Qt3DCore::QEntity * createTransformedPlane(Qt3DCore::QEntity * parent, QVector3D p0, QVector3D p1, QVector3D p3) {

// vectors that span the plane

QVector3D v1 = p1-p0;

QVector3D v2 = p3-p0;

// create standard mesh in xz plane

Qt3DExtras::QPlaneMesh *planeMesh = new Qt3DExtras::QPlaneMesh();

float wx = v1.length();

float wz = v2.length();

planeMesh->setWidth(wx);

planeMesh->setHeight(wz);

// Plane entity

Qt3DCore::QEntity * planeEntity = new Qt3DCore::QEntity(parent);

// add the mesh to the entity

planeEntity->addComponent(planeMesh);

// transformation

// compute normal vector

QVector3D n1 = QVector3D::crossProduct(v1,v2);

// determine rotation matrix to align normal vector of plane with normal vector of generated plane (i.e. y-axis)

QVector3D n2(0,1,0);

QQuaternion rot = QQuaternion::rotationTo(n2, n1);

// now we transform the w1 vector (corresponding to the v1 vector) into the target plane

QVector3D w1(-1,0,0);

// Mind: PlaneMesh is generated in x-z plane, with bottom-left point at q0=(w/2, 0, -h/2)

// If numbered counter clock-wise, the next point is at q1=(-w/2, 0, -h/2) and the normalized vector w1 between q0 and q1

// is w1=(-1,0,0)

QVector3D w1Rotated = rot.rotatedVector(w1);

// now we need to compute the rotation matrix to align the w1 vector with the v1 vector

QQuaternion rot2 = QQuaternion::rotationTo(w1Rotated, v1);

// combine both rotations (mind the matrix multiplication order!)

QQuaternion planeRotation = rot2*rot;

// anchor point of generated mesh

QVector3D q0(wx/2, 0, -wz/2);

// Point q0 after rotation

QVector3D q0rot = planeRotation.rotatedVector(q0);

//translation to target anchor point

QVector3D transVec = p0 - q0rot;

// create transformation

Qt3DCore::QTransform *transform = new Qt3DCore::QTransform();

transform->setTranslation(transVec);

transform->setRotation(planeRotation);

// and set it as component

planeEntity->addComponent(transform);

return planeEntity;

}

Qt3DCore::QEntity * createTransformedPlane(Qt3DCore::QEntity * parent, QVector3D p0, QVector3D p1, QVector3D p3) {
// vectors that span the plane
QVector3D v1 = p1-p0;
QVector3D v2 = p3-p0;
// create standard mesh in xz plane
Qt3DExtras::QPlaneMesh *planeMesh = new Qt3DExtras::QPlaneMesh();
float wx = v1.length();
float wz = v2.length();
planeMesh->setWidth(wx);
planeMesh->setHeight(wz);
// Plane entity
Qt3DCore::QEntity * planeEntity = new Qt3DCore::QEntity(parent);
// add the mesh to the entity
planeEntity->addComponent(planeMesh);
// transformation
// compute normal vector
QVector3D n1 = QVector3D::crossProduct(v1,v2);
// determine rotation matrix to align normal vector of plane with normal vector of generated plane (i.e. y-axis)
QVector3D n2(0,1,0);
QQuaternion rot = QQuaternion::rotationTo(n2, n1);
// now we transform the w1 vector (corresponding to the v1 vector) into the target plane
QVector3D w1(-1,0,0);
// Mind: PlaneMesh is generated in x-z plane, with bottom-left point at q0=(w/2, 0, -h/2)
// If numbered counter clock-wise, the next point is at q1=(-w/2, 0, -h/2) and the normalized vector w1 between q0 and q1
// is w1=(-1,0,0)
QVector3D w1Rotated = rot.rotatedVector(w1);
// now we need to compute the rotation matrix to align the w1 vector with the v1 vector
QQuaternion rot2 = QQuaternion::rotationTo(w1Rotated, v1);
// combine both rotations (mind the matrix multiplication order!)
QQuaternion planeRotation = rot2*rot;
// anchor point of generated mesh
QVector3D q0(wx/2, 0, -wz/2);
// Point q0 after rotation
QVector3D q0rot = planeRotation.rotatedVector(q0);
//translation to target anchor point
QVector3D transVec = p0 - q0rot;
// create transformation
Qt3DCore::QTransform *transform = new Qt3DCore::QTransform();
transform->setTranslation(transVec);
transform->setRotation(planeRotation);
// and set it as component
planeEntity->addComponent(transform);
return planeEntity;
}

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