Advanced Viewing

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Advanced Viewing

• Glenn G. ChappellCHAPPELLG_at_member.ams.org
• U. of Alaska Fairbanks
• CS 381 Lecture Notes
• Friday, October 31, 2003

2
ReviewProjection in 3-D 1/3

• We use the projection to handle camera
  properties.
• Perspective or parallel (orthogonal) projection.
• Wide or narrow angle.
• But not camera position orientation.
• How do we determine wide narrow angle using
  glFrustum or gluPerspective?
• With gluPerspective, change the 1st parameter
  (fovy).
• With glFrustum, multiply left, right, bottom, top
  by some number.
• Fancy projections can mess up screen text,
  buttons, etc. For these, use a separate
  gluOrtho2D projection.
• See printmatrix.cpp, on the web page, for sample
  code.

3
ReviewProjection in 3-D 2/3

• Computing Perspective Projection
• Based on the synthetic-camera model, we can find
  the coordinates of a projected point.
• We use similar triangles (outlined in red).

Screen
Center of Projection (eye)(0, 0, 0)
(x, y, z)
z
(x/z/near, y/z/near, near)
z near
View Frustum
z far
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ReviewProjection in 3-D 3/3

• We can perform this projection using the
  following matrix.
• This matrix is not exactly what glFrustum
  produces, since it deals with right, left, top,
  bottom, far, too.
• But this gives the general idea.

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ReviewMore on OpenGL Matrices 1/2

• We store an OpenGL matrix in an array of 16
  GLdoublesGLdouble matrixd16
• To put the model/view matrix into this
  arrayglGetDoublev(GL_MODELVIEW_MATRIX,
  matrixd)
• This is column-major. 0..3 are the first column,
  not the first row.
• To restore the saved model/view
  matrixglLoadMatrixd(matrixd) // Mode must be
  GL_MODELVIEW!
• More usefully, to multiply saved matrix by
  current matrixglMultMatrixd(matrixd) // Mode
  must be GL_MODELVIEW!

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ReviewMore on OpenGL Matrices 2/2

• How would you write glTranslate yourself?
• void myglTranslate(double x, double y, double z)
• GLdouble m16 // The translation matrix
• m 0 1. m 4 0. m 8 0. m12 x
• m 1 0. m 5 1. m 9 0. m13 y
• m 2 0. m 6 0. m10 1. m14 z
• m 3 0. m 7 0. m11 0. m15
  1.
• glMultMatrixd(m) // Multiply it
• Why dont I set GL_MODELVIEW mode in this
  function?

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Advanced ViewingProblem Solution

• So far, we have always created the model/view
  transformation from scratch for each frame.
• This can get unwieldy if an increasingly long
  sequence of transformations must be remembered.
• Consider flying.
• Solution
• Keep the current state of a sequence of
  transformations in a matrix.
• Modify the matrix appropriately when a new
  transformation is added.
• In the display function, just do glMultMatrix.

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Advanced ViewingExample 1 Zoom Pan 1/2

• In traditional zoom pan (with a real camera)
• Zoom means changing the wide/narrow-angle
  properties of the lens.
• Pan means rotating the camera.
• We will misuse these terms somewhat, in order to
  make a more helpful example.
• Our zoom will scale the world.
• Our pan will translate it.
• We will use model/view for both of these.
• Think What is a problem with panning while
  zoomed in close?

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Advanced ViewingExample 1 Zoom Pan 2/2

• Suppose we handle zoom pan with a saved
  viewing matrix.
• What do we do to this matrix, in order to pan?
• Translate, then do the saved transformations.
  Result is the new transformation.
• What do we do to this matrix, in order to zoom?
• Scale, then do the saved transformations. Result
  is the new transformation.
• How do we use this matrix in the display
  function?
• Load it (glLoadMatrixd).
• Or do whatever else needs to be done first, then
  multiply by it (glMultMatrixd).

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Advanced ViewingHandling the Saved Matrix

• Dont forget to initialize the saved matrix.
• glMatrixMode(GL_MODELVIEW)
• glPushMatrix()
• Transformation commands go here?
• glGetDoublev(GL_MODELVIEW_MATRIX,
  your_matrix_variable)
• glPopMatrix()
• Whenever you do anything with the model/view
  transformation, use push pop.
• Changing the matrix alters the display.
• So post a redisplay event whenever you change the
  matrix outside the display function.
• Generally, to alter a saved model/view matrix
  outside the display function
• glPushMatrix()
• glLoadIdentity() // May not
  be necessary
• Transformation commands go here
• glMultMatrixd(your_matrix_variable) // If
  this is appropriate
• glGetDoublev(GL_MODELVIEW_MATRIX,
  your_matrix_variable)
• glPopMatrix()

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Advanced ViewingExample 2 A Driving Interface

• Imagine a car at the center of the window,
  driving through the city streets.
• How can we turn our zoom-pan interface into a 2-D
  driving-style interface (viewed from above) with
  only minimal modifications?
• Change the pan-left and pan-right code to do
  rotations about the z-axis.

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Advanced ViewingExample 3 Flying 1/2

• We implemented the first two examples using a
  saved matrix to hold viewing transformations.
• Viewing transforms camera motions.
• Okay, the zoom part didnt quite fit this model
  
• The ultimate generality in camera motions is
  achieved in flying.
• Flying moving in the viewing direction
  rotating about the camera.
• How do we fly forward?
• Put a z translation before (in the code) all
  previous transformations.
• How to we turn?
• Put a y-axis (or x-axis, for going up down)
  rotation before (in the code) all previous
  transformations.

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Advanced ViewingExample 3 Flying 2/2

• Wouldnt it be nicer to use the mouse?
• Yes. Well talk about that next time.