CG endsem 3 and 4

Question 1

Explain interpolation and approximation

Answer 1

techniques used to construct curves, surfaces, or values from a set of known data points
- Interpol
estimating values within the range…by constructing a curve or function that passes exactly through those points.
1 Bezier curves and B-splines:
2 Color interpolation:
3 Keyframe animation:
linear, polynomial, spline
- Approx
estimating a function or shape that does not necessarily pass through all the given data points, fits them as closely as possible
1 Bézier and B-spline curves(maintain smoothness)
2 Rendering techniques: (lighting tech)
3 Surface fitting: (complex models)
b-spline, least squares

Question 2

Explain bezier curve. List its properties

Answer 2

• parametric curve to construct scalable, smooth shapes
• consists of control points and mathematical functions
  linear, quadratic, cubic, higher degree
  1 start and end points
  2 tangents
  3 convex hull
  4 smoothness
  5 local control
  6 symmetry (reverse curve)
  7 derivative
  applic - animation and motion paths, vector drawing

Question 3

Explain Hilbert’s curve with an example

Answer 3

• type of space-filling curve
• fills a 2D space entirely by passing through every point in a grid-based area without crossing itself.
• constructed recursively
  2x2
  4x4
  8x8
• continuous line, recursion level - infinity
  applic- image processing, scientific computing

Question 4

What is animation? What are the types of animation?

Answer 4

creating the illusion of motion by displaying a sequence of static images or frames over time
1 2d hand drawn
2 2d digital
3 3d
4 stop motion
5 real time
6 motion graphics (animated design elements)

Question 5

Explain method of controlling animation

Answer 5

how motion or changes over time are defined, managed, and manipulated
1 Keyframe animation (computer interpolates the frames in between.)
2 Scripting or programming (Motion and behavior are controlled through code or scripts)
3 Path-Based Animation (fixed path - Camera along bezier curve)
4 Parameter based (rules, math functions - bouncing ball)
5 MoCap (human movement applied to digital char)

Question 6

What are fractals (CG) ? Explain Triadic Koch in detail.

Answer 6

• patterns that repeat at different scales, creating self-similar shapes.
• Helge von Koch, who first described it in 1904.
  Method od construction ()
• properties: self-similarity, infinite length
• interations cause complexity and more detail
  use case: create fractal landscpaes, model natural phenomena like trees, mountains and clouds

Question 7

What are types of projections? Explain in detail

Answer 7

projections are techniques used to represent 3D objects on a 2D screen
1 parallel
- Projectors from the object to the projection plane are parallel.
- Does not provide depth
- Axonometric Projection (type of ortho where object is rotated about axis) subtype: isometric projection
- Orthographic projection (engineering drawings) subtype: top, front, side

2 perspective
- projectors converge at a single point
- mimics human perception
- one point
- two point
- three point

Question 8

Differentiate between parallel and perspective projections

Answer 8

Projector lines
Depth perception
Size representation
Realism
Computation complexity
Use cases
Distortion
Types
Lines parallel in 3D

Question 9

Diiferentiate between orthographic and isometric projections

Answer 9

Type
View orientation
Angle between axes
Visual depth
Use case
Perspective distortion
Common views