UBI 516 Advanced Computer Graphics

1
UBI 516 Advanced Computer Graphics

• Graphics Output Primitives
• ( Chapter 3 )

2
Screen Window Coordinates
Screen coordinates

• Setting a pixel
• glBegin(GL_POINTS) glVertex2f(px,py) glEnd()
• Setting Orthogonal Camera
• glMatrixMode(GL_PROJECTION)glLoadIdentity()glu
  Ortho2D(xmin,xmax,ymin,ymax)

(0,0)
x
y
(399,299) xmax,ymax
(px,py)
x
(0,0) xmin,ymin
(799,599)
y
3
CurvePolyline

• GLU has many polynomials that are defined with
  discrete point sets (like spheres, cylinders)

4
Pixels and Object Geometry
Pixel Line Rectangle
5
Drawing a Circle
Midpoint and modified midpoint algorithm.
6
Polygon Fill

• Convex Concave

(E1xE2)zgt0
(E2xE3)zgt0
(E3xE4)zlt0
(E4xE5)zgt0
(E5xE6)zgt0
7
Slitting of a Polygon into Triangles

• OpenGL guarentees correct rendering of polygons
  only if they are convex. A triangle is a convex
  polygon.
• But a polygon which has gt3 vertices can be
  concave.
• So, we must tesselate a given polygon into
  triangles.The GLU library has a tesselator.

8
Inside-Outside Testing
We want fill inside of a polygon with constant
color.

• Flat and convex polygons are guarenteed to be
  rendered correctly by OpenGL.
• For nonflat polygons
• We can work with their projections.
• Or we can use first three vertices to determine a
  flat plane to use for the interrior.
• For nonsimple flat polygons, we must decide how
  to determine whether a given point is inside or
  outside of the polygon (Jordan theorem).

9
Inside-Outside Testing

• Odd-even rule (easy implementation)
• crossing, odd parity rule, even-odd rule
• Crossed odd edges inside point
• Crossed even edges outside point

• Non-zero winding rule
• Clocwise edges 1
• Counterclocwise edges 1
• Dont fill while total 0

10
Polygon Tables
VERTEX TABLE
EDGE TABLE
POLYGON-SURFACE TABLE
V1 x1 y1 z1 V2 x2 y2 z2 V3 x3
y3 z3 V4 x4 y4 z4 V5 x5 y5 z5
E1 V 1, V 2 E2 V 2, V 3 E3 V 3,
V 1 E4 V 3, V 4 E5 V 4, V 5 E6 V
5, V 1
S1 E1, E 2, E3 S2 E 3, E4, E5, E6
V1
E6
E1
E3
S1
S2
V5
V3
E2
E2
E5
E4
V2
V4
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Vertex Arrays

• typedef GLint vertex33 vertex3 pt8
  (0,0,0), (0,1,0), (1,0,0), (1,1,0), (0,0,1),
  (0,1,1), (1,0,1), (1,1,1)
• void quad(GLint n1, GLint n2, GLint n3, GLint n4)
  glBegin(GL_QUADS) glVertx3iv( pt n1 )
  glVertx3iv( pt n2 ) glVertx3iv( pt n3 )
  glVertx3iv( pt n4 )
• void cube( ) quad( 6,2,3,7 ) quad( 5,1,0,4
  ) quad( 7,3,1,5 ) quad( 4,0,2,6 ) quad(
  2,0,1,3 ) quad( 7,5,4,6 )

4
5
6
7
0
1
2
3
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Plane Equations
(x,y,z)
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Surface Normal

• Surface (plane) equation AxByCzD0
• N (V1-V2)x(V1-V3) A B CT
• If P is any point on the plane
• NPD 0 NP -D

y
V1
V2
V3
x
z
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OpenGL Front/Back Rendering

• Each polygon has two sides, front and back
  (Example) glFrontFace(GL_CCW) glCullFace(GL_BAC
  K) glEnable(GL_CULL_FACE)
• OpenGL can render the two differently
• The ordering of vertices in the list determines
  which is the front side
• When looking at the front side, the vertices go
  counterclockwise
• This is basically the right-hand rule

15
Culling

• For convex objects, such as the cube, we could
  simply remove all the faces pointing away from
  viewer.
• glEnable(GL_CULL)
• Normally, if we use only the z-buffer algorithm,
  we pass 6n polygons through the pipeline.
• If we enable culling, only 3n polygons can pass
  throughthe pipeline.

