ALRUMTECH: Computer Graphics:Module 5

Module 5: 3D Transformations and Viewing

a) 3D Object Representation Methods

Different objects in the world are- trees, mountains, home, human, hair, geometrical shapes, clouds, vehicles etc.

All objects cannot be described by one single representation.

Hence there are various methods of 3D object Representation.

Representation methods:

•Polygon tables

In this representation method object is represented by series of tables containing vertices ,edges and surfaces.

•Polygon Equations

Polygons are also represented by equation: Ax+By+Cz+D=0

•Sweep Representation

using 2D object or shape and translational or rotational symmetry we can create 3D object that is called sweep representation.

for example: cylinder can be drawn using circle and translational symmetry.

•Constructive Solid Geometry (CSG)

in Constructive Solid Geometry (CSG) 3D basic objects like Cube, Cylinder, Sphere will be taken and set operations like union, difference, intersection to form new 3D object.

•Quadtree:

•Octree

•Fractals

b) 3D transformations

c) Projections:

Projecting three-dimensional object on two dimensional viewing plane is called projection.

Basically two types of projections: 1) Parallel Projection 2) Perspective Projection.

1)Parallel Projection: Coordinate positions transformed on viewing plane along parallel lines. It preserves relative proportion of object. Center of projection is at infinite distance.it is unable to realistic view of 3D object.

2)Perspective Projection: Coordinate positions transformed on viewing plane along the lines converging to point. It does not preserve relative proportion of object. Centre of projection is at finite distance. Gives realistic view of 3D object. Object at longer distance will look smaller and object nearer to viewing plane will look bigger in size.