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quaternion_demo.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "quaternion_demo.h"
#include "icosphere.h"
#include <Eigen/Geometry>
#include <Eigen/QR>
#include <Eigen/LU>
#include <iostream>
#include <QEvent>
#include <QMouseEvent>
#include <QInputDialog>
#include <QGridLayout>
#include <QButtonGroup>
#include <QRadioButton>
#include <QDockWidget>
#include <QPushButton>
#include <QGroupBox>
using namespace Eigen;
class FancySpheres
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW
FancySpheres()
{
const int levels = 4;
const float scale = 0.33;
float radius = 100;
std::vector<int> parents;
// leval 0
mCenters.push_back(Vector3f::Zero());
parents.push_back(-1);
mRadii.push_back(radius);
// generate level 1 using icosphere vertices
radius *= 0.45;
{
float dist = mRadii[0]*0.9;
for (int i=0; i<12; ++i)
{
mCenters.push_back(mIcoSphere.vertices()[i] * dist);
mRadii.push_back(radius);
parents.push_back(0);
}
}
static const float angles [10] = {
0, 0,
M_PI, 0.*M_PI,
M_PI, 0.5*M_PI,
M_PI, 1.*M_PI,
M_PI, 1.5*M_PI
};
// generate other levels
int start = 1;
for (int l=1; l<levels; l++)
{
radius *= scale;
int end = mCenters.size();
for (int i=start; i<end; ++i)
{
Vector3f c = mCenters[i];
Vector3f ax0 = (c - mCenters[parents[i]]).normalized();
Vector3f ax1 = ax0.unitOrthogonal();
Quaternionf q;
q.setFromTwoVectors(Vector3f::UnitZ(), ax0);
Affine3f t = Translation3f(c) * q * Scaling(mRadii[i]+radius);
for (int j=0; j<5; ++j)
{
Vector3f newC = c + ( (AngleAxisf(angles[j*2+1], ax0)
* AngleAxisf(angles[j*2+0] * (l==1 ? 0.35 : 0.5), ax1)) * ax0)
* (mRadii[i] + radius*0.8);
mCenters.push_back(newC);
mRadii.push_back(radius);
parents.push_back(i);
}
}
start = end;
}
}
void draw()
{
int end = mCenters.size();
glEnable(GL_NORMALIZE);
for (int i=0; i<end; ++i)
{
Affine3f t = Translation3f(mCenters[i]) * Scaling(mRadii[i]);
gpu.pushMatrix(GL_MODELVIEW);
gpu.multMatrix(t.matrix(),GL_MODELVIEW);
mIcoSphere.draw(2);
gpu.popMatrix(GL_MODELVIEW);
}
glDisable(GL_NORMALIZE);
}
protected:
std::vector<Vector3f> mCenters;
std::vector<float> mRadii;
IcoSphere mIcoSphere;
};
// generic linear interpolation method
template<typename T> T lerp(float t, const T& a, const T& b)
{
return a*(1-t) + b*t;
}
// quaternion slerp
template<> Quaternionf lerp(float t, const Quaternionf& a, const Quaternionf& b)
{ return a.slerp(t,b); }
// linear interpolation of a frame using the type OrientationType
// to perform the interpolation of the orientations
template<typename OrientationType>
inline static Frame lerpFrame(float alpha, const Frame& a, const Frame& b)
{
return Frame(lerp(alpha,a.position,b.position),
Quaternionf(lerp(alpha,OrientationType(a.orientation),OrientationType(b.orientation))));
}
template<typename _Scalar> class EulerAngles
{
public:
enum { Dim = 3 };
typedef _Scalar Scalar;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Quaternion<Scalar> QuaternionType;
protected:
Vector3 m_angles;
public:
EulerAngles() {}
inline EulerAngles(Scalar a0, Scalar a1, Scalar a2) : m_angles(a0, a1, a2) {}
inline EulerAngles(const QuaternionType& q) { *this = q; }
const Vector3& coeffs() const { return m_angles; }
Vector3& coeffs() { return m_angles; }
EulerAngles& operator=(const QuaternionType& q)