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OpenGL Bitmap Functions
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OpenGL Pixel Operations

• glReadPixels( xmin, ymin, width, height,
  dataFormat, dataType, array)glEnable(
  GL_COLOR_LOGIC_OP )glLogicOp( LogicOp
  )glDrawPixels( width, height, dataFormat,
  dataType, array )
• dataFormat GL_RGB, GL_LUMINANCE, ...dataType
  GL_UNSIGNED_BYTE, LogicOp GL_COPY,
  GL_AND, GL_XOR, ...

with GL_COPY_INVERTED
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Bitmap Fonts

• Text in computer graphics is problematic.
• OpenGL no text primitive (use window
  primitives)
• GLUT minimal support
• glRasterPosition2i(x1, y1) // First Character
  PositionglutBitmapCharacter(font,
  character)glRasterPosition2i(x2, y2) // Second
  Character PositionglutBitmapCharacter(font,
  character)
• Font GLUT_BITMAP_TIMES_ROMAN_10, GLUT_STROKE_RO
  MAN, ...

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Text

• Stroke Text
• Use vertices to define line segments or curves
  that outline each character.
• Advantages
• It is defined in the same way as other objects.
• It can be manipulated as other objects (rotate,
  make bigger, smaller, etc.)
• Disadvantages
• Take up too much memory and processing time
• Slow

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Text

• Raster Text
• Characters are defined as rectangles of bits
  called bit blocks.
• Each bit block defines a single character by the
  pattern of 0 and 1 bits in the block.

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Text

• Advantages
• Simple and fast
• A raster character can be placed in the frame
  buffer rapidly by a bit-block-transfer operation
  (butblt)
• Does not take up too much memory and processing
  time
• Disadvantages
• It can not be defined in the same way as other
  objects.
• It can not be manipulated as other objects.

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Display Lists

• Command block for often used objects.
• Creation GLuint blockNum blockNum
  glGenLists( 1 ) glNewList( blockNum,
  GL_COMPILE ) ... // OpenGL
  commands glEndList( )
• Execution glCallList( blockNum )
• Deletion glDeleteLists( blockNum, 1 )

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UBI 516 Advanced omputer Graphics

• Attributes of Graphics Primitives
• ( Chapter 4 )

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OpenGL is a State Machine

• Use current attribute, change it, use new
  attribute.

time1 glBegin( ... ) ... // Present color
? glEnd( )
time2 glColor3fv( Red ) // New color is
red
time3 glBegin( ... ) ... glEnd( )
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Light

• Visible Light in Electromagnetic Spectrum

red
green
yellow
blue
violet
ultraviolet
FM
infrared
AM
microwave
visible
X-ray
frequency (Hz)
104
106
108
1010
1012
1014
1016
1018
1020
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Color

• C(?) Strenght of wavelength ? in the color
  (energy distribution)
• Additive color model
• C(?) Sum of 3 colors energy
• Three-color theory
• C T1 R T2 G T3 B Desired color
• T1, T2, T3 (Tristimulus Values) The numbers
  that specify the values of R, G, B

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Human Visual System
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Human Visual System

• cones red, green, blue receptors
• sensitivy curve of a cone Si(?)
• brain perception values
• three-color theory works for human eye
• (Ared, Agreen, Ablue) three parameter of color

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Color Model

• Color model
• Colors are different on a CRT, a film or a
  printer.
• Color models RGB, CMY, YIQ, CIE,
• Color gamut
• The ranges of color produced by given system.
• Color solid ( color cube) (Example)
• Color model based on three primary colors.
• Three primary color are three axis of a cube.
• Color gamut is set of all points on the cube.

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RGB color model

• Red, Green, Blue
• Tri-stimulus theory.
• Additive system Adding ligths to blank points.
• RGB cube has 3 axis (0 to 1).

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CMY, CMYK color model

• Hard copy systems printing, paiting ...
• Subtractive system Addingcolors to white
  surface (expaper)
• Convertion CMY to RGB, and RGB to CMY.
• CMYK color model K (black) for cartridge
  saving.
• Normally, cyan magenta yellow black
• CMY can be used for dark gray.
• But, (K) ink will be used for black.

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RGB vs. CMY

• RGB color system
• Additive primaries
• Adding ligths
• For monitor, datashows
• R, G, B lights.
• Graphics system generally use RGB color system

• CMY color system
• Subtractive primiaries
• Adding color pigments
• For printer, plotter ...
• C, M, Y inks.

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Direct color system

• Video card characteristics
• Each pixel stored with RGB values on frame
  buffer
• If frame buffer stores n bit for every values
• 2n 2n 2n colors 23n colors
• 3n 24 true color system
• 8 bit for every RGB values (0255).
• Frame buffer wold have over 3MB of memory that
  would have to be redisplay at video rates.

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Direct color system

• OpenGL functions
• Video card has 3n system
• OpenGL always use 0.0 1.0 values for red,
  green, blue.
• It means, OpenGL is independent of hardware.
• glColor()
• For setting colors.

