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Scan Conversion, Lines, Circles and Ellipse

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Scan Conversion,Lines, Circles and Ellipse

Dr. Aree Ali Mohammed

Assistant Professor

2014-2015

3rdStage

aree.ali@univsul.net

University of Sulaimani– Computer Science Dept.

Points

Polygone

Line

Rectangle

Square

Triangle

r

Ellipse

(0, 0)

Circle

Curve

Scan Conversion or Rasterization

- Drawing lines, circles, and etc. on a grid implicitly involves approximation.
- The general process: Scan Conversion or Rasterization
- Ideally, the following properties should be considered
- smooth
- continuous
- pass through specified points
- uniform brightness
- efficient

Line Drawing Algorithms

Line Drawing Algorithms

Line Drawing Algorithms

Line Drawing Algorithms

DDA - Line Drawing Algorithms

DDA - Line Drawing Algorithms

DDA - Line Drawing Example

Bresenham’s Line Algorithm

Bresenham’s Line – Example

Review Questions and Homework

- Explain the steps in the incremental line drawing algorithm.
- Explain the steps in DDA line drawing algorithm.
- Explain the steps in Bresenham’s line drawing algorithm.
- HW/
- Draw the following lines using DDA and Bresenham:
- (from left to right):
- (-1, 2) and (7, 8)
- (1, -3) and (6, 5)
- (from right to left)
- (6, 2) and (-4, -3)
- (9, 4) and (2, -5)

- Scan Converting CirclesExampl

Midpoint Circle Algorithm

1. Input radius r and circle center (xc,yc) and obtain the first point on the circumference of the circle centered on the origin as (x0, y0) = (0, r)

2. Calculate the initial value of the decision parameter as

Po=5/4-r or [po=1-r for r an integer]

3. At each xk position starting at k = 0 , perform the following test. If pk < 0 , the next point along the circle centered on (0, 0) is (xk+1, yk) and

pk+1 = pk + (2xk+1) + 1

Otherwise the next point along the circle is (xk+1, yk-1) and

pk+1 = pk + (2xk+1) + 1 – (2yk+1)

Where 2xk+1 = 2xk+2 and 2yk+1 = 2yk – 2

4. Determine symmetry points in the other seven octants

5. Move each calculated pixel position (x,y) onto

the circular path centered on (xc, yc) and plot

the coordinate values

x = x+ xc , y= y+ yc

6. Repeat steps 3

through 5 until x >= y

- Scan Converting CirclesExampl

Scan Converting Circle - Example

- “Computer Graphics with OpenGL” , chapter 3.
- Raster versus Vector
http://www.sketchpad.net/basics1.htm