CS430 Computer Graphics

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CS430 Computer Graphics

• Rendering Pipeline and Primitive Rasterization

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Topics

• Introduction
• Viewport Transformation
• Primitive Rasterization
• Primitive Clipping

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Introduction

• Scan conversion
• Convert specification of a primitive into pixels
  in the frame buffer
• Simple rendering pipeline

Viewport Transformation
Scan Conversion
Pixels on display
Model
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Viewport Transformation

• Problem
• When we define a 2D model, we want to use
  whatever coordinate values and units convenient
  to use in the 2D Cartesian system.
• BUT, the coordinate values on the display (or in
  the screen window) are always nonnegative
  measured in pixels.
• ALSO, we might want to show different parts of
  our model in different places on the display (or
  in the screen window)
• Solution viewport transformation

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World Window and Viewport

• World coordinate
• Space in which objects are described
• World window
• A rectangle area specifies which part of the
  world should be drawn
• Viewport
• A rectangle area specifies which part on the
  display (or in the window) the world window is
  mapped to

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World Window and Viewport

• Example

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Window-to-Viewport Mapping

• (x, y) in world window should be mapped to (sx,
  sy) in viewport proportionally ? distortion is
  possible

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Window-to-Viewport Mapping

• Every vertex used in window to define an object
  should be mapped to viewport

(sx,sy)
(x,y)
x - W.l
sx - V.l
sy - V.b
y - W.b
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Window-to-Viewport Mapping
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How does OpenGL do it?

• Set up world window
• glMatrixMode(GL_PROJECTION)
• glLoadIdentity()
• gluOrtho2D(left, right, bottom, top)
• We can write a function setWindow()
• setWindow(GLdouble left, GLdouble right,
• GLdouble bottom, GLdouble top)
• glMatrixMode(GL_PROJECTION)
• glLoadIdentity()
• gluOrtho2D(left, right, bottom, top)

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How does OpenGL do it?

• Set up viewport
• glViewport(left, bottom, width, height)
• or
• glViewport(left, bottom, right-left,
  top-bottom)
• Default viewport screen window size
• Parameters to set up a window are doubles while
  those to set up a viewport are ints. (Why?)

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Example Tiling with Motif

• setWindow(0,640.0,0,440.0) // set a fixed window
• for (int i0 ilt5 i) // for each column
• for (int j0 jlt5 j) // for each row
• glViewport(i64, j44, 64, 44) // set the next
  viewport
• drawPolylineFile(dino.dat ) // draw it again

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Example Tiling with Motif

• for (int i 0 i lt 5 i)
• for (int j 0 j lt 5 j)
• if ((ij)2 1) // if (ij) is odd
• setWindow(0.0, 640.0, 0.0, 440.0) //
  right-side-up window
• else
• setWindow(0.0, 640.0, 440.0, 0.0) //
  upside-down window
• glViewport(i64, j44, 64, 44) // set the
  next viewport
• drawPolylineFile("dino.dat") // draw it
  again

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Zooming and Panning

• Zooming
• Scale the world window with respect to the center
  of the world window with viewport fixed
• Panning
• Shift the world window with viewport fixed

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Mapping without Distortion

• To prevent from distortion, a viewport with the
  same aspect ratio of world window is required.
• Aspect ratio width/height
• How do you draw the largest undistorted picture
  in the screen window?

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Mapping without Distortion

• If aspect ratio of world window R
• Two cases

glViewport(0,0,HR,H)
glViewport(0,0,W,W/R)
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Resize Screen Window

• glutReshapeFunc(myReshape)
• Prototype of myReshape
• void myReshape(GLsizei W, Glsizei H)
• W and H new width and height
• Making a matched viewport
• void myReshape(GLsizei W,GLsizei H)
• if (R gtW/H) //use (global)window aspect ratio
• setViewport(0, W, 0, W/R)
• else
• setViewport(0, HR, 0, H)

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Primitives Rasterization

• Line
• Brute force
• DDA
• Midpoint algorithm
• Circle
• Brute force
• Polar coordinates
• Midpoint algorithm
• Polyline and polygon

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Primitive Clipping

• Problem
• Not everything defined in the world will be
  included in the world window
• Solution
• Clipping
• Line clipping
• Polygon clipping
• OpenGL does clipping for you