Chapter 2 Graphics Programming

1
Chapter 2Graphics Programming
2
Sierpinski Gasket 1/2

• Pick an initial point at random inside the
  triangle
• Select one of the three vertices at random
• Find the point halfway between the initial point
  and the randomly selected vertex
• Display the new point
• Replace the initial point with this new point
• Return to step 2

3
Sierpinski Gasket 2/2

• main()
• initialize_the_system()
• for(some_number_of_points)
• pt generate_a_point()
• display_the_point(pt)
• cleanup()

4
Code of Sierpinski Gasket 1/3

• typedef GLfloat point22
• void display(void)
• point2 vertices30,0,250,500,500,0
• / an arbitrary triangle /
• static point2 p 75,50
• / any desired initial point /
• int j, k
• int rand() / standard random-number generator
  /

5
Code of Sierpinski Gasket 2/3

• for(k0klt5000k)
• jrand()3 / pick a random vertex from 0, 1,
  2 /
• p0(p0verticesj0)/2 / compute new
  point /
• p1(p1verticesj1)/2
• glBegin(GL_POINTS)
• glVertex2fv(p) / display new point /
• glEnd()
• glFlush()

6
Code of Sierpinski Gasket 3/3
7
Questions

• In what colors are we drawing
• Where on the screen does our image appear
• How large will the image be
• How do we create an area of the screen a window
  for our image?
• How long will the image remain on the screen?

8
Coordinate Systems
9
Graphics Functions 1/3
10
Graphics Functions 2/3

• Primitive functions points, line segments,
  polygons, pixels, text, curves, surfaces
• Attributes functionscolor, pattern, typeface
• Viewing functionsposition, orientation, clipping

11
Graphics Functions 3/3

• Transformation functionsrotation, translation,
  scaling
• Input functionskeyboards, mice, data tablets
• Control functionscommunicate with windows,
  initialization, error handling
• Inquiry functions number of colors, camera
  parameters/values

12
Points and Line Segments
13
Polygon Basics 1/3
Filled objects
Methods of displaying a polygon
14
Polygon Basics 2/3

• Simple, convex, and flat

Simple
Nonsimple
15
Polygon Basics 3/3
Convexity
Convex objects
16
Polygon Types in OpenGL 1/2
17
Polygon Types in OpenGL 2/2
Use triangles if possible because of efficiency!
18
Drawing a Sphere 1/5
19
Drawing a Sphere 2/5
z
x
?
y
?
20
Drawing a Sphere 3/5

• cM_PI/180.0 // degrees to radians,
  M_PI3.14159
• for(phi-80.0 philt80.0 phi20.0)
• glBegin(GL_QUAD_STRIP)
• for(theta-180.0 thetalt180.0 theta20.0)
• xsin(ctheta)cos(cphi)
• ycos(ctheta)cos(cphi)
• zsin(cphi)
• glVertex3d(x, y, z)
• xsin(ctheta)cos(c(phi20.0))
• ycos(ctheta)sin(c(phi20.0))
• zsin(c(phi20.0))
• glVertex3d(x, y, z)
• glEnd()

Drawing the portion of lower latitudes
21
Drawing a Sphere 4/5

• xy0
• z1
• glBegin(GL_TRIANGLE_FAN)
• glVertex3d(x, y, z)
• cM_PI/180.0
• zsin(c80.0)
• for(theta-180.0 thetalt180.0 theta20.0)
• xsin(ctheta)cos(c80.0)
• ycos(ctheta)sin(c80.0)
• glVertex3d(x, y, z)
• glEnd()

Drawing the portion around the north pole
22
Drawing a Sphere 5/5

• xy0
• z-1
• glBegin(GL_TRIANGLE_FAN)
• glVertex3d(x, y, z)
• z-sin(c80.0)
• for(theta-180.0 thetalt180.0 theta20.0)
• xsin(ctheta)cos(c80.0)
• ycos(ctheta)sin(c80.0)
• glVertex3d(x, y, z)
• glEnd()

Drawing the portion around the south pole
23
Text Stroke or Raster
24
Attributes for Lines, Texts
25
Color 1/4
CT1RT2GT3B, T1, T2, T3 are the tristimulus
values
Additive color matching
26
Color 2/4

• Basic tenet of three-color theoryIf two colors
  produce the same tristimulus values, then they
  are visually indistinguishable
• The range of colors that we can produce on a
  given system is called that systems color gamut

27
Color 3/4
Color Solid
28
Color 4/4
Subtractive Color
Additive Color
29
Indexed Color
Color-lookup table
Example km8 pick 256 out of 16M colors
30
Two-dimensional Viewing
Objects before clipping
Image after clipping
31
Viewing Volume
32
Orthographic View
33
Aspect Ratio
Viewing rectangle
Display window
34
Viewports
35
Sample main program

