Math::is_equal_approx(length_squared(), 1.0); + return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); } Vector3 Vector3::inverse() const { -- cgit v1.2.3