OpenGL and Projections

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OpenGL and Projections

• David E. Johnson

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Goals

• Quick overview of OpenGL
• Some derivation of projections and transformations

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OpenGL

• OpenGL is nothing more than a set of functions
  you call from your program
• Most functions map to GPU hardware
• Hides the details of the display adapter,
  operating system, etc.
• Has grown to become a flexible general purpose
  compute platform

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• As a programmer, you need to
• Specify the location/parameters of camera.
• Specify the geometry (and appearance).
• Specify the lights.
• OpenGL will compute the resulting 2D image!

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Basic Pipeline
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Basic Pipeline
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OpenGL Hierarchy

• Several levels of abstraction are provided
• GL
• Lowest level vertex, matrix manipulation
• glVertex3f(point.x, point.y, point.z)
• GLU
• Helper functions for shapes, transformations
• gluPerspective( fovy, aspect, near, far )
• GLUT
• Highest level Window and interface management
• glutSwapBuffers()
• All fairly raw most people have their own point
  class which gets transformed to GL arrays as
  needed.

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OpenGL Implementations

• OpenGL is an API
• include ltGL/gl.hgt
• include ltGL/glu.hgt
• include ltGL/glut.hgt
• Windows, Linux, UNIX, etc. all provide a platform
  specific implementation.
• Windows opengl32.lib glu32.lib glut32.lib
• Linux -l GL -l GLU l GLUT

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OpenGL Conventions

• OpenGL is largely state based
• Calls persist
• This instead of having functions with 100s of
  options
• Transformations live on stacks
• Layers of transformations possible
• Work is done on buffers (color, depth,)
• Many functions have multiple forms
• glVertex2f, glVertex3i, glVertex4dv, etc.
• Number indicates number of arguments
• Letters indicate type
• f float, d double, v pointer, etc.
• Programs tend to be event based

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A simple GLUT program

• // A simple OpenGL and glut program
• include ltGL/gl.hgt
• include ltGL/glut.hgt
• void display()
• glClear(GL_COLOR_BUFFER_BIT GL_DEPTH_BUFFER_BIT
  )
• glFlush()
• int main(int argc, char argv)
• glutInit(argc, argv)
• glutInitWindowSize(512,512)
• glutInitDisplayMode(GLUT_RGB GLUT_DEPTH )
• glutCreateWindow("The glut hello world
  program")
• glutDisplayFunc(display)
• glClearColor(0.0, 0.0, 0.0, 1.0)
• glutMainLoop() // Infinite event loop

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OpenGL Camera

• Two things to specify
• Physical location of camera in the scene
• Where is the camera?
• Which direction is it pointing?
• What is the orientation of the camera?
• Projection properties of the camera
• Depth of field?
• Field of view in the x and y directions?

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The OpenGL Camera

• Initially the object and camera frames are the
  same
• Default model-view matrix is an identity
• The camera is located at origin and points in the
  negative z direction
• OpenGL also specifies a default view volume that
  is a cube with sides of length 2 centered at the
  origin
• Default projection matrix is an identity

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Moving Camera Back
frames after translation by d
d gt 0

• default frames

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Moving the Camera

• We can move the camera to any desired position by
  a sequence of rotations and translations
• Example side view
• Rotate the camera
• Move it away from origin
• Model-view matrix C RT

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OpenGL code

• Remember that last transformation specified is
  first to be applied

glMatrixMode(GL_MODELVIEW) glLoadIdentity() glRot
atef(90.0, 0.0, 1.0, 0.0) glTranslatef(0.0, 0.0,
-d)
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The LookAt Function

• The GLU library contains the function gluLookAt
  to form the required modelview matrix through a
  simple interface
• Note the need for setting an up direction
• Still need to initialize
• Can concatenate with modeling transformations
• Example isometric view of cube aligned with axes

glMatrixMode(GL_MODELVIEW) glLoadIdentity() gluL
ookAt(1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0., 1.0. 0.0)
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gluLookAt

• glLookAt(eyex, eyey, eyez, atx, aty, atz, upx,
  upy, upz)

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Projections

• See notes