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Update Basis/Transform3D/Quaternion to match the engine

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This commit is contained in:
Aaron Franke
2022-09-19 18:15:04 -05:00
parent 8670305589
commit e83d472c00
7 changed files with 859 additions and 776 deletions
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889
src/variant/basis.cpp
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204
src/variant/quaternion.cpp
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@@ -35,13 +35,18 @@
namespace godot {
real_t Quaternion::angle_to(const Quaternion &p_to) const {
real_t d = dot(p_to);
return Math::acos(CLAMP(d * d * 2 - 1, -1, 1));
}
// get_euler_xyz returns a vector containing the Euler angles in the format
// (ax,ay,az), where ax is the angle of rotation around x axis,
// and similar for other axes.
// This implementation uses XYZ convention (Z is the first rotation).
Vector3 Quaternion::get_euler_xyz() const {
Basis m(*this);
return m.get_euler_xyz();
return m.get_euler(Basis::EULER_ORDER_XYZ);
}
// get_euler_yxz returns a vector containing the Euler angles in the format
@@ -50,17 +55,20 @@ Vector3 Quaternion::get_euler_xyz() const {
// This implementation uses YXZ convention (Z is the first rotation).
Vector3 Quaternion::get_euler_yxz() const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_normalized(), Vector3(0, 0, 0));
ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
#endif
Basis m(*this);
return m.get_euler_yxz();
return m.get_euler(Basis::EULER_ORDER_YXZ);
}
void Quaternion::operator*=(const Quaternion &p_q) {
x = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
y = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
z = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
real_t xx = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
real_t yy = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
real_t zz = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
x = xx;
y = yy;
z = zz;
}
Quaternion Quaternion::operator*(const Quaternion &p_q) const {
@@ -69,8 +77,8 @@ Quaternion Quaternion::operator*(const Quaternion &p_q) const {
return r;
}
bool Quaternion::is_equal_approx(const Quaternion &p_quat) const {
return Math::is_equal_approx(x, p_quat.x) && Math::is_equal_approx(y, p_quat.y) && Math::is_equal_approx(z, p_quat.z) && Math::is_equal_approx(w, p_quat.w);
bool Quaternion::is_equal_approx(const Quaternion &p_quaternion) const {
return Math::is_equal_approx(x, p_quaternion.x) && Math::is_equal_approx(y, p_quaternion.y) && Math::is_equal_approx(z, p_quaternion.z) && Math::is_equal_approx(w, p_quaternion.w);
}
real_t Quaternion::length() const {
@@ -91,15 +99,32 @@ bool Quaternion::is_normalized() const {
Quaternion Quaternion::inverse() const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_normalized(), Quaternion());
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The quaternion must be normalized.");
#endif
return Quaternion(-x, -y, -z, w);
}
Quaternion Quaternion::log() const {
Quaternion src = *this;
Vector3 src_v = src.get_axis() * src.get_angle();
return Quaternion(src_v.x, src_v.y, src_v.z, 0);
}
Quaternion Quaternion::exp() const {
Quaternion src = *this;
Vector3 src_v = Vector3(src.x, src.y, src.z);
real_t theta = src_v.length();
src_v = src_v.normalized();
if (theta < CMP_EPSILON || !src_v.is_normalized()) {
return Quaternion(0, 0, 0, 1);
}
return Quaternion(src_v, theta);
}
Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_normalized(), Quaternion());
ERR_FAIL_COND_V(!p_to.is_normalized(), Quaternion());
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
Quaternion to1;
real_t omega, cosom, sinom, scale0, scale1;
@@ -108,22 +133,16 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
cosom = dot(p_to);
// adjust signs (if necessary)
if (cosom < 0.0) {
if (cosom < 0.0f) {
cosom = -cosom;
to1.x = -p_to.x;
to1.y = -p_to.y;
to1.z = -p_to.z;
to1.w = -p_to.w;
to1 = -p_to;
} else {
to1.x = p_to.x;
to1.y = p_to.y;
to1.z = p_to.z;
to1.w = p_to.w;
to1 = p_to;
