UNIT-4: Representing Curves and Surfaces
In computer graphics,
curves and surfaces are represented using mathematical models. The most common
models are:
·
NURBS (Non-Uniform Rational B-Splines)
·
Bézier
Curves
·
Bézier
Surfaces
These models give
us precise control over the shape of curves and surfaces. They
are easy to manipulate and animate.
[IMAGE IDEA: Different
Types of Curves]
text
Copy
Download
Bézier Curve NURBS Curve B-Spline Curve
● ● ●
/
/ \ / \
/ / \ / \
● ● ● ● ●
\ \ / \ /
\ \ / \ /
● ● ●
(Simple curve) (More complex curve) (Smooth continuous curve)
Why are these models
popular?
·
Their parameters can
be changed to create many different shapes and styles
·
They are widely used
in computer graphics and animation
·
To use them, you need
to understand the math behind them and know the software tools
Polygon Meshes (Parametric)
A polygon mesh is
a way to represent surfaces in computer graphics. It is made up of many small
polygons (triangles or quadrilaterals).
[IMAGE IDEA: Polygon
Mesh]
text
Copy
Download
Simple Polygon Mesh Detailed 3D Model
┌─────┐ ┌─────────┐
│╲ │
│╲ │╲
│ ╲ │ │ ╲ │ ╲
│ ╲ │ │ ╲ │ ╲
│ ╲
│ │ ╲ │ ╲
│ ╲│
│ ╲ │ ╲
└─────┘ └─────╲──┘─────╲
╲ ╲
╲ ╲
╲ ╲
╲ ╲
╲ ╲
╲ ╲
╲╲
Surface divided into small triangles Complex shape from many triangles
Key Terms:
·
Vertices – Points in space that define the
corners of polygons
·
Polygons – Flat shapes (triangles or
quadrilaterals) that make up the mesh
·
Parametric
representation – Using math
equations to define each vertex's position
Example: Creating a Torus (Donut Shape)
[IMAGE IDEA: Torus
(Donut Shape)]
text
Copy
Download
┌─────────────────────────────┐
│ │
│
╭───╮ │
│
╱ ╲ │
│
│ ○ │ │
│
╲ ╱ │
│
╰───╯ │
│
│
└─────────────────────────────┘
A torus is a donut-shaped object
How to create a torus
using a polygon mesh:
1. Use a mathematical equation to define each
vertex's position
2. The equation uses two angles:
o
Polar
angle – determines the
radius of the donut
o
Azimuthal
angle – determines
position around the donut's circumference
3. Divide the torus surface into many small
polygons
4. Each polygon is defined by a set of vertices
5. Each vertex's position is calculated using the
parametric equation
Result: A precise, controllable shape that can
be easily changed and animated over time.
Cubic Curves
A cubic curve is
defined by cubic (third-degree) polynomials. It is a type of spline
curve.
[IMAGE IDEA: Cubic
Curve with Control Points]
text
Copy
Download
Control Point 2 ●
╲
╲
╲
╲
● Control Point 3
╲
╲
╲
╲
Control Point 1 ● ● Control Point 4
The curve passes near control points 1 and
4,
and is influenced by points 2 and 3
Properties of Cubic Curves:
·
Defined by a set
of control points
·
Smooth
and continuous between control
points
·
Used for modeling
smooth curves (like character limbs or object shapes)
·
Used in motion
graphics for smooth transitions between keyframes
Example: Animating a Bouncing Ball
[IMAGE IDEA: Bouncing
Ball Animation Path]
text
Copy
Download
Height
↑
│ ● (keyframe 1 - top)
│ /╲
│ / ╲
│ / ╲
│/ ╲
●
● (keyframe 3 - top)
│╲ ╱│
│ ╲ ╱ │
│ ╲ ╱ │
│ ╲╱ │
│ ● │ (keyframe 2 - bottom)
│ │
└─────────┼─────────→ Time
│
Cubic curve path
Steps to create the
animation:
1. Define keyframes – positions
and velocities at specific times
2. Use cubic curves to smoothly
interpolate between keyframes
3. The path of the ball becomes smooth and
continuous
4. No sudden, jagged changes in trajectory
Result: A smooth, natural-looking animation.
