cba90d6301
This is taken from the Godot repository, so formatting is similar. This updates the style rules as well. Also fix style in files to conform with this version.
323 lines
7.9 KiB
C++
323 lines
7.9 KiB
C++
#include "Quat.hpp"
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#include "Basis.hpp"
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#include "Defs.hpp"
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#include "Vector3.hpp"
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#include <cmath>
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namespace godot {
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const Quat Quat::IDENTITY = Quat();
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// set_euler_xyz expects a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses XYZ convention (Z is the first rotation).
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void Quat::set_euler_xyz(const Vector3 &p_euler) {
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real_t half_a1 = p_euler.x * 0.5;
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real_t half_a2 = p_euler.y * 0.5;
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real_t half_a3 = p_euler.z * 0.5;
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// R = X(a1).Y(a2).Z(a3) convention for Euler angles.
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// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-2)
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// a3 is the angle of the first rotation, following the notation in this reference.
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real_t cos_a1 = ::cos(half_a1);
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real_t sin_a1 = ::sin(half_a1);
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real_t cos_a2 = ::cos(half_a2);
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real_t sin_a2 = ::sin(half_a2);
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real_t cos_a3 = ::cos(half_a3);
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real_t sin_a3 = ::sin(half_a3);
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set(sin_a1 * cos_a2 * cos_a3 + sin_a2 * sin_a3 * cos_a1,
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-sin_a1 * sin_a3 * cos_a2 + sin_a2 * cos_a1 * cos_a3,
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sin_a1 * sin_a2 * cos_a3 + sin_a3 * cos_a1 * cos_a2,
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-sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
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}
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// get_euler_xyz returns a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses XYZ convention (Z is the first rotation).
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Vector3 Quat::get_euler_xyz() const {
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Basis m(*this);
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return m.get_euler_xyz();
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}
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// set_euler_yxz expects a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses YXZ convention (Z is the first rotation).
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void Quat::set_euler_yxz(const Vector3 &p_euler) {
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real_t half_a1 = p_euler.y * 0.5;
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real_t half_a2 = p_euler.x * 0.5;
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real_t half_a3 = p_euler.z * 0.5;
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// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
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// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
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// a3 is the angle of the first rotation, following the notation in this reference.
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real_t cos_a1 = ::cos(half_a1);
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real_t sin_a1 = ::sin(half_a1);
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real_t cos_a2 = ::cos(half_a2);
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real_t sin_a2 = ::sin(half_a2);
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real_t cos_a3 = ::cos(half_a3);
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real_t sin_a3 = ::sin(half_a3);
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set(sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
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sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
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-sin_a1 * sin_a2 * cos_a3 + cos_a1 * sin_a2 * sin_a3,
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sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
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}
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// get_euler_yxz returns a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses YXZ convention (Z is the first rotation).
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Vector3 Quat::get_euler_yxz() const {
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Basis m(*this);
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return m.get_euler_yxz();
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}
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real_t Quat::length() const {
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return ::sqrt(length_squared());
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}
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void Quat::normalize() {
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*this /= length();
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}
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Quat Quat::normalized() const {
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return *this / length();
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}
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bool Quat::is_normalized() const {
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return std::abs(length_squared() - 1.0) < 0.00001;
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}
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Quat Quat::inverse() const {
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return Quat(-x, -y, -z, w);
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}
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Quat Quat::slerp(const Quat &q, const real_t &t) const {
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Quat to1;
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real_t omega, cosom, sinom, scale0, scale1;
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// calc cosine
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cosom = dot(q);
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// adjust signs (if necessary)
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if (cosom < 0.0) {
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cosom = -cosom;
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to1.x = -q.x;
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to1.y = -q.y;
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to1.z = -q.z;
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to1.w = -q.w;
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} else {
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to1.x = q.x;
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to1.y = q.y;
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to1.z = q.z;
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to1.w = q.w;
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}
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// calculate coefficients
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if ((1.0 - cosom) > CMP_EPSILON) {
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// standard case (slerp)
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omega = ::acos(cosom);
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sinom = ::sin(omega);
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scale0 = ::sin((1.0 - t) * omega) / sinom;
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scale1 = ::sin(t * omega) / sinom;
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} else {
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// "from" and "to" quaternions are very close
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// ... so we can do a linear interpolation
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scale0 = 1.0 - t;
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scale1 = t;
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}
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// calculate final values
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return Quat(
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scale0 * x + scale1 * to1.x,
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scale0 * y + scale1 * to1.y,
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scale0 * z + scale1 * to1.z,
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scale0 * w + scale1 * to1.w);
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}
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Quat Quat::slerpni(const Quat &q, const real_t &t) const {
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const Quat &from = *this;
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real_t dot = from.dot(q);
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if (::fabs(dot) > 0.9999)
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return from;
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real_t theta = ::acos(dot),
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sinT = 1.0 / ::sin(theta),
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newFactor = ::sin(t * theta) * sinT,
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invFactor = ::sin((1.0 - t) * theta) * sinT;
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return Quat(invFactor * from.x + newFactor * q.x,
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invFactor * from.y + newFactor * q.y,
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invFactor * from.z + newFactor * q.z,
