Graphics

cgvr.korea.ac.kr Graphics Lab @ Korea University

Raster Graphics

고려대학교 컴퓨터 그래픽스 연구실

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

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

CGVR

Graphics Lab @ Korea University

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)

xk

yk

xk+1

yk+1

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Bresenham’s Algorithm(cont.)

Case) Positive Slope Less Than 1 y at sampling position xk

Difference

Decision parameter

xk

yk

xk+1

yk+1

bxmy k 1

kkk ybxmyyd 11

bxmyyyd kkk 1112

d1– d2 < 0 (xk+1, yk)

d1– d2 > 0 (xk+1, yk+1)

cyxxy

bxyyxxy

ddxp

kk

kk

k

22

1222221

d1

d2

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Bresenham’s Algorithm(cont.)

Case) Positive Slope Less Than 1 Decision parameter

Decision parameter of a starting pixel (x0, y0)

kkkk

kkkkkk

yyxxxy

cyxxycyxxypp

11

111

22

2222

kkkk yyxypp 11 22

xxbyxbxyxy

bxybmxxxy

bxyyxxyp

22222

12222

12222

00

00

000

xyp 20

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

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

xyp 20

ypp kk 21

xypp kk 221

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Polygons

Filling Polygons Scan-line fill algorithm

Inside-Outside tests

Boundary fill algorithm

1 2 3 4 5 6 7 8 91 234

6 7 8 91011

5

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Scan-Line Polygon Fill

Topological Difference between 2 Scan lines y : intersection edges are opposite sides y’ : intersection edges are same side

y

y’1

2

1

1 2

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Scan-Line Polygon Fill (cont.)

Edge Sorted Table

C

C’

B

D

E

A

01

yA

yD

yC

Scan-Line Number

yE xA1/mAE yB xA

1/mAB

yC’ xD1/mDC yE xD

1/mDE

yB xC1/mCB

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Inside-Outside Tests

Self-Intersections Odd-Even rule Nonzero winding

number rule

exterior

interior

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Boundary-Fill Algorithm

Proceed to Neighboring Pixels 4-Connected 8-Connected

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Antialiasing

Aliasing Undersampling: Low-frequency sampling

Nyquist sampling frequency: Nyquist sampling interval:

max2 ff s

2cyclex

xs

original

sample

reconstruct

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

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 obje

ct geometry

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Supersampling

Subpixels Increase resolution

10 11 12

20

21

22

(10, 20): Maximum Intensity

(11, 21): Next Highest Intensity

(11, 20): Lowest Intensity

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Supersampling

Subpixels Increase resolution

10 11 12

20

21

22

(10, 20): Maximum Intensity

(11, 21): Next Highest Intensity

(11, 20): Lowest Intensity

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Pixel-Weighting Masks

Give More Weight to Subpixels Near the Center of a Pixel Area

1 2 1

2 4 2

1 2 1

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CGVR

Graphics Lab @ Korea University

Area Sampling

Set Each Pixel Intensity Proportional to the Area of Overlap of Pixel 2 adjacent vertical (or horizontal) screen grid lines

trapezoid

10 11 12

20

21

22

(10, 20): 90%

(10, 21): 15%

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Filtering Techniques

Filter Functions (Weighting Surface)

Box Filter Cone Filter Gaussian Filter

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

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

CGVR

Graphics Lab @ Korea University

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

CGVR

Graphics Lab @ Korea University

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

CGVR

Graphics Lab @ Korea University

Color Perception

Tristimulus Theory of Color Spectral-response fun

ctions of each of the three types of cones on the human retina

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

Color Models

RGB XYZ CMY HSV Others

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

RGB Color Model

Colors are Additive R G B Color

0.0 0.0 0.0 Black

1.0 0.0 0.0 Red

0.0 1.0 0.0 Green

1.0 1.0 0.0 Yellow

1.0 0.0 1.0 Magenta

0.0 1.0 1.0 Cyan1.0 1.0 1.0 WhiteWhite

0.0 0.0 1.0 Blue

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

RGB Color Cube

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

RGB Spectral Colors

Amounts of RGB Primaries Needed to Display Spectral Colors

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

XYZ Color Model (CIE)

Amounts of CIE Primaries Needed to Display Spectral Colors

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

CIE Chromaticity Diagram

Normalized Amounts of X and Y for Colors in Visible Spectrum

(white)

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

CIE Chromaticity Diagram

Define Color Gamuts

Represent Complementary

Color

Determine Dominant Wavelength

and Purity

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

RGB Color Gamut

Color Gamut for a Typical RGB Computer Monitor

(red)

(green)

(blue)

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

CMY Color Model

Colors are Subtractive C M Y Color

0.0 0.0 0.0 WhiteWhite

1.0 0.0 0.0 Cyan

0.0 1.0 0.0 Magenta

1.0 1.0 0.0 Blue

1.0 0.0 1.0 Green

0.0 1.0 1.0 Red1.0 1.0 1.0 Black

0.0 0.0 1.0 Yellow

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

CMY Color Cube

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

HSV Color Model

Select a Spectral Color (Hue) and the Amount of White (Saturation) and Black (Value)

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

HSV Color Model

H S V Color

0 1.0 1.0 Red60 1.0 1.0 Yellow

120 1.0 1.0 Green

240 1.0 1.0 Blue

300 1.0 1.0 Magenta* 0.0 1.0 WhiteWhite* 0.0 0.5 Gray

180 1.0 1.0 Cyan

* * 0.0 Black

cgvr.korea.ac.kr

CGVR

Graphics Lab @ Korea University

HSV Color Model

Cross Section of the HSV Hexcone