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Direct color system

• RGBA color model
• RGB A (alpha channel opacity value)
• A 1.0 is for invisible objects.
• glColor4f(red, green, blue, alpha)
• Clearing system to color (i.e. pure white with
  alpha value of 0.0)
• glClearColor(1.0, 1.0, 1.0, 0.0)glClear(GL_COLO
  R_BUFFER_BIT).

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Indexed color system

• If the frame buffer is limited in depth (i.e.
  each pixel is only 8-bits deep), then we can
  select colors by interpreting our limited depth
  pixels as indices, rather than as color values.
• The indices point to a color-lookup table.
• Example
• For a frame buffer that has k-bits per pixel,
  each pixel index is a value from 0 to 2k-1.
• Assume that the display can display colors with
  an accuracy of m (2m reds, 2m greens, 2m blues).

color-lookup table
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Indexed color system

• Why indexed color system ?
• Image and frame buffer size is reduced.
• Image file format GIF, BMP use this system.
• OpenGL functions
• Sets current color to LUTindex.glIndexi(index)
  
• Change color at LUTindex.glutSetColor(index,
  red, green, blue)

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OpenGL Blending

• // destination
• Draw the rectangle (dr, dg, db, da)
  glEnable(GL_BLEND)glBlendFunc(GL_ONE_MINUS_SRC_A
  LPHA, GL_SRC_ALPHA)
• // source
• Draw the triangle (sr, sg, sb, sa)
• Dont forget disabling !glDisable(GL_BLEND)

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Point Attributes

• Point color size

Pixel size 1
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Line Attributes

• Line color, width style
• glLineWidth ( width )
• glLineStipple ( repeatFactor, pattern )
• // 0x1c47 for dash-dot pattern
• // binary 1110001000111
• glEnable ( GL_LINE_STIPPLE )
• ...
• glDisable ( GL_LINE_STIPPLE )
• See page 192 for example code.

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Line Attributes

• Implementation of line width

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Smooth Lines ?
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Fill-Area Attributes

• Hollow, solid or patterned. GLubyte fillPattern
  0xff,0,0xff,0,...
• glPolygonStipple ( fillPattern )
• glEnable ( GL_POLYGON_STIPPLE ) ...
• glDisable ( GL_POLYGON_STIPPLE )

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Smoothed Fill Patterns
45
OpenGL Polygon Modes

• glPolygonMode( face, displayMode ) (Example)
• Face GL_FRONT, GL_BACK, GL_FRON_AND_BACK
• Display Modes GL_POINT (Only edge
  points) GL_LINE (Wireframe) GL_FILL (Default)
• glFrontFace( faceOrder ) // GL_CW or GL_CCW
  glEdgeFlag( flag ) // GL_TRUE or GL_FALSE for
  line mode

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General Scan-Line Polygon-Fill Algorithm

• Consider the following polygon
• How do we know whether a given pixel on the
  scanline is inside or outside the polygon?

D
B
C
A
E
F
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Polygon Rasterization

• Inside-Outside PointsPoint a, c 1Point b, d
  -1if zero then fill
• For edge E ?
• For edges A and C?

Do not changes
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Flood-Fill Algorithm

• Set pixel to fill color value until bounds.
• An interior point (x, y)
• A boundary color
• A fill color

Fill color
Boundary color
Interior point (x, y)
49
4-connected vs. 8-connected

• 8-connected

• 4-connected

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Flood-Fill Algorithm

• Rough algorithm for 4-connected case
• void flood_fill4(int x, int y, Color fill, Color
  boundary) Color current getPixel(x, y)
• if (current ? boundary current ? fill)
  setPixel(x, y, fill) flood_fill4(x1, y,
  fill, boundary) // recursion ! flood_fill4(x1,
  y, fill, boundary) flood_fill4(x, y1,
  fill, boundary) flood_fill4(x, y1, fill,
  boundary)

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Character Attributes
52
Anti-aliasing

• Aliasing Information loss due to low-frequency
  sampling Jagged or stair-step appearance
• Anti-aliasing Modified Bresenhams line
  algorithm We put a pixels to yk, and lightened
  pixel yk-1 and yk1.

53
OpenGL Anti-aliasing

• In RGB display mode
• glEnable(mode) GL_POINT_SMOOTH GL_LINE_SMOOTH
  GL_POLYGON_SMOOTHAlso type these
  glEnable(GL_BLEND)glBlendFunc(GL_SRC_ALPHA, GL
  _ONE_MINUS_SRC_ALPHA)

54
Push/Pop Attributes

• glPushAttrib( mode )
• Modes GL_ALL_ATTRIB_BITS GL_POINT_BIT GL_LINE
  _BIT GL_POLYGON_BIT
• glPopAttrib( )

Current Style glPushAttrib() // Change
attribute glPopAttrib()