UNIT-5: Introductory Concept of
Multimedia
What is Multimedia?
The word Multimedia comes
from two words:
·
Multi = Many
·
Media = Material through which something is
transmitted
Multimedia combines all media elements (text, graphics,
audio, video, animation) to make information more effective and attractive.
[IMAGE IDEA:
Multimedia Components Diagram]
text
Copy
Download
┌─────────────────────────────────────┐
│ MULTIMEDIA │
└─────────────────────────────────────┘
│
┌─────────────┬───────────────┼───────────────┬─────────────┐
│ │ │
│ │
▼ ▼ ▼ ▼ ▼
┌───────┐ ┌───────┐ ┌───────┐ ┌───────┐ ┌─────────┐
│ TEXT │ │ AUDIO │ │GRAPHICS│ │ VIDEO │ │ANIMATION│
└───────┘ └───────┘ └───────┘ └───────┘ └─────────┘
│ │ │
│ │
▼ ▼ ▼ ▼ ▼
Titles, Music,
Images, Moving Moving
Headlines, Speech Drawings, pictures drawings
Menus Photos with sound
Components of Multimedia
1. Text
Text is the most
common way to represent information. In multimedia, text is mostly used for:
·
Titles
·
Headlines
·
Menus
Common software for
viewing text:
·
Microsoft Word
·
Notepad
·
WordPad
Common file
extensions: .DOC, .TXT
[IMAGE IDEA: Text
Examples]
text
Copy
Download
┌─────────────────────────────────────┐
│ │
│ WELCOME TO
MULTIMEDIA │ ← Title (Large text)
│ │
│ ┌─────────────────────────┐ │
│ │ • File │ │ ← Menu text
│ │ • Edit │ │
│ │ • View │ │
│ │ • Help │ │
│ └─────────────────────────┘ │
│ │
│ This is example of
normal │ ← Body text
│ text in a multimedia
project. │
│ │
└─────────────────────────────────────┘
2. Audio
Audio in multimedia
includes recording and playing sound. Audio makes information easier to
understand and improves clarity.
Types of audio:
·
Speech (voice)
·
Music
·
Sound effects
Common software for
playing audio:
·
Quick Time
·
Real Player
·
Windows Media Player
[IMAGE IDEA: Audio
Waveform]
text
Copy
Download
Amplitude
↑
│ /\ /\
/\
│ / \
/ \ / \
│ / \/
\ / \
│ / \/ \
│/ \
└──────────────────────────→ Time
(Sound wave representation)
3. Graphics
Every multimedia
presentation is based on graphics. Graphics make concepts more effective and
presentable.
Common software for
viewing graphics:
·
Windows Picture Viewer
·
Internet Explorer
Common software for
editing graphics:
·
Adobe Photoshop (can
edit and make graphics effective and attractive)
[IMAGE IDEA: Graphics
Example]
text
Copy
Download
┌─────────────────────────────────────┐
│ │
│ ● │
│ ╱ ╲ │
│ ╱ ╲
│
│ ╱ ╲
│
│ ╱ ╲ │
│ ╱
╲ │
│●───────────● │
│ │
└─────────────────────────────────────┘
(Example: A triangle graphic)
4. Video
Video means moving
pictures with sound. It is the best way to communicate. In multimedia, video
makes information more presentable and saves time.
Common software for
viewing video:
·
Quick Time
·
Windows Media Player
·
Real Player
[IMAGE IDEA: Video
Frames]
text
Copy
Download
Frame 1
Frame 2 Frame 3 Frame 4
┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐
│ ● │ │ ● │ │ ● │ │ ● │
│ │ → │ │ │ → │ │ │ → │ │ │
│ │ │ │ │ │ │ │ │ │ │ │
└─────┘ └─────┘ └─────┘ └─────┘
(A person walking - multiple frames create
motion)
5. Animation
Animation makes
changes to images so that a sequence of images appears to be moving pictures.
An animated sequence shows many frames per second to create the illusion of
motion.