{
Matrix3 m = q.toRotationMatrix();
return *this = m;
}
EulerAngles& operator=(const Matrix3& m)
{
// mat = cy*cz -cy*sz sy
// cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
m_angles.coeffRef(1) = std::asin(m.coeff(0,2));
m_angles.coeffRef(0) = std::atan2(-m.coeff(1,2),m.coeff(2,2));
m_angles.coeffRef(2) = std::atan2(-m.coeff(0,1),m.coeff(0,0));
return *this;
}
Matrix3 toRotationMatrix(void) const
{
Vector3 c = m_angles.array().cos();
Vector3 s = m_angles.array().sin();
Matrix3 res;
res << c.y()*c.z(), -c.y()*s.z(), s.y(),
c.z()*s.x()*s.y()+c.x()*s.z(), c.x()*c.z()-s.x()*s.y()*s.z(), -c.y()*s.x(),
-c.x()*c.z()*s.y()+s.x()*s.z(), c.z()*s.x()+c.x()*s.y()*s.z(), c.x()*c.y();
return res;
}
operator QuaternionType() { return QuaternionType(toRotationMatrix()); }
};
// Euler angles slerp
template<> EulerAngles<float> lerp(float t, const EulerAngles<float>& a, const EulerAngles<float>& b)
{
EulerAngles<float> res;
res.coeffs() = lerp(t, a.coeffs(), b.coeffs());
return res;
}
RenderingWidget::RenderingWidget()
{
mAnimate = false;
mCurrentTrackingMode = TM_NO_TRACK;
mNavMode = NavTurnAround;
mLerpMode = LerpQuaternion;
mRotationMode = RotationStable;
mTrackball.setCamera(&mCamera);
// required to capture key press events
setFocusPolicy(Qt::ClickFocus);
}
void RenderingWidget::grabFrame(void)
{
// ask user for a time
bool ok = false;
double t = 0;
if (!m_timeline.empty())
t = (--m_timeline.end())->first + 1.;
t = QInputDialog::getDouble(this, "Eigen's RenderingWidget", "time value: ",
t, 0, 1e3, 1, &ok);
if (ok)
{
Frame aux;
aux.orientation = mCamera.viewMatrix().linear();
aux.position = mCamera.viewMatrix().translation();
m_timeline[t] = aux;
}
}
void RenderingWidget::drawScene()
{
static FancySpheres sFancySpheres;
float length = 50;
gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitX(), Color(1,0,0,1));
gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitY(), Color(0,1,0,1));
gpu.drawVector(Vector3f::Zero(), length*Vector3f::UnitZ(), Color(0,0,1,1));
// draw the fractal object
float sqrt3 = std::sqrt(3.);
glLightfv(GL_LIGHT0, GL_AMBIENT, Vector4f(0.5,0.5,0.5,1).data());
glLightfv(GL_LIGHT0, GL_DIFFUSE, Vector4f(0.5,1,0.5,1).data());
glLightfv(GL_LIGHT0, GL_SPECULAR, Vector4f(1,1,1,1).data());
glLightfv(GL_LIGHT0, GL_POSITION, Vector4f(-sqrt3,-sqrt3,sqrt3,0).data());
glLightfv(GL_LIGHT1, GL_AMBIENT, Vector4f(0,0,0,1).data());
glLightfv(GL_LIGHT1, GL_DIFFUSE, Vector4f(1,0.5,0.5,1).data());
glLightfv(GL_LIGHT1, GL_SPECULAR, Vector4f(1,1,1,1).data());
glLightfv(GL_LIGHT1, GL_POSITION, Vector4f(-sqrt3,sqrt3,-sqrt3,0).data());
glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, Vector4f(0.7, 0.7, 0.7, 1).data());
glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, Vector4f(0.8, 0.75, 0.6, 1).data());
glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, Vector4f(1, 1, 1, 1).data());
glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, 64);
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glEnable(GL_LIGHT1);
sFancySpheres.draw();
glVertexPointer(3, GL_FLOAT, 0, mVertices[0].data());
glNormalPointer(GL_FLOAT, 0, mNormals[0].data());
glEnableClientState(GL_VERTEX_ARRAY);
glEnableClientState(GL_NORMAL_ARRAY);
glDrawArrays(GL_TRIANGLES, 0, mVertices.size());
