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UNIT-1
Introduction to Computer Graphics
Computer Graphics is the area where we study about
audio,vedeo and animation of the objects or we can also
say that drawing pictures on the screen is also called
computer graphics.
We can also say that its an art of drawing pictures on
computer screen with the help of programming.
1/11/2017 Amit Kr Pathak(CSE Deptt) Asst.Prof. 1

APPLICATION OF COMPUTER GRAPHICS
Computer graphics user interfaces (GUIs) – A graphic, mouse-oriented
paradigm which allows the user to interact with a computer.
Cartography – Drawing maps.
Weather Maps – Real-time mapping, symbolic representations.
Satellite Imaging - Geodesic images.
Photo Enhancement - Sharpening blurred photos.
Medical imaging - MRIs, CAT scans, etc. - Non-invasive internal
examination.
Engineering drawings - mechanical, electrical, civil, etc. - Replacing the
blueprints of
the past.
Typography - The use of character images in publishing - replacing the
hard type of
the past.
Architecture - Construction plans, exterior sketches - replacing the
blueprints and hand drawings .

Types of computer graphics
Basically there are two types of computer graphics
Raster Graphics
Raster graphics can be prepared with the help of individual pixels & Its
also called Bitmap images. A bitmap image contains a grid of individual
images

Vector Graphics
In this technique, the electron beam is directed only to the part of the
screen where the picture is to be drawn rather than scanning from left to
right and top to bottom as in raster scan. It is also called vector display,
stroke-writing display, or calligraphic display. Its also useses mathematical
relationship between points & path.

Frame Buffer & video controller
A frame buffer is a memory of contiguous location & Typically it is stored
in the memory chips on the video adapter.

Video controller
It is used to control the operation of the display device (Monitor/Screen).
Video controller accesses the frame buffer to refresh the screen. In figure,
the basic refresh operations of the video-controller are shown.
Raster System
Register 1 Register 2
Memory References
Frame Buffer
Pixel
Record

Line Drawing Algorithms
For drawing a line we need two end points so there are some algorithms
that provide line generation.
We know that Y=Mx + C
Where M=(Y2-Y1)/(X2-X1)
DDAAlgorithm: The full name of this algorithm is Digital
Differential Analyzer & the basics concept of this algo is as follows
1.A line can be specified in the form: Y=mx+c
2.Let m be between 0 to 1, then the slope of the line is between 0 and 45
degrees.
3. For the x-coordinate of the left end point of the line, compute the
corresponding y value according to the line equation. Thus we get the left
end point as (x1,y1), where y1 may not be an integer

4. Calculate the distance of (x1,y1) from the center of the pixel immediately
above it and call it D1.
5.Calculate the distance of (x1,y1) from the center of the pixel immediately below
it and call it D2.
6.If D1 is smaller than D2, it means that the line is closer to the upper pixel than
the lower pixel, then, we set the upper pixel to on; otherwise we set the pixel.
7. This method assumes the width of the line to be zero.

The Bresenham’s algorithm
This is the another incremental scan conversion algorithm &
The major advantage of this algorithm is that, it uses only
integer calculations not the fraction. Moving across the x axis in
unit intervals and at each step choose between two different y
coordinates.
Step 1 − Input the two end-points of line, storing the left end-
point in (x0,y0).
Step 2 − Plot the point (x0,y0).
Step 3 − Calculate the constants dx, dy, 2dy, and (2dy – 2dx)
and get the first value for the decision parameter as p0=2dy−dx
Step 4 −
If pk < 0, the next point to plot is (xk+1,yk) and
pk+1=pk+2dy
Otherwise,
pk+1=pk+2dy−2dx
Step 5 − Repeat step 4 (dx – 1) times.
For m > 1, find out whether we need to increment x while
incrementing y each time.

Circle Generation Algorithm
The first thing we can notice to make our circle drawing
algorithm more efficient is that circles centred at (0, 0) have
Eight-way symmetry
(x, y)
(y, x)
(y, -x)
(x, -y)(-x, -y)
(-y, -x)
(-y, x)
(-
x,y)
2
R

Mid Point Circle Generation Algo
Mid Point algo is the one of the circle generation algo which
is depend on eight point symmetry.