Common software for
viewing animation:
·
Internet Explorer
·
Windows Pictures
·
Fax Viewer
[IMAGE IDEA: Animation
Frames for a Bouncing Ball]
text
Copy
Download
Frame 1
Frame 2 Frame 3 Frame 4 Frame 5
● ● ●
● ● ●
● ● ●
● ●
●
(Ball moving down and up - each frame is
slightly different)
Applications of Multimedia
Multimedia is used in
many fields: Education, Entertainment, Business, and more.
1. Multimedia in Education
Multimedia is becoming
very popular in education. It is used to:
·
Prepare study
materials for students
·
Provide better
understanding of different subjects
Edutainment (Education + Entertainment) is now very
popular. It provides learning AND entertainment to the user.
[IMAGE IDEA:
Edutainment]
text
Copy
Download
┌─────────────────────────────────────┐
│ │
│ ┌─────────┐ ┌─────────┐ │
│ │LEARNING │ + │FUN/PLAY │ │
│ └─────────┘ └─────────┘ │
│ ↓ ↓ │
│ ┌─────────────────┐ │
│ │ EDUTAINMENT
│ │
│ └─────────────────┘ │
│
│
└─────────────────────────────────────┘
2. Multimedia in Entertainment
Computer graphics
techniques are now commonly used in movies and games.
Movies:
·
Multimedia gives
special audio and video effects
·
Has changed the art of
making movies
·
Difficult effects and
action scenes are only possible through multimedia
Games:
·
Uses computer
graphics, animation, videos
·
Provides fast action,
3D effects, and high-quality sound effects
·
Only possible through
multimedia
3. Multimedia in Business
Multimedia is used in
every aspect of business today.
a) Video Conferencing:
·
Enables communication
using audio and video between two locations
·
Users communicate
through their computers
·
Saves time, energy,
and money
[IMAGE IDEA: Video
Conferencing]
text
Copy
Download
Location A Location B
┌─────────────┐ ┌─────────────┐
│ │ │ │
│ ● Person │ Audio + Video │ ● Person │
│ A │ ←──────────────────→ │ B
│
│ │ via Internet │ │
└─────────────┘ └─────────────┘
Two people communicating from different
locations
b) Marketing and
Advertising:
·
Advertisements and
marketing ideas on television and internet are possible with multimedia
CD-ROM and Multimedia Highway
CD-ROM (Compact Disc - Read Only Memory)
CD-ROM has become the
most cost-effective way to distribute multimedia projects.
[IMAGE IDEA: CD-ROM
Disc]
text
Copy
Download
┌─────────────────────────────────────┐
│ ╭─────────────────────────────────╮ │
│ │ │ │
│ │ ┌───────┐
│ │
│ │ │ CD-ROM │
│ │
│ │ │
Disc │ │ │
│ │ └───────┘
│ │
│ │ │ │
│ │ Can hold:
│ │
│ │ • 80 minutes of video │ │
│ │ • Or 80 minutes of sound │ │
│ │ • Or images, text, animation │ │
│ │ │ │
│ ╰─────────────────────────────────╯
│
└─────────────────────────────────────┘
Key Facts about
CD-ROM:
·
Can be mass-produced
very cheaply (pennies per disc)
·
Can hold up to 80
minutes of full-screen video or sound
·
Can contain unique
mixes of images, sound, text, video, and animation
·
Controlled by an
authoring system for user interaction
DVD-ROM (Digital
Versatile Disc):
·
Multi-layered
technology
·
Increases capacity up
to 18 GB
·
CD and DVD burners can
read discs and make them
·
Used for audio, video,
and data formats
The Multimedia Highway (Data Highway)
Telecommunications
networks are now global. Information will be linked online as distributed
resources on a data highway (like a toll road).
