/*!
Finds the \a minimum_t and \a maximum_t values where \a ray intersects
this sphere. Returns true if intersections were found; or false if there
is no intersection.
If \a minimum_t and \a maximum_t are set to the same value, then \a ray
touches the surface of the sphere at a single point. If the t values are
negative, then the intersection occurs before the ray's origin point
in the reverse direction of the ray.
The \a minimum_t and \a maximum_t values can be passed to QRay3D::point()
to determine the actual intersection points, as shown in the following
example:
\code
qreal minimum_t, maximum_t;
if (sphere.intersection(ray, &minimum_t, &maximum_t)) {
qDebug() << "intersections at"
<< ray.point(minimum_t) << "and"
<< ray.point(maximum_t);
}
\endcode
\sa intersects(), QRay3D::point()
*/
bool QSphere3D::intersection(const QRay3D &ray, qreal *minimum_t, qreal *maximum_t) const
{
QVector3D centerToOrigin = ray.origin() - m_center;
qreal term1 = ray.direction().lengthSquared();
qreal term2 = 2.0f * QVector3D::dotProduct(centerToOrigin, ray.direction());
qreal term3 = centerToOrigin.lengthSquared() - m_radius * m_radius;
qreal det = term2 * term2 - (4.0f * term1 * term3);
if (term1 == 0.0f || det < 0.0f) {
*minimum_t = qSNaN();
*maximum_t = qSNaN();
return false;
} else if (det == 0.0f) {
*minimum_t = *maximum_t = -term2 / (2.0f * term1);
} else {
qreal sqrtDet = qSqrt(det);
qreal t1 = (-term2 - sqrtDet) / (2.0f * term1);
qreal t2 = (-term2 + sqrtDet) / (2.0f * term1);
if (t1 < t2) {
*minimum_t = t1;
*maximum_t = t2;
} else {
*minimum_t = t2;
*maximum_t = t1;
}
}
return true;
}
cv::Vec3f AreaLight::getIntensity(QVector3D direction) const
{
float c = QVector3D::dotProduct(direction.normalized(), normal.normalized()) / direction.lengthSquared() * normal.length();
assert(!isnan(c));
if(c < 0) c = 0;
return c * intensity;
}
/*!
\since 5.5
Returns the shortest arc quaternion to rotate from the direction described by the vector \a from
to the direction described by the vector \a to.
\sa fromDirection()
*/
QQuaternion QQuaternion::rotationTo(const QVector3D &from, const QVector3D &to)
{
// Based on Stan Melax's article in Game Programming Gems
const QVector3D v0(from.normalized());
const QVector3D v1(to.normalized());
float d = QVector3D::dotProduct(v0, v1) + 1.0f;
// if dest vector is close to the inverse of source vector, ANY axis of rotation is valid
if (qFuzzyIsNull(d)) {
QVector3D axis = QVector3D::crossProduct(QVector3D(1.0f, 0.0f, 0.0f), v0);
if (qFuzzyIsNull(axis.lengthSquared()))
axis = QVector3D::crossProduct(QVector3D(0.0f, 1.0f, 0.0f), v0);
axis.normalize();
// same as QQuaternion::fromAxisAndAngle(axis, 180.0f)
return QQuaternion(0.0f, axis.x(), axis.y(), axis.z());
}
d = std::sqrt(2.0f * d);
const QVector3D axis(QVector3D::crossProduct(v0, v1) / d);
return QQuaternion(d * 0.5f, axis).normalized();
}
/**
* @brief gives Quaternion to transform between 2 vectors
* @param v1 first vector
* @param v2 second vector
* @return Quaternion
*
* based on http://stackoverflow.com/a/11741520
*/
Quaternion Quaternion::between(const QVector3D &v1, const QVector3D &v2)
{
float kCosTheta = QVector3D::dotProduct(v1, v2);
float k = sqrt(v1.lengthSquared() * v2.lengthSquared());
if (kCosTheta / k == -1)
{
// 180 degree rotation around any orthogonal vector
