Clipping:
LINES
and
d
POLYGONS
OUTPUT
INPUT
Solving
g Simultaneous equations
q
using parametric form of a line:
P(t ) = (1 t ) P0 + tP1
where
h , P(0) = P0 ; P(1) = P1
S l
Solve
with
ith respective
ti
pairs:
i
Kx X0
t lx =
X1 X0
t ly =
K y Y0
Y1 Y 0
Verti

2D TRANSFORMATIONS AND MATRICES
Representation of Points:
2 x 1 matrix:
|x|
|y|
General Problem: |B| = |T| |A|
|T| represents a generic operator to be applied to the points in A. T
is the geometric transformation matrix. A & T are know, want to find B,
th

3D Viewing
Projection Transformations
and
Vi i Pipeline
Viewing
Pi li
Implementation of 3D Viewing
3-D world
coordinate
output
primitives
p
Apply
normalizing
li i
transformation
Clip against
canonical
View
Volume
2D device
coordinates
Transform into
p
vi

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CRT
DISPLAY DEVICES
Examples of Computer Graphics Devices:
CRT, EGA/CGA/VGA/SVGA monitors,
plotters, data matrix, laser printers, Films

Three - Dimensional
Graphics
Three-Dimensional
ee
e s o a Graphics
G ap cs
Use of a right-handed coordinate
(consistent with math)
Left-handed suitable to screens.
screens
system
To transform from right
g
to left, negate
g
the
z values.
Right
g
Handed Spa

SCAN CONVERTING
LINES,
CIRCLES and ELLIPSES
LINE DRAWING
Description: Given the specification for a
straight line, find the collection of
addressable pixels which most closely
approximates this line.
Goals (not all of them are achievable with
the discrete

SCAN CONVERSION - POLYFILL
Pixels are not at the center of the grid, but at the intersection of two
orthogonal scan lines (on the grid intersection points).
SCANLINE POLYFILL ALGORITHM
Steps (conceptual):
Find minimum enclosed rectangle
No. of scanlines