[IMAGE IDEA:
Multimedia Highway]
text
Copy
Download
┌─────────────────────────────────────────────────────────────┐
│
│
│ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │
│ │User │ │User │ │User │ │User │ │User │ │
│ │ A │ │ B │ │ C │ │ D │ │ E │ │
│ └──┬──┘ └──┬──┘ └──┬──┘ └──┬──┘ └──┬──┘ │
│ │ │
│ │ │ │
│ └──────────┼──────────┼──────────┼──────────┘ │
│ │ │
│ │
│
┌───┴──────────┴──────────┴───┐
│
│
│
│ │
│
│ MULTIMEDIA
HIGHWAY │ │
│ │
(Internet/Network) │ │
│
│
│ │
│
└───┬──────────┬──────────┬───┘
│
│ │ │
│ │
│
┌────┴────┐ ┌───┴────┐ ┌───┴────┐ │
│
│Database│ │Server │ │Cloud │
│
│
│ A │ │
B │ │Storage │ │
│
└────────┘ └────────┘ └────────┘ │
│
│
└─────────────────────────────────────────────────────────────┘
What is possible today
(not science fiction):
·
Full-text content from
books and magazines accessible by modem
·
Feature movies played
at home
·
Real-time news reports
from anywhere on earth
·
Lectures from
universities for education credits
·
Street maps of any
city with restaurant recommendations
·
Online travelogues
with testimonials and video tracks
Definition of Animation
Animation is one of the most exciting forms of
pictorial presentation.
"Animation refers
to a simulated motion picture depicting movement of drawn (or simulated)
objects."
Three main features of animation:
1. Picture – Animation is a kind of pictorial representation
2. Motion – Animation depicts apparent movement
3. Simulated – Objects are artificially created through drawing or
simulation
"The potential
educational benefits of animation arise from its capacity to portray temporal
change directly and explicitly."
Usages and Function of Multimedia Animation in Education
Typical Usages:
1. To attract attention
2. To inform about the state of a process (e.g., progress bars showing program
loading percentage)
3. Demonstrations (e.g., how a volcano erupts from moving
tectonic plates)
4. Interactive simulation (e.g., learner fuels and points a
rocket, then sees its flight path)
Pedagogical Functions:
|
Function |
Description |
|
Motivation |
Get students interested in a
phenomenon and explore it |
|
Representation |
Help support mental representation |
|
Organization |
Organize information better |
|
Interpretation |
Provoke cognitive conflicts that
make students think |
Types of Animation Techniques
[IMAGE IDEA: Animation
Types Overview]
text
Copy
Download
ANIMATION TYPES
│
┌─────────────────────┼─────────────────────┐
│ │ │
▼ ▼ ▼
┌─────────┐
┌─────────┐ ┌─────────┐
│ 2D
│ │ 3D │
│ Stop │
│Animation│
│Animation│ │ Motion │
└─────────┘
└─────────┘ └─────────┘
│ │ │
▼ ▼ ▼
Traditional Digital 3D Stop-motion
(Hand-drawn) (Computer) (Puppets/Objects)
1. Traditional Animation (Classical 2D Animation)
Traditional animation
involves animators drawing by hand for each and every frame.
[IMAGE IDEA:
Traditional Animation Process]
text
Copy
Download
Frame 1
Frame 2 Frame 3 Frame 4
┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐
│ ● │ │ ● │ │ ● │ │ ● │
│ │ │ │ │ │ │ │ │ │ │ │
└─────┘ └─────┘ └─────┘ └─────┘
↓ ↓ ↓ ↓
Drawing
Drawing Drawing Drawing
1 2 3 4
(Each frame drawn by hand on paper)
Process:
1. Create numerous drawings
2. Feed them into plastic cells
3. Hand paint them
4. Create animated sequence on painted background
image
Famous Traditional
Animation Movies:
·
Snow White and the
Seven Dwarfs
·
Peter Pan
·
Sleeping Beauty
·
Aladdin
2. Digital 2D Animation
Creating animations in
2D space with the help of digital technologies.
[IMAGE IDEA: Digital
2D Animation Workflow]
text
Copy
Download
Draw on
→ Scan or →
Animate on
Paper Draw on Tablet Computer
┌─────┐
┌─────┐ ┌─────┐
│ ● │
│ ● │
│ ● │
└─────┘
└─────┘ └─────┘
↓ ↓ ↓
Rough Digital Completed
Drawing Drawing Animation
Key features:
·
No need to create
digital models
·
Just need to draw the
frames
·
Using software like
Adobe Flash, animators can limit the number of drawings
·
Small variations
(color, frame rate) can be changed almost instantly
3. Digital 3D Animation
Making unreal characters
look realistic.
