Implementation of a Renderer

Consider Programs are processd by the system

line & polygon, outside the view volume Efficiently

Understanding of the implementation process, H/W & S/W

Extra functions Texture mapping and use of the alpha channel

Implementation tasks

Modeling Representation of geometric object

Geometric processing Transformation & Normalization Clipping Hidden surface removal

Rasterization 2D Image, Frame buffer Anti-aliasing

Display Output Screen, Automatically H/W

Basic implementation strategies

Object-Oriented Loop of Object

For (each object) render (object) large amount of memory object independently reguire other buffers such as depth buffer

Image-Oriented Loop of Pixel

For (each) render (pixel) need only limited display memory disadvantage - all time during the rendering process

Implementation of transformation

Model coordinates World coordinates Camera(eye) coordinates

projection matrix Clip coordinates - fit within the clipping volume

X

Y

Z

X

Y

Z

X

Y

Z

X

Y

Z

ObjectCoords.

EyeCoords.

ClipCoords.

NormalizedDeviceCoords.

ScreenCoords.

Implementation of transformation

Normalization device coordinates x’ = x y’ = y z’ = 0

Window(screen) coordinates

Clipping

Definition The process of determining which primitives,

and part of primitives, fit within the clipping volume define by the application

Term Clipper, Accepted – fit within the specified view

volume Rejected, Culled – primitives that can’t appear

on the display are eliminated

Cohen-Sutherland Clipping

8 Separate clipping region Each region assigned 4-bit binary number Outcode

bit 1 => if point above of window bit 2 => if point below of window bit 3 => if point right of window bit 4 => if point left of window

0 0 11

y ymax

x xmin

y ymin

x xmax

ymin

ymax

xmin xmax

1001 1000 1010

0001

0101 0100 0110

00100000

Cohen-Sutherland line clipping algorithm in 3D

B4 1 if Z > Znear B5 1 if Z < Zfar

Liang-Barsky Clipping

Parametric Line Clipping Algorithm Two define a line in the plane.

Polygon Clipping

Cohen-Sutherland and Liang-Barsky algorithms can be applied to polygons on an edge-by-edge basis.

Sutherland and Hodgeman Concave & Convex

1

2

3

45

1

2

3

4’5’

Sutherland-Hodgeman Polygon Clipping

Process polygon against each of the 4 boundaries in turn (left, right, bottom, top)

Top Bottom Right Left

Other method for polygon clipping

Bounding Boxes The smallest rectangle, aligned with the

window, that contains the polygon

Clipping in the Frame buffer - scissoring