glDisableClientState(GL_VERTEX_ARRAY);
glDisableClientState(GL_NORMAL_ARRAY);
glDisable(GL_LIGHTING);
}
void RenderingWidget::animate()
{
m_alpha += double(m_timer.interval()) * 1e-3;
TimeLine::const_iterator hi = m_timeline.upper_bound(m_alpha);
TimeLine::const_iterator lo = hi;
--lo;
Frame currentFrame;
if(hi==m_timeline.end())
{
// end
currentFrame = lo->second;
stopAnimation();
}
else if(hi==m_timeline.begin())
{
// start
currentFrame = hi->second;
}
else
{
float s = (m_alpha - lo->first)/(hi->first - lo->first);
if (mLerpMode==LerpEulerAngles)
currentFrame = ::lerpFrame<EulerAngles<float> >(s, lo->second, hi->second);
else if (mLerpMode==LerpQuaternion)
currentFrame = ::lerpFrame<Eigen::Quaternionf>(s, lo->second, hi->second);
else
{
std::cerr << "Invalid rotation interpolation mode (abort)\n";
exit(2);
}
currentFrame.orientation.coeffs().normalize();
}
currentFrame.orientation = currentFrame.orientation.inverse();
currentFrame.position = - (currentFrame.orientation * currentFrame.position);
mCamera.setFrame(currentFrame);
updateGL();
}
void RenderingWidget::keyPressEvent(QKeyEvent * e)
{
switch(e->key())
{
case Qt::Key_Up:
mCamera.zoom(2);
break;
case Qt::Key_Down:
mCamera.zoom(-2);
break;
// add a frame
case Qt::Key_G:
grabFrame();
break;
// clear the time line
case Qt::Key_C:
m_timeline.clear();
break;
// move the camera to initial pos
case Qt::Key_R:
resetCamera();
break;
// start/stop the animation
case Qt::Key_A:
if (mAnimate)
{
stopAnimation();
}
else
{
m_alpha = 0;
connect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));
m_timer.start(1000/30);
mAnimate = true;
}
break;
default:
break;
}
updateGL();
}
void RenderingWidget::stopAnimation()
{
disconnect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));
m_timer.stop();
mAnimate = false;
m_alpha = 0;
}
void RenderingWidget::mousePressEvent(QMouseEvent* e)
{
mMouseCoords = Vector2i(e->pos().x(), e->pos().y());
bool fly = (mNavMode==NavFly) || (e->modifiers()&Qt::ControlModifier);
switch(e->button())
{
case Qt::LeftButton:
if(fly)
{
mCurrentTrackingMode = TM_LOCAL_ROTATE;
mTrackball.start(Trackball::Local);
}
else
{
mCurrentTrackingMode = TM_ROTATE_AROUND;
mTrackball.start(Trackball::Around);
}
mTrackball.track(mMouseCoords);
break;
case Qt::MidButton:
if(fly)
mCurrentTrackingMode = TM_FLY_Z;
else
mCurrentTrackingMode = TM_ZOOM;
break;
case Qt::RightButton:
mCurrentTrackingMode = TM_FLY_PAN;
break;
default:
break;
}
}
void RenderingWidget::mouseReleaseEvent(QMouseEvent*)
{
mCurrentTrackingMode = TM_NO_TRACK;
updateGL();
}
void RenderingWidget::mouseMoveEvent(QMouseEvent* e)
{
// tracking
if(mCurrentTrackingMode != TM_NO_TRACK)
{
float dx = float(e->x() - mMouseCoords.x()) / float(mCamera.vpWidth());
float dy = - float(e->y() - mMouseCoords.y()) / float(mCamera.vpHeight());
// speedup the transformations
if(e->modifiers() & Qt::ShiftModifier)
{
dx *= 10.;
dy *= 10.;
}
switch(mCurrentTrackingMode)
{
case TM_ROTATE_AROUND:
case TM_LOCAL_ROTATE:
if (mRotationMode==RotationStable)
{
// use the stable trackball implementation mapping
// the 2D coordinates to 3D points on a sphere.
mTrackball.track(Vector2i(e->pos().x(), e->pos().y()));
}
else
{
// standard approach mapping the x and y displacements as rotations
// around the camera's X and Y axes.