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invFactor * from.w + newFactor * q.w);
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}
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Quat Quat::cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) const {
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//the only way to do slerp :|
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real_t t2 = (1.0 - t) * t * 2;
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Quat sp = this->slerp(q, t);
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Quat sq = prep.slerpni(postq, t);
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return sp.slerpni(sq, t2);
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}
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void Quat::get_axis_and_angle(Vector3 &r_axis, real_t &r_angle) const {
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r_angle = 2 * ::acos(w);
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r_axis.x = x / ::sqrt(1 - w * w);
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r_axis.y = y / ::sqrt(1 - w * w);
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r_axis.z = z / ::sqrt(1 - w * w);
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}
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void Quat::set_axis_angle(const Vector3 &axis, const float angle) {
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ERR_FAIL_COND(!axis.is_normalized());
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real_t d = axis.length();
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if (d == 0)
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set(0, 0, 0, 0);
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else {
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real_t sin_angle = ::sin(angle * 0.5);
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real_t cos_angle = ::cos(angle * 0.5);
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real_t s = sin_angle / d;
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set(axis.x * s, axis.y * s, axis.z * s,
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cos_angle);
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}
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}
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Quat Quat::operator*(const Vector3 &v) const {
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return Quat(w * v.x + y * v.z - z * v.y,
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w * v.y + z * v.x - x * v.z,
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w * v.z + x * v.y - y * v.x,
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-x * v.x - y * v.y - z * v.z);
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}
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Vector3 Quat::xform(const Vector3 &v) const {
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Quat q = *this * v;
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q *= this->inverse();
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return Vector3(q.x, q.y, q.z);
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}
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Quat::operator String() const {
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return String(); // @Todo
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}
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Quat::Quat(const Vector3 &axis, const real_t &angle) {
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real_t d = axis.length();
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if (d == 0)
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set(0, 0, 0, 0);
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else {
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real_t sin_angle = ::sin(angle * 0.5);
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real_t cos_angle = ::cos(angle * 0.5);
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real_t s = sin_angle / d;
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set(axis.x * s, axis.y * s, axis.z * s,
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cos_angle);
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}
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}
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Quat::Quat(const Vector3 &v0, const Vector3 &v1) // shortest arc
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{
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Vector3 c = v0.cross(v1);
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real_t d = v0.dot(v1);
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if (d < -1.0 + CMP_EPSILON) {
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x = 0;
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y = 1;
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z = 0;
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w = 0;
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} else {
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real_t s = ::sqrt((1.0 + d) * 2.0);
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real_t rs = 1.0 / s;
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x = c.x * rs;
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y = c.y * rs;
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z = c.z * rs;
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w = s * 0.5;
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}
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}
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real_t Quat::dot(const Quat &q) const {
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return x * q.x + y * q.y + z * q.z + w * q.w;
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}
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real_t Quat::length_squared() const {
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return dot(*this);
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}
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void Quat::operator+=(const Quat &q) {
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x += q.x;
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y += q.y;
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z += q.z;
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w += q.w;
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}
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void Quat::operator-=(const Quat &q) {
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x -= q.x;
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y -= q.y;
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z -= q.z;
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w -= q.w;
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}
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void Quat::operator*=(const Quat &q) {
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set(w * q.x + x * q.w + y * q.z - z * q.y,
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w * q.y + y * q.w + z * q.x - x * q.z,
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w * q.z + z * q.w + x * q.y - y * q.x,
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w * q.w - x * q.x - y * q.y - z * q.z);
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}
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void Quat::operator*=(const real_t &s) {
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x *= s;
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y *= s;
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z *= s;
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w *= s;
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}
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void Quat::operator/=(const real_t &s) {
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*this *= 1.0 / s;
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}
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Quat Quat::operator+(const Quat &q2) const {
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const Quat &q1 = *this;
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return Quat(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
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}
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Quat Quat::operator-(const Quat &q2) const {
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const Quat &q1 = *this;
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return Quat(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
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}
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Quat Quat::operator*(const Quat &q2) const {
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Quat q1 = *this;
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q1 *= q2;
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return q1;
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}
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Quat Quat::operator-() const {
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const Quat &q2 = *this;
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return Quat(-q2.x, -q2.y, -q2.z, -q2.w);
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}
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Quat Quat::operator*(const real_t &s) const {
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return Quat(x * s, y * s, z * s, w * s);
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}
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Quat Quat::operator/(const real_t &s) const {
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return *this * (1.0 / s);
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}
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bool Quat::operator==(const Quat &p_quat) const {
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return x == p_quat.x && y == p_quat.y && z == p_quat.z && w == p_quat.w;
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}
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bool Quat::operator!=(const Quat &p_quat) const {
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return x != p_quat.x || y != p_quat.y || z != p_quat.z || w != p_quat.w;
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}
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} // namespace godot
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