cg - output primitives

Output Primitives

Organized By: Vinay Arora

Assistant Professor, CSED

Thapar University, Patiala

Vinay Arora

CSED

Disclaimer

This is NOT A COPYRIGHT MATERIAL

Content has been taken mainly from the following books & websites:

Computer Graphics C Version By Donald Hearn, M. Pauline BakerSchaum's outline of theory and problems of computer graphics By Zhigang Xiang, Roy A. Plastock

Computer Graphics: Principles and Practice By James D. Foley

http://en.wikipedia.org/wiki/Computer_graphics

http://www.howstuffworks.com/3dgraphics.htm

http://www.graphics.cornell.edu/online/tutorial/

http://www.cgarena.com/

etc…

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CSED

Object Model

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CSED

Primitives

� 2-D Drawing or a 3-D Object consist of Graphical Primitives such as

Points, Lines, Circles & Filled Polygons.

� Graphics System or the Application Program convert each primitive

from its geometric definition into a set of Pixels that make up the

primitive in the Image Space.

� This Conversion is referred to as SCAN CONVERSION or

RASTERIZATION.

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CSED

Definitions

� RASTERIZATION: Process of determining which pixels provide the best

approximation to a desired line on the screen.

� SCAN CONVERSION: Combination of rasterization and generating the

picture in scan line order.

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CSED

General Requirement

� Straight lines must appear as straight lines.

� They must start and end accurately.

� Lines should have constant brightness along their length.

� Lines should drawn rapidly.

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Straight lines must appear as Straight

Lines

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� For horizontal, vertical and 45º lines, the choice of raster elements is

obvious. This lines exhibit constant brightness along the length:

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� For any other orientation the choice is more difficult:

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Intersection Points

� In general Line doesn’t pass through Intersection Points.

� Points are very close & dense that’s why – it appears as Straight Line.

� We have to find Addressable Pixels.

� Points Distributed over the line & the most closest to the line.

� No Addressable Pixel is having any Floating Point number/value.

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CSED

Jaggies

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Staircase Effect

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Staircase Effect

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CSED

Direct Scan Conversion

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CSED

DDA – Digital Differential Analyzer

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CSED

DDA – Pseudo code

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Section of Display Screen in case of Positive

Slope Line

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Section of Display Screen in case of

Negative Slope Line

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Screen Grid showing a Pixel in column xk on scan line yk that is to be

plotted along the path of line with slope 0 < m <1

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CSED

Distance between pixel positions & the line y

coordinate at sampling position xk+1

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Bresenham’s Algorithm

They coordinate on mathematical line at pixel column position xk+l is calculated as

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CSED

Bresenham’s Algorithm (Conti…)

where term yk+1 - yk is either 0 or 1, depending on the sign of parameter pk.

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CSED

Algorithm

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Line Drawing

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Example

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Solution

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Representation of Circle

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Representation of Circle

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Mid Point Representation

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Mid Point Representation

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Mid Point Circle Algo. – Basic Steps

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Mid Point Circle Algo. – Basic Steps

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Mid Point Circle Algo. – Basic Steps

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Mid Point Circle Algorithm

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Mid Point Circle Algorithm (Contd)

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Example

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Ellipse

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Ellipse (Contd.)

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General Equation

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Scan Converting an Ellipse

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Equation for Ellipse

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Equation for Ellipse – For Region 1

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Scan Line for Polygon Filling

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Scan Line for Polygon Filling

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CSED

Selecting Vertex

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Formula for Next Value for x

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Saving Intersection Points

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Color Boundaries for Boundary Fill

Procedure

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4-Connected & 8-Connected

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Boundary Fill Algorithm

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Partially Filled in 4 - Connected

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Boundary Fill across Pixel spans for a

4 – connected area

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CSED

Boundary Fill across Pixel spans for a

4 – connected area

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CSED

Flood Fill

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Flood Fill Algorithm

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CSED

Thnx…