[IMAGE IDEA: 3D
Animation Process]
text
Copy
Download
2D Sketch 3D Model Textured Animated
(Wireframe) Model Character
┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐
│ ● │
→ │ ┌─┐ │ → │ ███ │ → │ ███ │
│ │ │ │ │ │ │ ███ │ │ ███→│
└─────┘ └─┴─┘ ┘ └─────┘ └─────┘
Advantages:
·
Characters are much
faster to create
·
Highly realistic
·
Popular in movie making
industry
·
Used for short films,
full-length movies, TV commercials
4. Stop-Motion Animation
Using frame-by-frame
animation, physical static objects are moved around and shown in fluid movement
during post-production.
[IMAGE IDEA:
Stop-Motion Setup]
text
Copy
Download
Camera
│
▼
┌─────────────────────┐
│
┌───┐ │
│
│ │ │
│
│ ○ │ (Move │
│
│ │ slightly │
│
└───┘ each │
│
frame) │
└─────────────────────┘
Take photo → move object slightly → take
another photo
(Repeat many times)
History:
·
Has been around since
the evolution of puppets
·
"Fun in a Bakery
Shop" (1902)
·
"The Teddy
Bears" by Edwin Porter (one of the earliest stop-motion films)
5. Mechanical Animation
Instead of robotics,
machines can be animated using mechanical animation technique.
Benefits:
·
No need to create the
original machine
·
Helps animator
understand how the machine works
·
Easy to explain
functionality of machines
6. Audio-Animatronics and Autonomatronics
Audio-Animatronics:
·
Trademark created by
Walt Disney Imagineering
·
Used in Disney theme
parks
·
Repeats a
pre-programmed show over and over again
Autonomatronics:
·
More advanced
technology
·
Uses sophisticated
cameras and sensors
·
Otto (a robot) can
sense a person in a room
·
Can converse with them
·
Can tell if they are
happy
·
Can make choices about
what to say and do
7. Chuckimation
Created by
"Action League Now!" creators.
Characteristics:
·
Combination of
stop-frame animation and live shots
·
Characters are dropped
into a particular frame
·
Similar to famous
puppet shows
8. Puppetry Animation
Created using
life-like puppets instead of objects.
[IMAGE IDEA: Puppetry
Animation]
text
Copy
Download
Puppet on set (moved slightly each frame)
│
▼
┌─────────────────┐
│ │
│
┌─┐ │
│
│P│ (move │
│
│u│ puppet│
│
│p│ frame │
│
│p│ by │
│ │e│
frame)│
│
│t│ │
│
└─┘ │
└─────────────────┘
History:
·
"The Humpty
Dumpty Circus" (1908) – first stop-motion animation film featuring puppets
·
Created by J. Stuart
Blackton and Albert Smith
Famous Examples:
·
King Kong (1933) –
used puppet animation
·
The Nightmare Before
Christmas (1993) – American stop-motion musical fantasy horror film
o
Used 227 puppets to
represent characters
o
Used 400 heads to show
every possible emotion
Summary Table of Animation Types
|
Animation Type |
Description |
Examples |
|
Traditional (2D) |
Hand-drawn frame by frame |
Snow White, Aladdin |
|
Digital 2D |
Computer-assisted 2D drawing |
Web animations, Flash |
|
Digital 3D |
Computer-generated 3D models |
Modern movies, games |
|
Stop-Motion |
Physical objects moved frame by
frame |
The Nightmare Before Christmas |
|
Mechanical |
Animating machines virtually |
Product demonstrations |
|
Audio-Animatronics |
Pre-programmed animatronic
characters |
Disney theme parks |
|
Autonomatronics |
Sensor-driven, interactive robots |
Otto (Disney) |
|
Chuckimation |
Dropping characters into frames |
Action League Now! |
|
Puppetry |
Using puppets in stop-motion |
King Kong, The Nightmare Before
Christmas |