Transcript Output Primitives - Lecture`s of computer graphics

OUTPUT PRIMITIVES
Computer Graphics
OUTPUT PRIMITIVES

Output Primitives: Basic geometric
structures used to describe scenes.

(points, straight line segment, circles and
other conic sections, quadric surfaces,
spline curve and surfaces, polygon color
areas, and character strings)

These picture components are often
defined in a continuous space.
OUTPUT PRIMITIVES

In order to draw the primitive objects,
one has to first scan convert the object.

Scan convert: Refers to the operation of
finding out the location of pixels to be
intensified and then setting the values of
corresponding bits, in the graphic
memory, to the desired intensity code.
A
SCAN CONVERTING A
POINT
random-scan (vector) system
stores point-plotting instructions in
the display list, and coordinate
values in
these instructions are converted to
deflection voltages that position
the electron beam at the screen
locations to be plotted during each
refresh cycle.
Scan Converting A Point
SCAN CONVERTING A
POINT

A mathematical point P(x,y) needs to
be scan converted to a pixel. If the
coordinate values of point P are
(3.3, 7.3) then the floor function of
x’=3 and y’=7, is plotted.
POINT DRAWING (RASTER DISPLAY)
y
x
SCAN CONVERTING A POINT (IN VECTOR
DISPLAY)
x  x  x  1
y  y  y  1

x´=Floor(x) and y´=Floor(y)

All points that satisfy:
are mapped to pixel (x´,y´)
Scan Converting A Line
SCAN CONVERTING A LINE
y  m x  b

The Cartesian slope- intercept equation
for a straight line is:
y y
m
x x
2
1
2
1
b  y  m x
1
y  mx
1
y
x 
m
SCAN CONVERTING A LINE

These equation form the basic for
determining deflection voltage in
analog devices.
y  mx
|m|<1
y
x 
m
|m|>1
y2
y1
x1
x2
LINE DRAWING ALGORITHMS
SCAN CONVERTING A LINE

On raster system, lines are plotted
with pixels, and step size (horizontal
& vertical direction) are constrained
by pixel separation.
SCAN CONVERTING A LINE

We must sample a line at discrete
positions and determine the
nearest pixel to the line at each
sampled position.
Digital Differential
Analyzer
(DDA Algorithm)
DDA ALGORITHM

Algorithm is an incremental scan
conversion method.

Based on calculating eitherx ory

If |m|<1,
(x  1)
Y  1
y  mx
y  y m
K 1
k
DDA ALGORITHM
y
x 
m
1
xK 1  xk 
m

If |m|>1,
If (x  1)
(y  1)
y  mx
y  y m
K 1
k
Circle Generation
Algorithms
CIRCLE GENERATION ALGORITHMS

The equation of a circle:
We could solve for y in terms of x
CIRCLE GENERATION ALGORITHMS

Computation can be reduced by
considering the symmetry of circles
Character Generation
CHARACTER GENERATION
Letters, numbers, and other
character can be displayed in a
variety of size and styles.
CHARACTER GENERATION
Attributes of characters
CHARACTER GENERATION

There are three basic methods to
generate characters,
1. Hardware based: Logic is built into the
graphics terminal and drawn quickly.
2. Bitmap based: utilizes pixels and copies
appropriate portion from frame buffer to
display
3. Vector based: provides with unlimited
possibilities with character style, size, shape