Unit IV PART B, C with Answer

Unit IV PART B, C with Answer

Unit IV 2 marks

Unit IV 2 marks

Unit III Expected Part B, C Questions

Unit III Expected Part B, C Questions

Qn 1. Write notes on i) Polygon surfaces ii) Quadric surfaces 

Polygon tables-Basic concept

Polygon table

data is placed into the polygon table for processing

Polygon data table can be organised into two groups

geometric table

attribute table

Storing geometric data

To store geometric data three lists are created

Vertex table – contains coordinate values for each vertex

Edge table – contains pointers back into the vertex table

Polygon table – contains pointers back into the edge table

Advantages of three table

efficient display of objects

For faster info. Extraction

expand edge table to include forward pointers to the polygon table

Plane Equation

Ax + By + Cz + D = 0

eqn. is solved by Cramer’s rule

Identification of points

if Ax + By + Cz + D < 0 ,the points (x,y,z) is inside the surface

if Ax + By + Cz + D > 0 ,the points (x,y,z) is outside the surface

Quadric surfaces-definition

Described with second degree eqns.

Ex. Sphere,ellipsoids,tori,paraboloids,hyperboloids

Sphere-definition-equations-diagram

Sphere

A spherical surface with radius ‘r’ centered on the coordinate origin is defined as a set of points(x,y,z) that satisfy the equation

x2 + y2 + z2 = r2

In parametric form,

x = r CosΦCosΘ

y = r Cos ΦSinΘ

z = r Sin Φ

Ellipsoid-definition-equations-diagram

Ellipsoid

Extension of spherical surface ,where the radii in three mutually perpendicular directions have different values

(x/rx)2 + (y/ry)2 + (z/rz)2 = 1

Qn 2. 3D object representation methods

1. Polygon surfaces-polygon tables-plane equations-polygon meshes
1. Object descriptions are stored as sets of surface polygons
2. The surfaces are described with linear equations
2. Polygon table
1. data is placed into the polygon table for processing
2. Polygon data table can be organised into two groups
3. geometric table
4. attribute table
3. Quadric surfaces-sphere-ellipsoid-torus
1. Described with second degree eqns.
2. Ex. Sphere,ellipsoids,tori,paraboloids,hyperboloids
3. Sphere
4. A spherical surface with radius ‘r’ centered on the coordinate origin is defined as a set of points(x,y,z) that satisfy the equation

x2 + y2 + z2 = r2

5. In parametric form,

x = r CosΦCosΘ

y = r Cos ΦSinΘ

z = r Sin Φ

4. Blobby objects-definition and example
1. Don’t maintain a fixed shape
2. Change surface characteristics in certain motions
3. Ex. Water droplet, Molecular structures

f(x,y,z) = Σk b ke-ak rk2 - T = 0

r = √x2 + y2 + z2

T =some threshold

a,b used to adjust the amount of bloobiness.

5. Spline-representation-interpolation
1. it is a composite curve formed with polynomial pieces satisfying a specified continuity conditions at the boundary of the pieces
6. Bezier curves
1. can be fitted to any no. of control points
2. degree of bezier polynomial is determined by the number of control points and their relative position
3. Bezier curve is specified by
1. Boundary conditions
2. Characterising matrix
3. Blending function

Qn 3. Differentiate parallel and perspective projection and derive its matrix

Parallel - Defn, Types, Oblique Matrix
Perspective - Defn, Types, Perspective Matrix

Qn 4. Visible Surface Detection Methods

Basic Category - 

     Image Spaced

     Object Spaced

9 Types

   Back Face Detection, Depth Buffer, A Buffer, Scan Line, BSP, OC Tree, Area Subdivision, Ray Casting, Depth Sorting

Qn 5. Bezier Curves

Defn

Eqn

Properties

Cubic Bezier

Bezier Surfaces

Applns

Qn 6. 3D Viewing

·        Viewing – transfers positions from world coordinate plane to pixels positions in the plane of the output device

·        Viewing pipeline:

MC => MT => WC => VT => VC => PT => PC => WT =>DC

MC – Modeling Coordinates

MT – Modeling Tx

WC – World Coordinate

VT – Viewing Tx

VC – Viewing coordinate

PT – Projection transformation

PC – Projection coordinate

WT – Workstation Tx

DC – Device Coordinate

·        Transformation from world to viewing coordinates: sequences

·        Translate view reference point to the origin of world coordinate system

·        Apply rotation to align xv , yv , zv axes with the world xw ,yw ,zw axes

Unit III Visible Surface Detection Methods

Visible Surface Detection Methods

Unit III 3D Transformation

3D Transformation

Unit III 3D Object Representation

3D Object Representation

Unit III. 3D display methods

3D display methods

Unit III 2 marks

Unit III 2 marks