}
// calculate coefficients
if ((1.0 - cosom) > CMP_EPSILON) {
if ((1.0f - cosom) > (real_t)CMP_EPSILON) {
// standard case (slerp)
omega = Math::acos(cosom);
sinom = Math::sin(omega);
@@ -132,7 +151,7 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
} else {
// "from" and "to" quaternions are very close
// ... so we can do a linear interpolation
scale0 = 1.0 - p_weight;
scale0 = 1.0f - p_weight;
scale1 = p_weight;
}
// calculate final values
@@ -145,21 +164,21 @@ Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) con
Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_normalized(), Quaternion());
ERR_FAIL_COND_V(!p_to.is_normalized(), Quaternion());
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
const Quaternion &from = *this;
real_t dot = from.dot(p_to);
if (Math::abs(dot) > 0.9999) {
if (Math::absf(dot) > 0.9999f) {
return from;
}
real_t theta = Math::acos(dot),
sinT = 1.0 / Math::sin(theta),
sinT = 1.0f / Math::sin(theta),
newFactor = Math::sin(p_weight * theta) * sinT,
invFactor = Math::sin((1.0 - p_weight) * theta) * sinT;
invFactor = Math::sin((1.0f - p_weight) * theta) * sinT;
return Quaternion(invFactor * from.x + newFactor * p_to.x,
invFactor * from.y + newFactor * p_to.y,
@@ -167,25 +186,126 @@ Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) c
invFactor * from.w + newFactor * p_to.w);
}
Quaternion Quaternion::cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V(!is_normalized(), Quaternion());
ERR_FAIL_COND_V(!p_b.is_normalized(), Quaternion());
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
//the only way to do slerp :|
real_t t2 = (1.0 - p_weight) * p_weight * 2;
Quaternion sp = this->slerp(p_b, p_weight);
Quaternion sq = p_pre_a.slerpni(p_post_b, p_weight);
return sp.slerpni(sq, t2);
Quaternion from_q = *this;
Quaternion pre_q = p_pre_a;
Quaternion to_q = p_b;
Quaternion post_q = p_post_b;
// Align flip phases.
from_q = Basis(from_q).get_rotation_quaternion();
pre_q = Basis(pre_q).get_rotation_quaternion();
to_q = Basis(to_q).get_rotation_quaternion();
post_q = Basis(post_q).get_rotation_quaternion();
// Flip quaternions to shortest path if necessary.
bool flip1 = Math::sign(from_q.dot(pre_q));
pre_q = flip1 ? -pre_q : pre_q;
bool flip2 = Math::sign(from_q.dot(to_q));
to_q = flip2 ? -to_q : to_q;
bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : Math::sign(to_q.dot(post_q));
post_q = flip3 ? -post_q : post_q;
// Calc by Expmap in from_q space.
Quaternion ln_from = Quaternion(0, 0, 0, 0);
Quaternion ln_to = (from_q.inverse() * to_q).log();
Quaternion ln_pre = (from_q.inverse() * pre_q).log();
Quaternion ln_post = (from_q.inverse() * post_q).log();
Quaternion ln = Quaternion(0, 0, 0, 0);
ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
Quaternion q1 = from_q * ln.exp();
// Calc by Expmap in to_q space.
ln_from = (to_q.inverse() * from_q).log();
ln_to = Quaternion(0, 0, 0, 0);
ln_pre = (to_q.inverse() * pre_q).log();
ln_post = (to_q.inverse() * post_q).log();
ln = Quaternion(0, 0, 0, 0);
ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
Quaternion q2 = to_q * ln.exp();
// To cancel error made by Expmap ambiguity, do blends.
return q1.slerp(q2, p_weight);
}
Quaternion Quaternion::spherical_cubic_interpolate_in_time(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight,
const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
#endif
Quaternion from_q = *this;
Quaternion pre_q = p_pre_a;
Quaternion to_q = p_b;
Quaternion post_q = p_post_b;
// Align flip phases.
from_q = Basis(from_q).get_rotation_quaternion();
pre_q = Basis(pre_q).get_rotation_quaternion();
to_q = Basis(to_q).get_rotation_quaternion();
post_q = Basis(post_q).get_rotation_quaternion();
// Flip quaternions to shortest path if necessary.
bool flip1 = Math::sign(from_q.dot(pre_q));
pre_q = flip1 ? -pre_q : pre_q;
bool flip2 = Math::sign(from_q.dot(to_q));
to_q = flip2 ? -to_q : to_q;
bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : Math::sign(to_q.dot(post_q));
post_q = flip3 ? -post_q : post_q;
// Calc by Expmap in from_q space.