BRESENHAM’S CIRCLE ALGORITHM
1. Set X = 0 and Y = R
2.Set D = -(-3 +2R)
3.Repeat While (X < Y)
4. Call Draw Circle(X1, Y1, X, Y)
5. Set X = X + 1
6. If (D < 0) Then
7. D = D + 4X + 6
8. Else

Continued……
9. Set Y = Y –1
10. D = D + 4(X –Y) + 10
[End of If]
11. Call Draw Circle(X1, Y1, X, Y)
[End of While]
12.Exit

UNIT-II
Transformations
Basic Transformation
Transformed point=Transformation Matrix*Original Matrix
Translation
Rotation
Scaling

Matrix Representation
T = 1 0 tx
0 1 ty
0 0 1

Translation
A translation basically means adding a vector to a point, making a
point transforms to a new point
Changing the position of the object
P’(x’,y’)
Translated Place
P(x,y)
Original Place

Coordinate System
Rotation
Changing the position with angle
Ø

Coordinate System
Scaling
Reduces the size of the object(Magnifies)
a’=aSa
b=bSb

Composite Transformation
It is a special type of transformation which consider various aspects
of transformation compare to basic.

Some are as follows
1. Rotation about an arbitrary point
2. Scaling about a arbitrary Point
3. Reflection of an object about any line

Equations
1. RØ,P=TvRØT-v
2. S(Sx,Sy) , P(h,k)=Tv Sxy Sy T-v
3.Mr=TvRØMxR-ØT-v

Windowing & Clipping
windowing system is a system for sharing a computer's graphical display
presentation resources to various multiple applications at the same time
Clipping is the process of cutting the portion of the object with the help of specific
algorithm or dimension.

Clipping
 We need to clip objects outside the canonical
view volume
 Clipping lines (Cohen-Sutherland algorithm)
 Clipping polygons (Sutherland-Hodgman algorithm)

Clipping
aaa
X Axis

Clipping

Line Clipping Algo.
1. Cohen Sutherland Line clipping algo.
2.Liang Barsky line clipping algo.

Cohen–Sutherland algo
 This algo is used for line clipping & follow the divide-and-
conquer strategy.
 The algorithm divides a two-dimensional space into 9 regions
 Efficiently determines the lines and portions of lines that are
visible in the centre region of interest (the viewport).

Cohen–Sutherland algo
 Given a line segment with endpoint A(q1,q2) and B(q2,q3)
 Compute the 4-bit codes for each endpoint.
If both codes are 0000,(bitwise OR of the codes yields 0000 )
line lies completely inside the window
If both codes have a 1 in the same bit position (bitwise AND
of the codes is not 0000), the line lies outside the window.

Continued….
 If a line cannot be trivially accepted or rejected, at least one of the
two endpoints must lie outside the window and the line segment
crosses a window edge.
 Examine one of the endpoints, say P1=(q1,q2) . Read P1 as 4-bit code
in order: Left-to-Right, Bottom-to-Top.
 When a set bit (1) is found, compute the intersection I of the
corresponding window edge with the line from to . P1 to P2 Replace
P1 with I and repeat the algorithm.

Continued….
After clipping

Liang Barsky algorithm
Liang and Barsky have created an algorithm that uses floating-point
arithmetic but finds the appropriate end points with at most four
computations
 Express line segments in parametric form.
 Derive equations for testing if a point is inside the window
 Compute new parameter values for visible portion of line segment, if
any
 Display visible portion of line segment

Liang Barsky algorithm
 Read two end points of line P1 (x1, y1) and P2 (x2, y2)
 Read two corner vertices, left top and right bottom of
window: (XwMIN, YwMAX) and (XwMAX, YwMIN)
 Calculate values of parameters pi and qi for I =1, 2, 3, 4
such that
p1 = -Δx
q1 = x1 – XwMIN
p2 = Δx
q2 = XwMAX – xi
q1 = – Δy
q3 = y1 – YwMIN

Continued….
q2 = Δy
q4 = YwMAX – y1
 If pi = 0 then,
{
Line is parallel to ith boundary.
If qi < 0 then,
{
Line is completely outside the boundary. Therefore, discard
line segment and Go to Step 10.
}