QVector3D other = (abs(QVector3D::dotProduct(v1, QVector3D(1, 0, 0))) < 1.0) ? QVector3D(1, 0, 0) : QVector3D(0, 1, 0);
return Quaternion(QQuaternion::fromAxisAndAngle((QVector3D::crossProduct(v1, other).normalized()), 180));
}
return Quaternion(kCosTheta + k, QVector3D::crossProduct(v1, v2)).normalized();
}
void Material::fresnelDielectric(const QVector3D &d, const QVector3D &normal, float ni, float nt, QVector<QPair<float, QVector3D> > &rays)
{
QVector3D n = normal;
float ndd = QVector3D::dotProduct(n, d);
if (ndd > -Config::Epsilon && ndd < Config::Epsilon) {
return ;
}
if (ndd > 0) {
n *= -1;
ndd *= -1;
}
QVector3D r = d - 2.0f * ndd * n;
r.normalize();
QVector3D z = (d - ndd * n) * ni / nt;
float z2 = z.lengthSquared();
if (z2 >= 1.0f) {
rays.append(QPair<float, QVector3D>(1.0f, r));
return ;
}
QVector3D t = z - qSqrt(1.0f - z2) * n;
t.normalize();
float ndt = QVector3D::dotProduct(n, t);
float rPar = (nt * ndd - ni * ndt) / (nt * ndd + ni * ndt);
float rPerp = (ni * ndd - nt * ndt) / (ni * ndd + nt * ndt);
float fr = 0.5f * (rPar * rPar + rPerp * rPerp);
rays.append(QPair<float, QVector3D>(fr, r));
rays.append(QPair<float, QVector3D>(1.0f - fr, t));
}
static double squaredDistanceToAABB(const QVector3D& point,
const AxisAlignedBox& box) {
const QVector3D center = (box.Max() + box.Min()) / 2;
const QVector3D half_sz = (box.Max() - box.Min()) / 2;
const QVector3D vec(max(0.0, fabs(center.x() - point.x()) - half_sz.x()),
max(0.0, fabs(center.y() - point.y()) - half_sz.y()),
max(0.0, fabs(center.z() - point.z()) - half_sz.z()));
return vec.lengthSquared();
}
void SpringMesh::integrate(int algorithm /*= 0*/)
{
// Apply internal force and integrate
for (auto vertex : mesh->vertSet)
{
if (fixedPoint.find(vertex->index) != fixedPoint.end())
{
continue;
}
//cout << vertex->in_force.length() << endl;
vertex->vel += vertex->in_force * timestep;
vertex->pos += 0.5 * (vertex->pre_vel + vertex->vel) * timestep;
/*cout << (vertex->in_force * timestep).length() << endl;
vector<QVector3D> K0, K1, K2, K3, K4;
K0.push_back(vertex->pre_pos); K0.push_back(vertex->pre_vel);
K1.push_back(vertex->in_force * timestep); K1.push_back(vertex->in_force);
K1 = stateMul(K1, timestep);
//K2 = statePlus(K0, K1, 1, 0.5);
K2 = stateMul(stateDeriv(K0, statePlus(K0, K1, 1, 0.5)), timestep);
K3 = stateMul(stateDeriv(K0, statePlus(K0, K2, 1, 0.5)), timestep);
K4 = stateMul(stateDeriv(K0, statePlus(K0, K3)), timestep);
K0 = statePlus(K0,
statePlus(statePlus(K1, K2, 1, 2), statePlus(K3, K4, 2, 1)) ,
1, 1.0 / 6.0);
vertex->pos = K0.front();
vertex->vel = K0.back();*/
if ((vertex->pos - sphere_pos).length() < sphere_r)
//&& (vertex->pre_pos - sphere_pos).length() > sphere_r)
{
QVector3D v10 = (vertex->pre_pos - vertex->pos).normalized();
QVector3D cv0 = sphere_pos - vertex->pre_pos;
QVector3D h = cv0 - (cv0 * v10) * v10;
QVector3D hitp = sphere_pos + h
+ sqrt(sphere_r * sphere_r - h.lengthSquared()) * v10;
QVector3D n = (hitp - sphere_pos).normalized();
/*vertex->pos = hitp + n * 0.01;// +vertex->pos - ((vertex->pos - hitp) * n) * n;*/
vertex->vel = vertex->pre_vel - 2 * (vertex->pre_vel * n) * n;
vertex->pos = vertex->pre_pos;
//vertex->vel = 0.5 * (vertex->vel + vertex->pre_vel) * friction;
}
if (vertex->pos.y() < plane_height)
{
vertex->vel.setY(-vertex->vel.y());
vertex->vel *= friction;
vertex->pos.setY(plane_height * 2 - vertex->pos.y());
}
}
}
float NavigationMath::distanceToClosestPoint(