Quaternion ln_from = Quaternion(0, 0, 0, 0);
Quaternion ln_to = (from_q.inverse() * to_q).log();
Quaternion ln_pre = (from_q.inverse() * pre_q).log();
Quaternion ln_post = (from_q.inverse() * post_q).log();
Quaternion ln = Quaternion(0, 0, 0, 0);
ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
Quaternion q1 = from_q * ln.exp();
// Calc by Expmap in to_q space.
ln_from = (to_q.inverse() * from_q).log();
ln_to = Quaternion(0, 0, 0, 0);
ln_pre = (to_q.inverse() * pre_q).log();
ln_post = (to_q.inverse() * post_q).log();
ln = Quaternion(0, 0, 0, 0);
ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
Quaternion q2 = to_q * ln.exp();
// To cancel error made by Expmap ambiguity, do blends.
return q1.slerp(q2, p_weight);
}
Quaternion::operator String() const {
return String::num(x, 5) + ", " + String::num(y, 5) + ", " + String::num(z, 5) + ", " + String::num(w, 5);
return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
}
Vector3 Quaternion::get_axis() const {
if (Math::abs(w) > 1 - CMP_EPSILON) {
return Vector3(x, y, z);
}
real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
return Vector3(x * r, y * r, z * r);
}
real_t Quaternion::get_angle() const {
return 2 * Math::acos(w);
}
Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
#ifdef MATH_CHECKS
ERR_FAIL_COND(!p_axis.is_normalized());
ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
#endif
real_t d = p_axis.length();
if (d == 0) {
@@ -194,8 +314,8 @@ Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
z = 0;
w = 0;
} else {
real_t sin_angle = Math::sin(p_angle * 0.5);
real_t cos_angle = Math::cos(p_angle * 0.5);
real_t sin_angle = Math::sin(p_angle * 0.5f);
real_t cos_angle = Math::cos(p_angle * 0.5f);
real_t s = sin_angle / d;
x = p_axis.x * s;
y = p_axis.y * s;
@@ -209,9 +329,9 @@ Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
// and similar for other axes.
// This implementation uses YXZ convention (Z is the first rotation).
Quaternion::Quaternion(const Vector3 &p_euler) {
real_t half_a1 = p_euler.y * 0.5;
real_t half_a2 = p_euler.x * 0.5;
real_t half_a3 = p_euler.z * 0.5;
real_t half_a1 = p_euler.y * 0.5f;
real_t half_a2 = p_euler.x * 0.5f;
real_t half_a3 = p_euler.z * 0.5f;
// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)

87
src/variant/transform3d.cpp
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@@ -58,13 +58,13 @@ Transform3D Transform3D::inverse() const {
return ret;
}
void Transform3D::rotate(const Vector3 &p_axis, real_t p_phi) {
*this = rotated(p_axis, p_phi);
void Transform3D::rotate(const Vector3 &p_axis, real_t p_angle) {
*this = rotated(p_axis, p_angle);
}
Transform3D Transform3D::rotated(const Vector3 &p_axis, real_t p_phi) const {
Transform3D Transform3D::rotated(const Vector3 &p_axis, real_t p_angle) const {
// Equivalent to left multiplication
Basis p_basis(p_axis, p_phi);
Basis p_basis(p_axis, p_angle);
return Transform3D(p_basis * basis, p_basis.xform(origin));
}
@@ -74,51 +74,29 @@ Transform3D Transform3D::rotated_local(const Vector3 &p_axis, real_t p_angle) co
return Transform3D(basis * p_basis, origin);
}
void Transform3D::rotate_basis(const Vector3 &p_axis, real_t p_phi) {
basis.rotate(p_axis, p_phi);
void Transform3D::rotate_basis(const Vector3 &p_axis, real_t p_angle) {
basis.rotate(p_axis, p_angle);
}
Transform3D Transform3D::looking_at(const Vector3 &p_target, const Vector3 &p_up) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(origin.is_equal_approx(p_target), Transform3D(), "The transform's origin and target can't be equal.");
#endif