• void main(int argc, char argv)
• glutInit(argc,argv)
• glutInitDisplayMode(GLUT_SINGLE
  GLUT_RGB)glutInitWindowSize(500, 500)
• glutInitWindowPosition(0, 0)glutCreateWindow(S
  imple OpenGL example)
• glutDisplayFunc(display)
• myinit()
• glutMainLoop()

For most non-interactive applications
36
Gasket Program 1/3

• void myinit(void)
• / attributes /
• glClearColor(1.0, 1.0, 1.0, 1.0) / white
  background /
• glColor3f(1.0, 0.0, 0.0) / draw in red /
• / set up viewing /glMatrixMode(GL_PROJECTION)
  glLoadIdentity()gluOrtho2D(0.0, 500.0, 0.0,
  500.0)glMatrixMode(GL_MODELVIEW)

37
Gasket Program 2/3

• void display(void)
• typedef GLfloat point22 / define a point
  data type /point2 vertices30.0,0.0,250.0,
  500.0,500.0,0.0 / triangle /
• int i, j, kint rand()
• point2 p75.0, 50.0 / arbitrary point
  inside triangle /
• glClear(GL_COLOR_BUFFER_BIT) / clear the
  window /

38
Gasket Program 3/3

• / compute and output 5000 new points /
• for(k0 klt5000 k)
• jrand()3 / compute point halfway between
  vertex and old point / p0(p0vertexj0)/
  2.0 p1(p1vertexj1)/2.0
• glBegin(GL_POINTS) / plot point /
  glVertex2fv(p) glEnd()
• glFlush()

39
Using Recursion 1/3

• void triangle(point2 a, point2 b, point2 c)
• glBegin(GL_TRIANGLES)
• glVertex2fv(a)
• glVertex2fv(b)
• glVertex2fv(c)
• glEnd()

40
Using Recursion 2/3

• void divide_triangle(point2 a, point2 b, point2
  c, int k)
• point2 ab, ac, bc
• int j
• if(kgt0)
• for(j0 jlt2 j) abj(ajbj)/2
• for(j0 jlt2 j) acj(ajcj)/2
• for(j0 jlt2 j) bcj(bjcj)/2
• divide_triangle(a, ab, ac, k-1)
• divide_triangle(c, ac, bc, k-1)
• divide_triangle(b, bc, ab, k-1)
• else triangle(a, b, c) / draw triangle at end
  of of recursion /

a
ab
ac
b
c
bc
41
Using Recursion 3/3

• Void display(void)
• glClear(GL_COLOR_BUFFER_BIT)
• divide_triangle(v0, v1, v2, n)
• glFlush()

42
Three-Dimensional Gasket 1/2

• typedef Glfloat point33
• point3 vertices4 0,0,0,0,250,500,100,500
  ,250,250,250,100,250
• Point3 new,old250, 100, 250
• jrand()4
• new0(old0verticesj0)/2
• new1(old1verticesj1)/2
• new2(old2verticesj2)/2

tetrahedron
43
Three-Dimensional Gasket 2/2

• / plot point /
• glBegin(GL_POINTS)
• glVertex3fv(new)
• glEnd()
• / replace old point by new /
• old0new0
• old1new1
• old2new2

44
3D Recursive Gasket 1/3

• void triangle(point3 a, point3 b, point3 c)
• glBegin(GL_POLYGON)
• glVertex3fv(a)
• glVertex3fv(b)
• glVertex3fv(c)
• glEnd()

45
3D Recursive Gasket 2/3

• void divide_triangle(point3 a, point3 b, point3
  c, int k)
• point3 ab, ac, bc
• int j
• if(kgt0)
• for(j0 jlt3 j) abj(ajbj)/2
• for(j0 jlt3 j) acj(ajcj)/2
• for(j0 jlt3 j) bcj(bjcj)/2
• divide_triangle(a, ab, ac, k-1)
• divide_triangle(c, ac, bc, k-1)
• divide_triangle(b, ab, ab, k-1)
• else triangle(a, b, c) / draw triangle at end
  of recursion/

46
3D Recursive Gasket 3/3

• void tetrahedron(int n)
• glColor3f(1.0, 0.0, 0.0)
• divide_triangle(v0, v1, v2, k)
• glColor3f(0.0, 1.0, 0.0)
• divide_triangle(v3, v2, v1, k)
• glColor3f(0.0, 0.0, 1.0)
• divide_triangle(v0, v3, v1, k)
• glColor3f(0.0, 0.0, 0.0)
• divide_triangle(v0, v2, v3, k)

47
Hidden-Surface Removal 1/3
48
Hidden-Surface Removal 2/3

• Sorting?
• Z-Buffer algorithm

49
Hidden-Surface Removal 3/3

• void display()
• glClear(GL_COLOR_BUFFER_BIT
  GL_DEPTH_BUFFER_BIT)
• tetrahedron(n)
• glFlush()

50
Summary and Notes

• Graphics (primitives, attributes), viewing,
  control, communications with windows
• Sample codes