Continued….
else
If line endpoints lie within the bounded area then
use them to draw line. Otherwise use boundary
coordinates to draw line. Go to Step 10.
 Initialize t1 = 0 and t2 = t1
 Calculate values for qi/pi for i= 1,2,3,4

Continued….
 Select values of qi/pi where pi<0 and assign maximum out of them
as t1.
 Select values of qi/pi where pi>0 and assign maximum out of them
as t2.
 If (t1 < t2)
{
Calculate endpoints of clipped line:
xx1 = x1 + t1 Δx
xx2 = x1 + t2 Δx
yy1 = y1 + t1 Δy
yy2 = y1 + t2 Δy
Draw line (xx1, yy1, xx2, yy2)
}
 Stop.

Polygon clipping
1.Sutherland Hodgeman Algorithm
2. Weiler and Atherton polygon clipping

Sutherland Hodgeman Algorithm
 Polygons can be clipped against each edge of the window one at a
time. windows/edge intersections, if any, are easy to find since the X or
Y coordinates are already known.
 Vertices which are kept after clipping against one window edge are
saved for clipping against the remaining edges

Sutherland …….
 Note that the number of vertices usually changes and will often
increases.
 We are using the Divide and Conquer approach.

Conditions of Polygon Clipping Algo
C 1 : Wholly inside visible region - save endpoint
C 2: Exit visible region - save the intersection
C 3 : Wholly outside visible region - save nothing
C 4 : Enter visible region - save intersection and end point .

Steps of Sutherland …….
Step 1: Clip Right of the Boundary
Step 2: Clip Bottom Boundary
Step 3:Clip Left Boundary
Step 4:Clip Top Boundary

Weiler and Atherton polygon clipping
This algorithm is used for clipping concave polygons

Weiler and Atherton Algo.
 In this algorithm we take a starting vertex like I1
 And traverse the polygon like I1, V3, I2.
 Leaving intersection the algorithm follows the clip polygon vertex list from
leaving vertex in downward direction.

Weiler and Atherton Algo.
 At occurrence of entering intersection the algorithm follows subject
polygon vertex list from the entering intersection vertex.
 This process is repeated till we get starting vertex.
 This process has to be repeated for all remaining entering
intersections which are not included in the previous traversing of
vertex list.

TYPE OF TEXT CLIPPING
A. Stardust
B. Bitmap
C. Stroke

STARDUST
 This method of character generation is called
stardust method because of its characteristics
appearance.
 a code conversion software is used in it to display a
character .
 A character quality is also poor.

BITMAP
 In bitmap method characters are represented by array of dots in the
matrix form.
 It is 2D array that means having rows and columns.
 Each dot in the matrix is pixel.
 The value of pixel control the intensity of the pixel.

STROKE
 This method uses small line segments to generate a character
 we can built our own stoke method character generate by call through the
line drawing algorithm.
 In this method a fixed pattern of line segments are used to generate the
characters.
 There are 24 line segments. out of these 24 line segments the segments
required to display for a particular character are highlighted.

UNIT-III
3D Geometric Primitives
 Polygon meshes and polyhedra are the geometric figures that are created
with a surface modeler.
 A polygon mesh is a collection of edges, vertices and polygons connected
in such a way that each edge is shared by at most two polygons.
 Polyhedra are volumetric solids, such as the cube or a sphere, represented
as facets.

3D Object Representation
 Polygon and Quadric surfaces
 Spline surfaces and construction
 Procedural methods

3D Transformation
Rotation
Scaling
Translation

Rotation
In 3D rotation, we have to specify the angle of rotation along with the axis
of rotation
Rotation about x-axis
X-Axis
Y Axis
Z Axis1/11/2017 Amit Kr Pathak(CSE Deptt) Asst.Prof. 52

Y Axis
X Axis
Z Axis
Rotation About Y Axis

Y Axis
X Axis
Z Axis
Rotation About Z Axix

3D Viewing
For representing 3D-objects on a 2D -screen in a nice or recognizable
way, many techniques are combined. First, the projection has to be
defined, which will be described in the next paragraph

Possible Qualities
Wire-Frame-Representation: Only the edges of polygons are drawn.
Depth-Cueing = Edges or parts which are nearer to the viewer are displayed
with more intensity.
Correct Visibility = Surface-elements (edges, polygons), which are occluded
by other surface-elements, are not drawn so that only visible areas are shown.

