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Investigations on update_camera()

In the second part of axes::properties::update_camera () the view transformation "x_gl_mat1" and projection matrix "x_gl_mat2" are put together. The following images illustrate some of the properties of "x_gl_mat1".

The Octave coordinate system

In Octave a plot scene is defined by a "view point", a "camera target" and an "up vector".

Octave view point setup to scale.png

The role of "x_gl_mat1"

The following section of code assembles the matrix "x_view", which is a subset of "x_gl_mat1". The matrix "x_gl_mat1" consists of different translations, scalings and a rotation operation.

Code: Section of axes::properties::update_camera ()"
  // Unit length vectors for direction of view "f" and up vector "UP"
  ColumnVector F (c_center), f (F), UP (c_upv);
  normalize (f);
  normalize (UP);

  // Calculate the vector rejection UP onto f
  // s, f and u are used to assemble the rotation matrix l
  ColumnVector s = cross (f, UP);
  ColumnVector u = cross (s, f);
  
  // Construct a 4x4 matrix "x_view" that is a subset of "x_gl_mat1"
  // Start with identity I = [1,0,0,0; 0,1,0,0; 0,0,1,0; 0,0,0,1]
  Matrix x_view = xform_matrix ();
  // Step #7 -> #8
  scale (x_view, 1, 1, -1);
  Matrix l = xform_matrix ();
  l(0,0) = s(0); l(0,1) = s(1); l(0,2) = s(2);
  l(1,0) = u(0); l(1,1) = u(1); l(1,2) = u(2);
  l(2,0) = -f(0); l(2,1) = -f(1); l(2,2) = -f(2);
  // Step #6 -> #7 (rotate on the Z axis)
  x_view = x_view * l;
  // Step #5 -> #6
  translate (x_view, -c_eye(0), -c_eye(1), -c_eye(2));
  // Step #4 -> #5
  scale (x_view, pb(0), pb(1), pb(2));
  // Step #3 -> #4
  translate (x_view, -0.5, -0.5, -0.5);

To visualize the matrix properties, the "x_gl_mat1" matrix is multiplied by the object coordinates. The plot box is now aligned with the Z-axis and the view point is at the origin . The matrix transforms world coordinates into camera coordinates. The purple planes show the near and far clipping planes.

Octave x gl mat1 setup.png

The individual translation, scaling and rotation operations of "x_gl_mat1", are shown in the following figure:

Octave x gl mat1 steps.png