1. Basic Raster Graphics Algorithms for Drawing 2D Primitives
Prof. Lizhuang Ma
Shanghai Jiao Tong University

2. Contents Architecture of a Raster Display Scan Converting Lines
Filling Rectangles
Filling Polygons
Clipping Lines
Clipping Polygons
Antialiasing

3. Architecture of a Raster Display Video

4. Definitions Pixel: a screen consists of N x M pixels
Bilevel = monochrome, 1 bit / pixel
Color: RGB/CYK/LUV…
Bitmap / pixmap
Frame buffer: an array of data in memory mapped to screen

5. Scan Converting Line
A scan-converted line showing intensified pixels as black circles

6. The Basic Incremental Algorithm
A scan-converted line showing intensified pixels as black circles

7. The Basic Incremental Algorithm
void Line (intx0, inty0, intx1, inty1, value) {
Int x;
Float dy, dx, y, m;
dy=y1-y0;
dx=x1-x0;
m=dy/dx;
y=y0;
for(x=x0; x<=x1; x++) {
WritePixel(x, (int)floor(y+0.5), value);
y+=m; }

8. Midpoint Line Algorithm

9. Midpoint Line Algorithm

10. Midpoint Line Algorithm
void MidpointLine(intx0, inty0, intx1, inty1, value) {
int dx, dy, incrE, incrNE, d, x, y;
dy=y1-y0;dx=x1-x0;d=dy*2-dx;
incrE=dy*2;incrNE=(dy-dx)*2;
x=x0;y=y0;
WritePixel(x, y, value);
while(x<x1) {
if(d<=0) {d+=incrE;x++; }
else {d+=incrNE;x++;y++;

11. Filling Rectangles for(y from ymin to ymax of the rectangle) {
for(x from xmin to xmax) {
WritePixel(x, y, value); }

12. Filling Polygons

13. Filling Polygons

14. Filling Polygons
Find the intersections of the scan line with all edges of the polygon
Sort the intersections by increasing x coordinate
Fill in all pixels between pairs of intersections that lie interior to the polygon

15. Special Cases
Slivers
Horizontal Edges

16. Clipping Lines

17. The Cohen-Sutherland Algorithm

18. The Cohen-Sutherland Algorithm

19. Clipping Polygons

20. The Sutherland-Hodgman Polygon-Clipping Algorithm

22. Liang-Barsky Algorithm
Starting point is parametric form
Compute four intersections with extended
clipping rectangle
Will see that this can be avoided

23. Ordering of intersection Ordering of intersection points
Order the intersection points
• Figure (a): 1 > a4 > a3 > a2 > a1 > 0
• Figure (b): 1 > a4 > a2 > a3 > a1 > 0

24. Ordering of intersection Li Liang-Barsky Efficiency Improvements
– Compute intersections one by one
– Often can reject before all four are computed
• Efficiency improvement 2:
– Equations for a3, a2
– Compare a3, a2 without floating-point division

25. Antialiasing