const QVector3D & eye
, const QVector3D & center
, const QVector3D & point)
{
const QVector3D ray(center - eye);
const QVector3D b(point - eye);
const float m = ray.lengthSquared(); // magnitude of ray
const float theta = QVector3D::dotProduct(b, ray);
if(m == 0.0)
return 0.0;
return theta / m; // distance from camera to closest point c;
}
void View::mouseMoveEvent(QMouseEvent *event)
{
if(m_isTouchEvent)
return;
const qreal c_mouseFactor = 0.2;
QPoint newPos = event->pos();
if((event->buttons() & Qt::LeftButton) && (event->modifiers() & Qt::ControlModifier))
{
QPoint center(width()/2, height()/2);
QLineF oldLine( center, m_mousePos);
QLineF newLine( center, newPos);
qreal angle = oldLine.angleTo(newLine);
if(angle > 180.0)
angle = angle - 360.0;
setRoll( roll() + angle*c_mouseFactor*2 );
}
else if(event->buttons() & Qt::LeftButton)
{
QVector3D diffRotate = QVector3D(newPos.y() - m_mousePos.y(),
0,
newPos.x() - m_mousePos.x()) * c_mouseFactor;
setRotate( rotate() + diffRotate );
const qreal c_treshold = 15.0;
const qreal c_speedFactor = 0.5;
if(diffRotate.lengthSquared() > c_treshold)
camera()->setAnimatedRotation( -diffRotate*c_speedFactor );
else
camera()->setAnimatedRotation( QVector3D() );
}
else if((event->buttons() & Qt::MidButton) && isFreeMode())
{
QVector3D diffShift = c_mouseFactor* QVector3D(newPos.x() - m_mousePos.x(),
newPos.y() - m_mousePos.y(),
0 );//newPos.x() - m_mousePos.x()) * c_mouseFactor;
shift(diffShift);
}
m_mousePos = newPos;
}
QT_BEGIN_NAMESPACE
/*!
\class QSphere3D
\brief The QSphere3D class represents a mathematical sphere in 3D space.
\since 4.8
\ingroup qt3d
\ingroup qt3d::math
QSphere3D can be used to represent the bounding regions of objects
in a 3D scene so that they can be easily culled if they are out of view.
It can also be used to assist with collision testing.
\sa QBox3D
*/
/*!
\fn QSphere3D::QSphere3D()
Constructs a default sphere with a center() of (0, 0, 0)
and radius() of 1.
*/
/*!
\fn QSphere3D::QSphere3D(const QVector3D ¢er, qreal radius)
Constructs a sphere with the specified \a center and \a radius.
*/
/*!
\fn QVector3D QSphere3D::center() const
Returns the center of this sphere.
\sa setCenter(), radius()
*/
/*!
\fn void QSphere3D::setCenter(const QVector3D ¢er)
Sets the \a center of this sphere.
\sa center(), setRadius()
*/
/*!
\fn qreal QSphere3D::radius() const
Returns the radius of this sphere.
\sa setRadius(), center()
*/
/*!
\fn void QSphere3D::setRadius(qreal radius)
Sets the \a radius of this sphere.
\sa radius(), setCenter()
*/
/*!
\fn bool QSphere3D::contains(const QVector3D &point) const
Returns true if \a point is contained within the bounds of
this sphere; false otherwise.
*/
/*!
Returns true if this sphere intersects \a ray; false otherwise.
\sa intersection()
*/
bool QSphere3D::intersects(const QRay3D &ray) const
{
QVector3D centerToOrigin = ray.origin() - m_center;
qreal term1 = ray.direction().lengthSquared();
qreal term2 = 2.0f * QVector3D::dotProduct(centerToOrigin, ray.direction());
qreal term3 = centerToOrigin.lengthSquared() - m_radius * m_radius;
qreal det = term2 * term2 - (4.0f * term1 * term3);
return term1 != 0.0f && det >= 0.0f;
}
QVector3D Connections::proj(QVector3D a, QVector3D b, QVector3D p) {
QVector3D ba = b-a;
QVector3D pa = p-a;
return a + ba*QVector3D::dotProduct(ba,pa) / ba.lengthSquared();
}