Graphics Graphics Korea University cgvr.korea.ac.kr Raster Graphics 고려대학교 컴퓨터 그래픽스 연구실

CGVR Graphics Korea University cgvr.korea.ac.kr 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 Graphics Korea University cgvr.korea.ac.kr 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 ( x k, y k ) is displayed, next which pixel is decided to plot in column x k+1 ?  ( x k +1, y k ) or ( x k +1, y k +1 ) xkxk ykyk x k +1 y k +1

CGVR Graphics Korea University cgvr.korea.ac.kr Bresenham’s Algorithm(cont.) Case) Positive Slope Less Than 1 y at sampling position x k Difference Decision parameter xkxk ykyk x k +1 y k +1 d 1 – d 2 < 0  (x k +1, y k ) d 1 – d 2 > 0  (x k +1, y k +1) d1d1 d2d2

CGVR Graphics Korea University cgvr.korea.ac.kr Bresenham’s Algorithm(cont.) Case) Positive Slope Less Than 1 Decision parameter Decision parameter of a starting pixel ( x 0, y 0 )

CGVR Graphics Korea University cgvr.korea.ac.kr Bresenham’s Algorithm(cont.) Algorithm for 0< m <1 Input the two line endpoints and store the left end point in ( x 0, y 0 ) Load ( x 0, y 0 ) 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 x k along the line, start at k =0, perform the following test:  If p k < 0, the next point to plot is ( x k +1, y k ) and  Otherwise, the next point to plot is ( x k +1, y k +1 ) and Repeat step 4 Δx times

CGVR Graphics Korea University cgvr.korea.ac.kr Polygons Filling Polygons Scan-line fill algorithm  Inside-Outside tests Boundary fill algorithm

CGVR Graphics Korea University cgvr.korea.ac.kr Scan-Line Polygon Fill Topological Difference between 2 Scan lines y : intersection edges are opposite sides y’ : intersection edges are same side y y’

CGVR Graphics Korea University cgvr.korea.ac.kr Scan-Line Polygon Fill (cont.) Edge Sorted Table C C’ B D E A 0 1 yAyA yDyD yCyC Scan-Line Number yEyE xAxA 1/m AE yByB xAxA 1/m AB y C’ xDxD 1/m DC yEyE xDxD 1/m DE yByB xCxC 1/m CB

CGVR Graphics Korea University cgvr.korea.ac.kr Inside-Outside Tests Self-Intersections Odd-Even rule Nonzero winding number rule exterior interior

CGVR Graphics Korea University cgvr.korea.ac.kr Boundary-Fill Algorithm Proceed to Neighboring Pixels 4-Connected 8-Connected

CGVR Graphics Korea University cgvr.korea.ac.kr Antialiasing Aliasing Undersampling: Low-frequency sampling Nyquist sampling frequency: Nyquist sampling interval: original sample reconstruct

CGVR Graphics Korea University cgvr.korea.ac.kr 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 Graphics Korea University cgvr.korea.ac.kr Supersampling Subpixels Increase resolution (10, 20): Maximum Intensity (11, 21): Next Highest Intensity (11, 20): Lowest Intensity

CGVR Graphics Korea University cgvr.korea.ac.kr Supersampling Subpixels Increase resolution (10, 20): Maximum Intensity (11, 21): Next Highest Intensity (11, 20): Lowest Intensity

CGVR Graphics Korea University cgvr.korea.ac.kr Pixel-Weighting Masks Give More Weight to Subpixels Near the Center of a Pixel Area

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

CGVR Graphics Korea University cgvr.korea.ac.kr Filtering Techniques Filter Functions (Weighting Surface) Box FilterCone FilterGaussian Filter

CGVR Graphics Korea University cgvr.korea.ac.kr 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 Graphics Korea University cgvr.korea.ac.kr Electromagnetic Spectrum Visible Light Frequencies Range between Red: 4.3 x hertz (700nm) Violet: 7.5 x hertz (400nm)

CGVR Graphics Korea University cgvr.korea.ac.kr 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 Graphics Korea University cgvr.korea.ac.kr Color Perception Tristimulus Theory of Color Spectral-response functions of each of the three types of cones on the human retina

CGVR Graphics Korea University cgvr.korea.ac.kr Color Models RGB XYZ CMY HSV Others

CGVR Graphics Korea University cgvr.korea.ac.kr RGB Color Model Colors are Additive R GBColor 0.0 Black Red Green Yellow Magenta Cyan 1.0 White Blue

CGVR Graphics Korea University cgvr.korea.ac.kr RGB Color Cube

CGVR Graphics Korea University cgvr.korea.ac.kr RGB Spectral Colors Amounts of RGB Primaries Needed to Display Spectral Colors

CGVR Graphics Korea University cgvr.korea.ac.kr XYZ Color Model (CIE) Amounts of CIE Primaries Needed to Display Spectral Colors

CGVR Graphics Korea University cgvr.korea.ac.kr CIE Chromaticity Diagram Normalized Amounts of X and Y for Colors in Visible Spectrum (white)

CGVR Graphics Korea University cgvr.korea.ac.kr CIE Chromaticity Diagram Define Color Gamuts Represent Complementary Color Determine Dominant Wavelength and Purity

CGVR Graphics Korea University cgvr.korea.ac.kr RGB Color Gamut Color Gamut for a Typical RGB Computer Monitor (red) (green) (blue)

CGVR Graphics Korea University cgvr.korea.ac.kr CMY Color Model Colors are Subtractive C MYColor 0.0 White Cyan Magenta Blue Green Red 1.0 Black Yellow

CGVR Graphics Korea University cgvr.korea.ac.kr CMY Color Cube

CGVR Graphics Korea University cgvr.korea.ac.kr HSV Color Model Select a Spectral Color (Hue) and the Amount of White (Saturation) and Black (Value)

CGVR Graphics Korea University cgvr.korea.ac.kr HSV Color Model H SVColor Red Yellow Green Blue Magenta * White * Gray Cyan * *0.0Black

CGVR Graphics Korea University cgvr.korea.ac.kr HSV Color Model Cross Section of the HSV Hexcone