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# The frameTransform example

Coordinate transformation between different Frames.

This example illustrates the camera and world coordinate systems relationship. The position of the camera in the world coordinate system is printed from `camera()->position()`. Symmetrically, the position of the world origin is given in the camera coordinate system by `camera()->cameraCoordinatesOf(0,0,0)`.

Three sets of lines (red, green, blue) are drawn. They have different starting points, but common end points, located on a circle in the XY plane.

All the red lines start from the camera position, and will hence always be aligned with the viewing direction, making them invisible.

The green lines starting points' positions are determined from the camera coordinate system, using `camera()->worldCoordinatesOf()`. As a result, these points will seem to be fixed on the screen, even when the camera is moved

Finally, the blue lines are classically defined in the world coordinate system, and will move with the camera.

Beautiful Moire pattern can be obtained with a proper rotation.

## frameTransform.h

    #include <QGLViewer/qglviewer.h>

    class Viewer : public QGLViewer
    {
    protected :
      virtual void draw();
      virtual void init();
      virtual QString helpString() const;
    };

## frameTransform.cpp

    #include "frameTransform.h"

    using namespace std;
    using namespace qglviewer; // Vec

    void Viewer::init()
    {
      restoreStateFromFile();

      setSceneRadius(1.5);
      showEntireScene();
      setAxisIsDrawn();
      glDisable(GL_LIGHTING);

      help();
    }

    void Viewer::draw()
    {
      // Draws line sets (red, green, blue) with different origins, but with a common
      // end point, located on a circle in the XY plane.
      const float nbLines = 50.0;

      glBegin(GL_LINES);

      for (float i=0; i<nbLines; ++i)
        {
          float angle = 2.0*M_PI*i/nbLines;

          glColor3f(0.8f, 0.2f, 0.2f);
          // These lines will never be seen as they are always aligned with the viewing direction.
          glVertex3fv(camera()->position());
          glVertex3f (cos(angle), sin(angle), 0.0);

          glColor3f(0.2f, 0.8f, 0.2f);
          // World Coordinates are infered from the camera, and seem to be immobile in the screen.
          glVertex3fv(camera()->worldCoordinatesOf(Vec(.3*cos(angle), .3*sin(angle), -2.0)));
          glVertex3f (cos(angle), sin(angle), 0.0);

          glColor3f(0.2f, 0.2f, 0.8f);
          // These lines are defined in the world coordinate system and will move with the camera.
          glVertex3f(1.5*cos(angle), 1.5*sin(angle), -1.0);
          glVertex3f(cos(angle), sin(angle), 0.0);
        }
      glEnd();

      // Here, the camera position in world coord. system  is camera()->position().
      // The world origin position in camera frame can be obtained from camera()->cameraCoordinatesOf(Vec(0.0, 0.0, 0.0))
    }

    QString Viewer::helpString() const
    {
      QString text("<h2>F r a m e T r a n s f o r m</h2>");
      text += "This example illustrates how easy it is to switch between the camera and ";
      text += "the world coordinate systems using the <i>camera()->cameraCoordinatesOf()</i> ";
      text += "and <i>camera::worldCoordinatesOf()</i> functions.<br><br>";
      text += "You can create your own hierarchy of local coordinates systems and each of ";
      text += "them can be manipulated with the mouse (see the <i>manipulatedFrame</i> and <i>luxo</i> examples). ";
      text += "Standard functions allow you to convert from any local frame to any other, ";
      text += "the world/camera conversion presented here simply being an illustration.<br><br>";
      text += "See <i>examples/frameTransform.html</i> for an explanation of the meaning of these weird lines.";
      return text;
    }

## main.cpp

    #include "frameTransform.h"
    #include <qapplication.h>

    int main(int argc, char** argv)
    {
      QApplication application(argc,argv);

      Viewer viewer;

      viewer.setWindowTitle("frameTransform");

      viewer.show();

      return application.exec();
    }

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