Computer Graphics involves technology to access. The Process transforms and presents information in a visual form. The role of computer graphics insensible.

Graphics Programming
Basic of computer graphics with OpenGL

Handful graphics function
 OpenGL :
 by silicon graphics
 PHIGS :
 Programmer’s Hierarchical Graphics System
 GKS :
 Graphics Kernel System
 JAVA-3D/JOGL
 By Sun micro-system
 DirectX: Microsoft corp.

Target Coordinate Systems
 CG system is unable define exactly unit like cm, inch etc
 CG is a device independent system
 Current coordinate is user coordinate = world coordinate
 It should be match with Display coordinate system (Raster
coordinate)

Graphics function properties
 7 groups of function
 Primitive: What is object ?
 low level objects or atomic entities, ex. point, polygon etc,
 Attribute
 How the appear: fill, bold character
 Viewing
 How we saw the image
 Transformation
 Transform of object: rotate, move
 Input
 Deal with the devices: keyboard, mouse etc.
 Control function
 Multiwindow, multiprocessing environment handling.
 Inquiry function
 Information providing for different API

Pipeline and State Machine
 Entire graphics system thinking as a state machine
 There are 2 types of Graphics functions
 Things that define primitives
 Things that changes the state

The OpenGL Interface
 Begin with “gl”
 Stored in library and referred to as GL
 There are
 Graphics Utility Library (GLU)
 GLU Toolkit (GLUT)
 GLX or WGL : glue for GL to OS
 Defined in standard header folder “GL” filename “glut.h”

Primitives and Attributes
 API should contain small set of primitives that
every hardware can be supported
 Ex. Line, polygons, text
 Variety of primitive such as circle, curves,
surface and solids able to build sophisticated
object but few hardware supported
 OpenGL takes an intermediate
 Support 2 classes of primitives
 Geometric primitives : pass through a geometric
pipeline
 Raster primitives: pass through pixel pipeline

 Geometric
 Able to manipulated
 Raster
 Lack of geometric properties

The 2D Modeling
 Special case of 3D
 Suppose z=0, every point refer to (x, y,0)
 Generally object created from set points
 In graphics system , the word “vertex” more preferred that “point”
 OpenGL function form
glVertex*();
where
*: nt or ntv , 2 or 3 characters form
n : number of dimension ( 2, 3 or 4)
t : data type (ingeter, float, double, v for pointer)
 Ex. glVertex2i(); /* vertex for 2D integer type*/
 The data type may change to GL type instead of C
 Ex. GLfloat = float in C
 Note:
 All of them have already defined in header fine <GLglut.h>

OpenGL Object form
 Defined object in
glBegin-glEnd loop
 2 kinds of primitives that
is used to defined object
 No interior, eg. points, line
 Have surface, eg. polygon
glBegin(type);
glVertex*(…);
.
.
.
glEnd();
Difference type of object form
C command for defining object

Polygon Basics
 Close object that has interior
 Able to use as curve surface
 Number of generated polygons per time is used as
graphics performance
 Display either only edges or fill
 Correct properties should be simple, convex, and flat
 3D polygon is unnecessarily flat
Filled objects
polygons displaying simple polygon nonsimple polygon convex property

Convex object properties
 3D convex object: 3 vertices are not collinear
 Safe for rendering if use triangle
 Hardware and software often support

Polygon display mode
 GL_POLYGONS
 Edges are perform line loop and close
 Edges has no with
 define either fill or edges using glPolygonMode
 If both, draw twice

Special types polygon
 Triangles and Quadrilaterals
(GL_TRIANGLES, GL_QUADS)
 Strips and Fans
(GL_TRIANGLE_STRIP, GL_QUAD_STRIP, GL_TRIANGLE_FAN)

Sample object:
Generating a Sphere
 assign to be polygons and used GL_QUAD_STRIP
 Use longitude and latitude schemes for the middle body
 For pole uses
GL_TRIANGLE_FAN
C=M_PI/180.0; //degrees to radians, M_PI = 3.14159…
for (phi = -80.0; phi <= 80.0; phi += 20.0) {
glBegin(GL_QUAD_STRIP);
for (theta = -180.0; theta <= 180.0; theta += 20.0)
{
x=sin(c*theta)*cos(c*phi);
y=cos(c*theta)*cos(c*phi);
z=sin(c*phi);
glVertex3d(x,y,z);
x=sin(c*theta)*cos(c*(phi+20.0));
y=cos(c*theta)*cos(c*(phi+20.0));
z=sin(c*(phi+20.0));
glVertex3d(x,y,z);
}
glEnd();
}

x=y=0; // North pole modeling
z = 1;
glBegin(GL_TRIANGLE_FAN);
glVertex3d(x,y,z);
c=M_Pi/180.0;
z=sin(c*80.0);
for(theta=-180.0; theta<=180.0;theta+=20.0){
x=sin(c*theta)*cos(c*80.0);
y=cos(c*theta)*cos(c*80.0);
}
glVertex3d(x,y,z);
glEnd();
x=y=0,z=-1; // South pole modeling
glBegin(GL_TRIANGLE_FAN);
glVertex3d(x,y,z);
z = -sin(c*80.0);
for(theta = -180.0; theta <= 180.0; theta=20.0){
x=sin(c*theta)*cos(c*80.0);
y=cos(c*theta)*cos(c*80.0);
glVertex3d(x,y,z);
}
glEnd();