Quaternionf q = AngleAxisf( dx*M_PI, Vector3f::UnitY())
* AngleAxisf(-dy*M_PI, Vector3f::UnitX());
if (mCurrentTrackingMode==TM_LOCAL_ROTATE)
mCamera.localRotate(q);
else
mCamera.rotateAroundTarget(q);
}
break;
case TM_ZOOM :
mCamera.zoom(dy*100);
break;
case TM_FLY_Z :
mCamera.localTranslate(Vector3f(0, 0, -dy*200));
break;
case TM_FLY_PAN :
mCamera.localTranslate(Vector3f(dx*200, dy*200, 0));
break;
default:
break;
}
updateGL();
}
mMouseCoords = Vector2i(e->pos().x(), e->pos().y());
}
void RenderingWidget::paintGL()
{
glEnable(GL_DEPTH_TEST);
glDisable(GL_CULL_FACE);
glPolygonMode(GL_FRONT_AND_BACK,GL_FILL);
glDisable(GL_COLOR_MATERIAL);
glDisable(GL_BLEND);
glDisable(GL_ALPHA_TEST);
glDisable(GL_TEXTURE_1D);
glDisable(GL_TEXTURE_2D);
glDisable(GL_TEXTURE_3D);
// Clear buffers
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
mCamera.activateGL();
drawScene();
}
void RenderingWidget::initializeGL()
{
glClearColor(1., 1., 1., 0.);
glLightModeli(GL_LIGHT_MODEL_LOCAL_VIEWER, 1);
glDepthMask(GL_TRUE);
glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE);
mCamera.setPosition(Vector3f(-200, -200, -200));
mCamera.setTarget(Vector3f(0, 0, 0));
mInitFrame.orientation = mCamera.orientation().inverse();
mInitFrame.position = mCamera.viewMatrix().translation();
}
void RenderingWidget::resizeGL(int width, int height)
{
mCamera.setViewport(width,height);
}
void RenderingWidget::setNavMode(int m)
{
mNavMode = NavMode(m);
}
void RenderingWidget::setLerpMode(int m)
{
mLerpMode = LerpMode(m);
}
void RenderingWidget::setRotationMode(int m)
{
mRotationMode = RotationMode(m);
}
void RenderingWidget::resetCamera()
{
if (mAnimate)
stopAnimation();
m_timeline.clear();
Frame aux0 = mCamera.frame();
aux0.orientation = aux0.orientation.inverse();
aux0.position = mCamera.viewMatrix().translation();
m_timeline[0] = aux0;
Vector3f currentTarget = mCamera.target();
mCamera.setTarget(Vector3f::Zero());
// compute the rotation duration to move the camera to the target
Frame aux1 = mCamera.frame();
aux1.orientation = aux1.orientation.inverse();
aux1.position = mCamera.viewMatrix().translation();
float duration = aux0.orientation.angularDistance(aux1.orientation) * 0.9;
if (duration<0.1) duration = 0.1;
// put the camera at that time step:
aux1 = aux0.lerp(duration/2,mInitFrame);
// and make it look at the target again
aux1.orientation = aux1.orientation.inverse();
aux1.position = - (aux1.orientation * aux1.position);
mCamera.setFrame(aux1);
mCamera.setTarget(Vector3f::Zero());
// add this camera keyframe
aux1.orientation = aux1.orientation.inverse();
aux1.position = mCamera.viewMatrix().translation();
m_timeline[duration] = aux1;
m_timeline[2] = mInitFrame;
m_alpha = 0;
animate();
connect(&m_timer, SIGNAL(timeout()), this, SLOT(animate()));
m_timer.start(1000/30);
mAnimate = true;
}
QWidget* RenderingWidget::createNavigationControlWidget()
{
QWidget* panel = new QWidget();
QVBoxLayout* layout = new QVBoxLayout();
{
QPushButton* but = new QPushButton("reset");
but->setToolTip("move the camera to initial position (with animation)");
layout->addWidget(but);
connect(but, SIGNAL(clicked()), this, SLOT(resetCamera()));
}
{
// navigation mode
QGroupBox* box = new QGroupBox("navigation mode");
QVBoxLayout* boxLayout = new QVBoxLayout;
QButtonGroup* group = new QButtonGroup(panel);
QRadioButton* but;