Transform3D t = *this;
t.set_look_at(origin, p_target, p_up);
t.basis = Basis::looking_at(p_target - origin, p_up);
return t;
}
void Transform3D::set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up) {
#ifdef MATH_CHECKS
ERR_FAIL_COND(p_eye == p_target);
ERR_FAIL_COND(p_up.length() == 0);
ERR_FAIL_COND_MSG(p_eye.is_equal_approx(p_target), "The eye and target vectors can't be equal.");
#endif
// RefCounted: MESA source code
Vector3 v_x, v_y, v_z;
/* Make rotation matrix */
/* Z vector */
v_z = p_eye - p_target;
v_z.normalize();
v_y = p_up;
v_x = v_y.cross(v_z);
#ifdef MATH_CHECKS
ERR_FAIL_COND(v_x.length() == 0);
#endif
/* Recompute Y = Z cross X */
v_y = v_z.cross(v_x);
v_x.normalize();
v_y.normalize();
basis.set(v_x, v_y, v_z);
basis = Basis::looking_at(p_target - p_eye, p_up);
origin = p_eye;
}
Transform3D Transform3D::interpolate_with(const Transform3D &p_transform, real_t p_c) const {
/* not sure if very "efficient" but good enough? */
Transform3D interp;
Vector3 src_scale = basis.get_scale();
Quaternion src_rot = basis.get_rotation_quaternion();
@@ -128,7 +106,6 @@ Transform3D Transform3D::interpolate_with(const Transform3D &p_transform, real_t
Quaternion dst_rot = p_transform.basis.get_rotation_quaternion();
Vector3 dst_loc = p_transform.origin;
Transform3D interp;
interp.basis.set_quaternion_scale(src_rot.slerp(dst_rot, p_c).normalized(), src_scale.lerp(dst_scale, p_c));
interp.origin = src_loc.lerp(dst_loc, p_c);
@@ -154,11 +131,11 @@ void Transform3D::scale_basis(const Vector3 &p_scale) {
basis.scale(p_scale);
}
void Transform3D::translate(real_t p_tx, real_t p_ty, real_t p_tz) {
translate(Vector3(p_tx, p_ty, p_tz));
void Transform3D::translate_local(real_t p_tx, real_t p_ty, real_t p_tz) {
translate_local(Vector3(p_tx, p_ty, p_tz));
}
void Transform3D::translate(const Vector3 &p_translation) {
void Transform3D::translate_local(const Vector3 &p_translation) {
for (int i = 0; i < 3; i++) {
origin[i] += basis[i].dot(p_translation);
}
@@ -184,6 +161,16 @@ Transform3D Transform3D::orthonormalized() const {
return _copy;
}
void Transform3D::orthogonalize() {
basis.orthogonalize();
}
Transform3D Transform3D::orthogonalized() const {
Transform3D _copy = *this;
_copy.orthogonalize();
return _copy;
}
bool Transform3D::is_equal_approx(const Transform3D &p_transform) const {
return basis.is_equal_approx(p_transform.basis) && origin.is_equal_approx(p_transform.origin);
}
@@ -207,8 +194,22 @@ Transform3D Transform3D::operator*(const Transform3D &p_transform) const {
return t;
}
void Transform3D::operator*=(const real_t p_val) {
origin *= p_val;
basis *= p_val;
}
Transform3D Transform3D::operator*(const real_t p_val) const {
Transform3D ret(*this);
ret *= p_val;
return ret;
}
Transform3D::operator String() const {
return basis.operator String() + " - " + origin.operator String();
return "[X: " + basis.get_column(0).operator String() +
", Y: " + basis.get_column(1).operator String() +
", Z: " + basis.get_column(2).operator String() +
", O: " + origin.operator String() + "]";
}
Transform3D::Transform3D(const Basis &p_basis, const Vector3 &p_origin) :
@@ -218,9 +219,9 @@ Transform3D::Transform3D(const Basis &p_basis, const Vector3 &p_origin) :
Transform3D::Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin) :
origin(p_origin) {
basis.set_axis(0, p_x);
basis.set_axis(1, p_y);
basis.set_axis(2, p_z);
basis.set_column(0, p_x);
basis.set_column(1, p_y);
basis.set_column(2, p_z);
}
Transform3D::Transform3D(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz) {