3D-Viewing-Pipeline
Object
Coordinate
world Co. Viewing Co.
Projection Co.
Normdivice Co.
Device Coordinate
Creation of
Object
Creation of
Object
Definition Projection
Mapping
Transform to
specific region

Projections
Process of moving in positive with time through imaging of future events or
calculation based on past trends.
However, in computer graphics mainly only the parallel and the perspective
projection are used generally. In geometry science various types of
projections are known

Projections
Y
Z
X

Projections
Parallel Projection
Perspective Projection

Perspective
Projections
One Point
Two Point
Three Point

For parallel projections, we specify a direction of projection instead of a
Centre of projection
There are two types of parallel projections:
Orthographic projection – DOP perpendicular to PP
Oblique projection --- DOP not perpendicular to PP

3D Clipping
In 3D clipping you do everything in 3D space. Map graphics
are clipped to one side of an arbitrary clipping plane in one
or more clipping stages.

Cohen Sutherland 3D Clipping Algo
The outcode for 3D clipping is a 6-bit code
 Bit 1 - point above view volume
 Bit 2 - point below view volume
 Bit 3 - point to the right of view volume
 Bit 4 - point to the left of view volume
 Bit 5 - point behind view volume
 Bit 6 - point in front of view volume

UNIT-IV
Bézier curve
A Bézier curve approximates any number of control points for a curve section

Curves and Surfaces
Quadric surfaces
X
Y

X
Y
Quadratic Surfaces

Blobby Object
 A Blobby Object is non rigid object like
 Like rubber,liquids,water droplets cloths etc.
 These objects tend to exhibit a degree of fluidity

Continued….
 Several models have been developed to handle
these kind of objects.
 One technique is to use a combination of Gaussian
density functions (Gaussian bumps)

Spline Representations
 A spline is a flexible strip used to produce a smooth curve through a designated
set of points
 Small weights would be distributed along the strip to hold
 it in position on the drafting table

Spline Specifications
There are three different ways to specify splines
 state the set of boundary conditions that are imposed on the spline
 state the matrix that characterizes the spline
 state a set of blending/basis function that determines how specified constraints
on the curve are combined to calculate positions along the curve path

Boundary Condition Example
 Boundary conditions may be the coordinates of x(0), x(1) and the derivatives
x’(0), x’(1). These four numbers are enough to fix ax, bx, cx, dx
 After this representation we can connected to the other representations.

Interpolation and Approximation Splines
To specify a spline we need to give a set of coordinate positions called control
points

Hidden Lines and Surfaces
 Back-Face Detection
 Depth-Buffer Methods
 A-Buffer Methods
 Scan-Line Methods
 Depth-Sorting Method

Basic illumination models
 Light Sources
 Basic Illumination Models
 Displaying Light Intensities

Ambient Light
 Approximates the indirect illumination
 Equal amount of light from all directions
 I K=(I is intensity of ambient light & K=percentage of the light
reflected by the object)

Lighting at a point on surface surface
I = Ikdcosθ
I=intensity of light
K=coefficient of diffuse reflection

A
B
C
Surface
P

Diffuse reflection
I = Idkd(N.L)
Id(N.L) is like the irradiance
kdI is like the reflectivit
No dependency on viewer

Specular reflection and Phong model
P
A
A2

Specular Component Component
 One area depend on other
 Some time depends on both
 Numbers controls the view dependency.

Intensity Attenuation
 Providing enough control so that one can simulate
effect via trial and error of many different
parameters
 May be not be close to the physical phenomenon
 If we see different brightness of the same light can
be used for different component computation

Properties of Bézier curves
 Passes through start and end points P0 & Pn.
 First derivates at start and end
 Lies in the convex hull

Shading
 Independent of the Illumination model used
 Phong Shading and Phong Illumination
 Simple and hence widely used

Phong Shading
 Calculate the illumination at every pixel using rasterization
 Interpolate the normal across the triangle
 Slower than Gauaurd

Gouraud Shading Shading
 Edges get same color, irrespective of which triangle
they are rendered from Shading is continuous at edges
 Tends to spread sharp illumination spots over the triangle
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