Transcript CS430 Computer Graphics - Winona State University

CS430
Computer Graphics
Rendering Pipeline and
Primitive Rasterization
Chi-Cheng Lin, Winona State University
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
Model
Viewport
Transformation
Scan
Conversion
Pixels on
display
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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
y - W.b
sy - V.b
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Window-to-Viewport Mapping
sx  V .l
x  W .l
V .r  V .l
V .r  V .l

 sx 
x  (V .l 
W .l )
V .r  V .l W .r  W .l
W .r  W .l
W .r  W .l
Similarly,
sy  V .b
y  W .b
V .t  V .b
V .t  V .b

 sy 
y  (V .b 
W .b)
V .t  V .b W .t  W .b
W .t  W .b
W .t  W .b
T herefore,
sx  A  x  C
and
sy  B  y  D
where
V .r  V .l
A
, C  V .l  A  W .l
W .r  W .l
V .t  V .b
B
, D  V .b  B  W .b
W .t  W .b
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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 i=0; i<5; i++) // for each column
for (int j=0; j<5; j++) { // for each row
glViewport(i*64, j*44, 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 < 5; i++)
for (int j = 0; j < 5; j++) {
if ((i+j)%2 = 1) // if (i+j) 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(i*64, j*44, 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,W,W/R);
glViewport(0,0,H*R,H);
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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 >W/H) //use (global)window aspect ratio
setViewport(0, W, 0, W/R);
else
setViewport(0, H*R, 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

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