but = new QRadioButton("turn around");
but->setToolTip("look around an object");
group->addButton(but, NavTurnAround);
boxLayout->addWidget(but);
but = new QRadioButton("fly");
but->setToolTip("free navigation like a spaceship\n(this mode can also be enabled pressing the \"shift\" key)");
group->addButton(but, NavFly);
boxLayout->addWidget(but);
group->button(mNavMode)->setChecked(true);
connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setNavMode(int)));
box->setLayout(boxLayout);
layout->addWidget(box);
}
{
// track ball, rotation mode
QGroupBox* box = new QGroupBox("rotation mode");
QVBoxLayout* boxLayout = new QVBoxLayout;
QButtonGroup* group = new QButtonGroup(panel);
QRadioButton* but;
but = new QRadioButton("stable trackball");
group->addButton(but, RotationStable);
boxLayout->addWidget(but);
but->setToolTip("use the stable trackball implementation mapping\nthe 2D coordinates to 3D points on a sphere");
but = new QRadioButton("standard rotation");
group->addButton(but, RotationStandard);
boxLayout->addWidget(but);
but->setToolTip("standard approach mapping the x and y displacements\nas rotations around the camera's X and Y axes");
group->button(mRotationMode)->setChecked(true);
connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setRotationMode(int)));
box->setLayout(boxLayout);
layout->addWidget(box);
}
{
// interpolation mode
QGroupBox* box = new QGroupBox("spherical interpolation");
QVBoxLayout* boxLayout = new QVBoxLayout;
QButtonGroup* group = new QButtonGroup(panel);
QRadioButton* but;
but = new QRadioButton("quaternion slerp");
group->addButton(but, LerpQuaternion);
boxLayout->addWidget(but);
but->setToolTip("use quaternion spherical interpolation\nto interpolate orientations");
but = new QRadioButton("euler angles");
group->addButton(but, LerpEulerAngles);
boxLayout->addWidget(but);
but->setToolTip("use Euler angles to interpolate orientations");
group->button(mNavMode)->setChecked(true);
connect(group, SIGNAL(buttonClicked(int)), this, SLOT(setLerpMode(int)));
box->setLayout(boxLayout);
layout->addWidget(box);
}
layout->addItem(new QSpacerItem(0,0,QSizePolicy::Minimum,QSizePolicy::Expanding));
panel->setLayout(layout);
return panel;
}
QuaternionDemo::QuaternionDemo()
{
mRenderingWidget = new RenderingWidget();
setCentralWidget(mRenderingWidget);
QDockWidget* panel = new QDockWidget("navigation", this);
panel->setAllowedAreas((QFlags<Qt::DockWidgetArea>)(Qt::RightDockWidgetArea | Qt::LeftDockWidgetArea));
addDockWidget(Qt::RightDockWidgetArea, panel);
panel->setWidget(mRenderingWidget->createNavigationControlWidget());
}
int main(int argc, char *argv[])
{
std::cout << "Navigation:\n";
std::cout << " left button: rotate around the target\n";
std::cout << " middle button: zoom\n";
std::cout << " left button + ctrl quake rotate (rotate around camera position)\n";
std::cout << " middle button + ctrl walk (progress along camera's z direction)\n";
std::cout << " left button: pan (translate in the XY camera's plane)\n\n";
std::cout << "R : move the camera to initial position\n";
std::cout << "A : start/stop animation\n";
std::cout << "C : clear the animation\n";
std::cout << "G : add a key frame\n";
QApplication app(argc, argv);
QuaternionDemo demo;
demo.resize(600,500);
demo.show();
return app.exec();
}
#include "quaternion_demo.moc"

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