Applications of Computer Graphics. Business applications Maps Industrial applications Consumer applications Entertainment Education.
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Applications of Computer Graphics
• Business applications
• Maps
• Industrial applications
• Consumer applications
• Entertainment
• Education
Weather maps: Temperature, heat flow, rainfall
architecture
CAD
Mechanical engineering
Electric circuit design
simulators
Chemical plants
Consumer products
Medical applications
Molecular Biology
movies
Video games
Computer art
Hierarchical modeling
2. Transformations
3. Clipping
4. Creating Curved surfaces
3D Graphics
5. 3D Transformations
6. Parallel projections
7. Perspective views
Hidden Surface elimination
8. Hidden Surface elimination
Painter’s algorithm
• Depth sorting
Steps in painter’s algorithm
Generation of surfaces
Surfaces
Bilinear Interpolation
v
u
b00
b10
b11b01
u
v
Bilinear interpolation fits the simplest surface for the four corner points
Shape Representation
Surfaces
Bilinear Interpolation
Two Stage Process
v
v
bb
bb uu
ubbuvubvuX
vbbvb
vbbvb
11
)1(),(),(
)1(
)1(
1110
0100
0110
0100
1100
11100110
01000100
1
0
1
0
11 )()(),(i j
jiij vBuBbvuX
b11b01
b01
b01
Shape Representation
Surfaces
Coon’s Patch
Given Four Boundaries C1(u),C2(u),D1(v),D2(v)
)(),1(
)(),0(
)()1,(
)()0,(
2
1
2
1
vDvX
vDvX
uCuX
uCuX
v
u
C2
C1
D1D2
Shape Representation
Surfaces
Coon’s Patch
C1
C2
rC
Ruled surface between C1(u),C2(u)
D1
D2
rD
Ruled surface between D1(v),D2(v)
Shape Representation
9. Bezier surface
Bezier surface patch
Bezier surface patches
Bspline surface patch
Rendering
Illumination and shading models
10. Shading
• Diffused lighting • Specular Phong model
Diffuse lighting model
Diffuse lighting model
Phong specular model
Phong specular model
n=15
10
large n: metalssmall n: paper
Specular Reflection
Background
IlluminationRendering
Transparent & translucent objects
Transparent objects
Polygon Shading
Flat Shading
• Computationally fast• Not smooth• Mach Band effect
ShadingRendering
Flat shading & Gourad shading
Flat polygon shading
Gouraud Shading
Interpolation
Ia Ib
I2
I3
I4Is
Scan line
Polygon Shading
I1 (x1, y1)
(x2, y2)
(x3, y3)
(x4, y4) Scan conversion!
ShadingRendering
Phong Shading
Polygon Shading
Na Nb
N2
N3
N4Ns
Scan line
N1 (x1, y1)
(x2, y2)
(x3, y3)
(x4, y4)
Ns Is
Illumination using Ns
ShadingRendering
Generation of solids
11. Generation of solids
Surfaces
Sweep Surfaces
Translation sweep of a circle generates a cylinder
Translation sweep of a circle accompanied by scaling generates cone
Shape Representation
Sweep solids
9b. Constructive solid geometry
CSG
AU
Fractals
12. Fractals
Generating a dragon fractal
Fractal dimension
Computer Animation
Computer Animation
Conventional Animation
Process
• Story boardSequence of drawings with descriptions
• Key framesA few important frames as drawings
• InbetweensDraw the rest of the frames
• PaintingRedraw onto acetate Cels, color them
Computer Animation
Conventional Animation
Stretch and Squash
Exaggeration with believability
Computer Animation
Real Time vs. Image by Image
a) Real Time: Compute - Drawb) Image by Image: Compute – Store - Drawc) Display rate: 30 fps or 25 fps
Animation characteristics
• Spatial (position, orientation, form )• Temporal (velocity, acceleration )• Visual (color, texture )
Computer Animation
Key Framing
• Selected (key) frames are specified• Interpolation of intermediate frames• Simple and popular approach• May give incorrect (inconsistent) results
Computer Animation
Key Framing
Interpolation
Spline
Computer Animation
• Characteristic parameters for motion are specified and interpolated.• Less data is required
e.g for motion of an arm, the parameter could be rotation angle.
Parametric
Computer Animation
Laws of motion: physical or procedural animation
t
y linear
actual
Algorithmic
Simulation
Computer Animation
Example
Computer Animation
Transformation of object shapes from one form to another
• Each form may be considered as a key frame• Establish common topology for the two key frames• Interpolate the intermediate frames
t
added point
Intermediate form
Morphing
Computer Animation
Transformation of one image (source) to another image (target)
• Normalization of both images• Feature correspondence• Warping of the two images (spatial deformation)• Color blending
Image Morphing
Computer Animation
Without feature correspondence (cross dissolving)
Source Destination
Image Morphing
Computer Animation
Image Morphing
Correspondence
Computer Animation
Image Morphing
Correspondence
Computer Animation
Triangle Method• Feature points are marked on source and target.• These feature are given the correspondence. • Triangulate the points.• Interpolate triangulation for intermediate frames.• Warp the images, and blend colors.
Source Target
Image Morphing
Computer Animation
Particle Systems
An object is represented as cloud of particles
Particles are not static; particle system evolves
Non deterministic
Particles are simple (computationally efficient) but can model complex amorphous objects and behaviors
Dust, Water fall, Rain, Fire, Cloud, Stars, Grass, Fur, etc
Computer Animation
Particle Systems
• Generate new particles with initial attributes
• Particles have lifespan: Kill-off dead particles
• Modify particle attributes: color, position
• Render particles
In a typical particle system
Computer Animation
Particle Systems
Particle Termination
For each new frame, particle’s life time is decremented by one
When life time = zero, the particle is removed
Computer Animation
Particle Systems
Particle Animation
Particle dynamics
From force find acceleration
velocity
position
Other attributes (color, opacity, etc.) may also change with time
Computer Animation
Particle Systems
Examples
Computer Animation
Particle Systems
More Examples
Smoke and Fire
Computer Animation
Particle Systems
A grass clump is a particlesystem
A particle is a blade of grass
Draw parabolic streak over entire life time
• Obvious approach for any camera moving shot
• The camera-character relationship is very
fundamental to animation
• View dependent animation – animation that
automatically changes in response to changes in
view point
View Dependent Character Animation
View Dependent Character Animation
View Dependent Character Animation
Camera Recovery
View Dependent Character Animation
Deformation
View Dependent Character Animation
View Dependent Character Animation
Cloth Modeling
Suggested Readings
• Computer graphics by Hearn and Baker, Pearson Publications
• Computer graphics by Foley, Van Dam, and others, Pearson Publications
• Computer graphics by Hanmandlu, BPB publications
• Procedural elements of Computer Graphics by Rogers, McGraw Hill
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