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

Z – buffer algorithm

Painter’s algorithm Depth sorting

Steps in painter’s algorithm

Generation of surfaces

Surfaces Bilinear Interpolation v u b 00 b 10 b 11 b 01 u v Bilinear interpolation fits the simplest surface for the four corner points Shape Representation

Surfaces Bilinear Interpolation Two Stage Process b 11 b 01 Shape Representation

Surfaces Coon’s Patch Given Four Boundaries C 1 (u),C 2 (u),D 1 (v),D 2 (v) v u C2C2 C1C1 D1D1 D2D2 Shape Representation

Surfaces Coon’s Patch C1C1 C2C2 rCrC Ruled surface between C 1 (u),C 2 (u) D1D1 D2D2 rDrD Ruled surface between D 1 (v),D 2 (v) Shape Representation

9. Bezier surface

Bezier surface patch

Bezier surface patches

Bspline surface patch

Rendering Illumination and shading models

10. Shading

Diffused lightingSpecular Phong model

Diffuse lighting model

Phong specular model

Powers of cos Ə

n= large n: metals small n: paper Specular Reflection Background Illumination Rendering

Transparent & translucent objects

Transparent objects

Polygon Shading Flat Shading Computationally fast Not smooth Mach Band effect Shading Rendering

Flat shading & Gourad shading

Flat polygon shading

Gouraud Shading Interpolation IaIa IbIb I2I2 I3I3 I4I4 IsIs Scan line Polygon Shading I1I1 (x 1, y 1 ) (x 2, y 2 ) (x 3, y 3 ) (x 4, y 4 ) Scan conversion! Shading Rendering

Phong Shading Polygon Shading NaNa NbNb N2N2 N3N3 N4N4 NsNs Scan line N1N1 (x 1, y 1 ) (x 2, y 2 ) (x 3, y 3 ) (x 4, y 4 ) N s I s Illumination using N s Shading Rendering

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

AUAU

Fractals

12. Fractals

Generating a dragon fractal

Fractal dimension

Computer Animation

Conventional Animation Process Story board Sequence of drawings with descriptions Key frames A few important frames as drawings Inbetweens Draw the rest of the frames Painting Redraw 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 - Draw b) Image by Image: Compute – Store - Draw c) 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 ylinear 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) SourceDestination 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. SourceTarget 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 particle system 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

Camera Recovery View Dependent Character Animation

Deformation 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