Raster Graphics

1. Raster Graphics 고려대학교 컴퓨터 그래픽스 연구실 cgvr.korea.ac.kr

2. Contents • Display Hardware • How are images display? • Raster Graphics Systems • How are imaging system organized • Output Primitives • How can we describe shapes with primitives? • Color Models • How can we describe and represent colors? cgvr.korea.ac.kr

3. yk+1 yk xk xk+1 Bresenham’s Line Algorithm • Accurate and Efficient • Use only incremental integer calculations • Test the sign of an integer parameter • Case) Positive Slope Less Than 1 • After the pixel (xk, yk) is displayed, next which pixel is decided to plot in column xk+1? (xk+1, yk) or (xk+1, yk+1) cgvr.korea.ac.kr

4. yk+1 yk xk xk+1 Bresenham’s Algorithm(cont.) • Case) Positive Slope Less Than 1 • y at sampling position xk • Difference • Decision parameter d2 d1 d1– d2 < 0  (xk+1, yk) d1– d2 > 0  (xk+1, yk+1) cgvr.korea.ac.kr

5. Bresenham’s Algorithm(cont.) • Case) Positive Slope Less Than 1 • Decision parameter • Decision parameter of a starting pixel (x0, y0) cgvr.korea.ac.kr

6. Bresenham’s Algorithm(cont.) • Algorithm for 0<m<1 • Input the two line endpoints and store the left end point in (x0, y0) • Load (x0, y0) into the frame buffer; that is, plot the first point • Calculate constants Δx, Δy, 2Δy, and 2Δy− 2Δx, and obtain the starting value for the decision parameter as • At each xk along the line, start at k =0, perform the following test: • If pk< 0, the next point to plot is (xk+1, yk) and • Otherwise, the next point to plot is (xk+1, yk+1) and • Repeat step 4 Δx times cgvr.korea.ac.kr

7. Filling Polygons Scan-line fill algorithm Inside-Outside tests Boundary fill algorithm Polygons 11 1 2 3 4 5 6 7 8 9 10 5 6 7 8 9 4 3 1 2 cgvr.korea.ac.kr

8. Scan-Line Polygon Fill • Topological Difference between 2 Scan lines • y : intersection edges are opposite sides • y’ : intersection edges are same side y 1 2 2 y’ 1 1 cgvr.korea.ac.kr

9. Scan-Line Polygon Fill (cont.) • Edge Sorted Table B yC yB xC 1/mCB C C’ E yD yC’ xD 1/mDC yE xD 1/mDE D yA yE xA 1/mAE yB xA 1/mAB A 1 Scan-Line Number 0 cgvr.korea.ac.kr

10. Self-Intersections Odd-Even rule Nonzero winding number rule Inside-Outside Tests exterior interior cgvr.korea.ac.kr

11. Boundary-Fill Algorithm • Proceed to Neighboring Pixels • 4-Connected • 8-Connected cgvr.korea.ac.kr

12. Antialiasing • Aliasing • Undersampling: Low-frequency sampling • Nyquist sampling frequency: • Nyquist sampling interval: original sample reconstruct cgvr.korea.ac.kr

13. Antialiasing (cont.) • Supersampling(Postfiltering) • Pixel-weighting masks • Area Sampling (Prefiltering) • Pixel Phasing • Shift the display location of pixel areas • Micropositioning the electron beam in relation to object geometry cgvr.korea.ac.kr

14. Supersampling • Subpixels • Increase resolution 22 (10, 20): Maximum Intensity (11, 21): Next Highest Intensity (11, 20): Lowest Intensity 21 20 10 11 12 cgvr.korea.ac.kr

15. Supersampling • Subpixels • Increase resolution 22 (10, 20): Maximum Intensity (11, 21): Next Highest Intensity (11, 20): Lowest Intensity 21 20 10 11 12 cgvr.korea.ac.kr

16. 1 2 1 2 4 2 1 2 1 Pixel-Weighting Masks • Give More Weight to Subpixels Near the Center of a Pixel Area cgvr.korea.ac.kr

17. Area Sampling • Set Each Pixel Intensity Proportional to the Area of Overlap of Pixel • 2 adjacent vertical (or horizontal) screen grid lines  trapezoid 22 (10, 20): 90% (10, 21): 15% 21 20 10 11 12 cgvr.korea.ac.kr

18. Filtering Techniques • Filter Functions (Weighting Surface) Box Filter Cone Filter Gaussian Filter cgvr.korea.ac.kr

19. Contents • Display Hardware • How are images display? • Raster Graphics Systems • How are imaging system organized? • Output Primitives • How can we describe shapes with primitives? • Color Models • How can we describe and represent colors? cgvr.korea.ac.kr

20. Electromagnetic Spectrum • Visible Light Frequencies Range between • Red: 4.3 x 1014 hertz (700nm) • Violet: 7.5 x 1014 hertz (400nm) cgvr.korea.ac.kr

21. Visible Light • The Color of Light is Characterized by • Hue: dominant frequency (highest peak) • Saturation: excitation purity (ratio of highest to rest) • Brightness: luminance (area under curve) White Light Orange Light cgvr.korea.ac.kr

22. Color Perception • Tristimulus Theory of Color • Spectral-response functions of each of the three types of cones on the human retina cgvr.korea.ac.kr

23. Color Models • RGB • XYZ • CMY • HSV • Others cgvr.korea.ac.kr

24. RGB Color Model R G B Color • Colors are Additive 0.0 0.0 0.0 Black 1.0 0.0 0.0 Red 0.0 1.0 0.0 Green 0.0 0.0 1.0 Blue 1.0 1.0 0.0 Yellow 1.0 0.0 1.0 Magenta 0.0 1.0 1.0 Cyan 1.0 1.0 1.0 White cgvr.korea.ac.kr

25. RGB Color Cube cgvr.korea.ac.kr

26. RGB Spectral Colors • Amounts of RGB Primaries Needed to Display Spectral Colors cgvr.korea.ac.kr

27. XYZ Color Model (CIE) • Amounts of CIE Primaries Needed to Display Spectral Colors cgvr.korea.ac.kr

28. CIE Chromaticity Diagram • Normalized Amounts of X and Y for Colors in Visible Spectrum (white) cgvr.korea.ac.kr

29. CIE Chromaticity Diagram Define Color Gamuts Represent Complementary Color Determine Dominant Wavelength and Purity cgvr.korea.ac.kr

30. RGB Color Gamut • Color Gamut for a Typical RGB Computer Monitor (green) (red) (blue) cgvr.korea.ac.kr

31. CMY Color Model C M Y Color • Colors are Subtractive 0.0 0.0 0.0 White 1.0 0.0 0.0 Cyan 0.0 1.0 0.0 Magenta 0.0 0.0 1.0 Yellow 1.0 1.0 0.0 Blue 1.0 0.0 1.0 Green 0.0 1.0 1.0 Red 1.0 1.0 1.0 Black cgvr.korea.ac.kr

32. CMY Color Cube cgvr.korea.ac.kr

33. HSV Color Model • Select a Spectral Color (Hue) and the Amount of White (Saturation) and Black (Value) cgvr.korea.ac.kr

34. HSV Color Model H S V Color 0 1.0 1.0 Red 60 1.0 1.0 Yellow 120 1.0 1.0 Green 180 1.0 1.0 Cyan 240 1.0 1.0 Blue 300 1.0 1.0 Magenta * 0.0 1.0 White * 0.0 0.5 Gray * * 0.0 Black cgvr.korea.ac.kr

35. HSV Color Model • Cross Section of the HSV Hexcone cgvr.korea.ac.kr