cg unit 7 full

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object-space methods and image-space methods.

An object-space method compam objects and parts of objects to each

other within the scene definition to determine which surfaces, as a whole, we

should label as visible.

In an image-space algorithm, visibility is decided point by

point at each pixel position on the projection plane.

BACK-FACE DETECTION

A point (x , y,z) is "inside" a polygon surface

if Ax+By+Cz+D < 0

If V.N > 0 then this polygon is back faced

BACK-FACE DETECTION

DEPTH-BUFFER METHOD

(Z-Buffer)

With object descriptions converted to projection coordinates, each (x, y, z )

position on a polygon surface corresponds to the orthographic projection point

(x, y) on the view plane.

DEPTH-BUFFER METHOD

Plane Value of Z

Back plane 0

Front plane Zmax

Types of Buffers

Depth Buffer

Refresh Buffer

Algorithm

1. Initialize the depth buffer and refresh buffer so that for all buffer positions(x , y),

depth(x,y)=0 and refresh(x,y)=Ibground

2. For each position on each polygon surface, compare depth values to previously stored values in the depth buffer to determine visibility.

- Calculate the depth t for each (x , y) position on the polygon.

- If z > depth(x, y), then set

depth(x,y)=Z and refresh(x,y)=Isurface(x,y).

where Ibground is the value for the background intensity, and Isurface(x,y) isthe projected intensity value for the surface at pixel position (x,y).

After all surfaces have been processed, the depth buffer contains

depth values for the visible surfaces and the refresh buffer contains

the corresponding intensity values for those surfaces.

Depth values for a surface position (x , y)

are calculated from the plane equation for

each surface:

A-BUFFER METHOD

An extension of the ideas in the depth-buffer method is the A-buffer method.

it deals only with opaque surfaces and cannot accumulate intensity values

for more than one surface.

Each position in the A-buffer has two fields:

1.depth field - stores a positive or negative real number 2. intensity field - stores surface-intensity information or a pointer value.

Foreground

Transprent

surface

Backgroundopaque

surface

Data for each surface in the linked list includes

RGB intensity components opacity parameter (percent of transparency)

percent of area coverage

surface identifier

other surface-rendering parameters

pointer to next surface

A-BUFFER METHOD

SC AN-LINE METHOD

It is an image-space technique.

It is an extended form of the scan-line fill alg.

Visible surface can be calculated by finding

the intersection between scan line and polygon surface.

Two tables are maintained ± Edge table

± Polygon table

For positions along this scan line between edges AB and BC, onlythe flag for surface Sl is on.

Similarly, between edges EH and FG, only the flag for surface S2 ison.

For scan lines 2 and 3 the active edge list contains edges AD, EH ,BC , and FG.

But between edges EH and BC , the flags for both surfaces are on.

SC AN-LINE METHOD

DEPTH-SORTING METHOD

Using both image-space and object-space

operations, the depth-sorting method

performs the following basic functions:

1. Surfaces are sorted in order of decreasing

depth.

2. Surfaces are scan converted in order,

starting with the surface of greatest depth.

DEPTH-SORTING METHOD

Triangle Behind counter List of triangles in f r ont of it

2 0 4,3,1

3 2 1,5

DEPTH-SORTING METHODTriangle Fr ont List Behind counter output New Behind

counter

1 5 2 1

2 4,3,1 0 -1

3 1,5 2 1

4 3 1 0

6 0 -1

counter

1 5 1 1

2 4,3,1 -1 -1

3 1,5 1 0

4 3 0 -1

6 -1 -1

counter

1 5 1 0

2 4,3,1 -1 -1

3 1,5 0 -1

4 3 -1 -1

6 -1 -1

counter

1 5 0 -1

2 4,3,1 -1 -1

3 1,5 -1 -1

4 3 -1 -1

6 -1 -1

counter

1 5 -1 -1

2 4,3,1 -1 -1

3 1,5 -1 -1

4 3 -1 -1

5 0 -1

6 -1 -1

BSP-TREE METHOD

binary space-partitioning (BSP)

ARE A-SUBDIVISION b1ETHOD

No further sub division is needed if

1. All surfaces are outside surface with

respect to the area.

2. Only one inside , overlapping, or surrounding surface is in the area.

3. A surrounding surface obscures all

other surfaces within the area

boundaries.

Surr ounding sur f ace-One that

completely encloses the area.

Overlapping sur f ace-One that is partlyinside and partly outside the area.

Inside sur f ace-One that is completely

inside the area.

Outside sur f ace-One that is completely

outside the area.

ARE A-SUBDIVISION METHOD

Surr ounding sur f ace

Overlapping sur f ace

Outside sur f ace

inside sur f ace

OCTREE METHODS

RAY-CASTING METHOD

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