Text
2 types of text
 Stroke Text
 Constructed via using
graphic primitives
 Able to transform like other
primitives
 Raster Text
 Character are defined as
rectangle of bits block

 Stroke text
 Consume a lot of memories
 Postscript as an example
 Raster text
 Rapidly be placed in buffer by using bit-block-transfer
(bitblt) operation
 Operate only character sizing
 Often store in ROM (hardware)
 Portability is limited by particular font
 GLUT provide 8x8 pixels function
 glutBitmapCharacter(GLUT_BITMAP_8_BY_13, C)
C: ASCII character number
 Character is placed in the present position of screen

Curved Objects
 Create by using 2 approach
 Use the primitive except points
 n side polygon instead of circle
 Approximate sphere with polyhedron
 Curved surface by a mesh of convex polygon
 Use mathematical definition
 Quadric surfaces and parametric polynomial curved and surfaces
 example:
 Define sphere by center and a point on surface
 Cubic Polynomial is defined by 4 points
 OpenGL able to do both

Attributes
 About how primitive display
 Line : display color, type of line (dash, solid)
 Concern with immediate mode: display as soon
as they are defined

Color
 Most interesting of perception and computer graphics
 Base on three color theory
 If using additive color model
- c = T1R+T2G+T3B
 C: color that we trying to match
 T1, T2, T3: strength of intensity, the tristimulus value

Human Visual System
 Our visual system do a continuous perception
 Depends on 3 types of cone cell
 Visually indistinguishable if they have the
same tristimulus value
 CRT is an example of additive color system
Ai: brain perception value
Si: cone cell sensitivity
Viewing a point as a
color solid cube
( ) ( )
i i
A S C d
  
 

Subtractive color model
 The complementary of additive color model
 Start with white surface
 If white light hit the surface, color will be absorb except the
object color which are reflect
 Ex. painting and printing
 Complementary color: cyan, magenta, yellow
additive color model subtractive color model

RGB-color model
 Use separate buffer for each color
 Each pixel has 3 bytes (24 bits) for each color
 16 Million shade of color
 OpenGL function
 glColor3f(r, g, b);
 ex. Red
 glColor3f(1.0, 0.0, 0.0);

RGBA, the 4 color model
 A: Alpha channel
 Store in frame buffer like RGB
 For creating effect ex. fog, combining images.
 OpenGL treat as opacity or transparency
 Ex. OpenGL command for 4 color model
 glClearColor(1.0, 1.0, 1.0, 1.0);
 White color and opaque

Indexed Color
 Difficult to support in hardware
 Higher memory requirements but now
memory is cheaper
 Use color tray of artist as principle
 Infinite color can be produced from different
quantity of primary colors

OpenGL indexed color function
glIndex(element);
 Select color out of table
glutSetcolor(int color, GLfloat red, GLfloat blue, GLfloat green);
 Set color entry to map the color table

Color Attributes
 For RGB mode
glClearColor(1.0, 1.0, 1.0); /* clear to white */
glColor3f(1.0, 0.0, 0.0); /* setting point to red */
glPointSize(2.0); /* 2 pixel wide */
Note:
If 2 display differ in pixel size, rendered images
may appear slightly different

Viewing
 Method for objects appear on screen
 Use synthetic camera concept
 Fix lens and fix location
 Picture would be distort like real world
 If we need to take an elephant picture, camera
should far enough to take all information

2D Viewing
 Base on the 2D rectangular area
 Know as viewing rectangle or clipping rectangle
 Be a special case of 3D viewing ex. plane at z=0
 Default in 2x2x2 volume, origin at the center and bottom-
left corner is at (-1.0, -1.0)

Orthographic View
 2D view the orthographic projection of 3D
 Function
void glOrtho(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble
near, GLdouble far);
// near, far: distance which are measured from camera
/* orthographic projection from 3D */
void gluOrtho2D(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top);
/* 2D equivalent to glOrtho but near and far set to -1.0, 1.0 */
 Unlike camera, it is able to view behind object

Matrix Modes
 Between graphic pipeline states, any transformation
 2 important matrices:
 model-view
 Projection
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluOrtho2D(0.0, 500.0, 0.0, 500.0);
glMatrixMode(GL_MODELVIEW);

Control function
 Concern about software environment between
software and platform
 Different platform will have different interfacing
 GLUT also provide the utility : see further

Windows interfacing
Window :
 A rectangular area of our display, max = Screen
Window default origin (0,0)
 at lower-left corner like Screen but mouse at top-
left
OpenGL function (GLUT function) for window
glutInit (int *argcp, char **argv);
glutCreateWindow(char *title); /* given the window title */

Display setup
glutInitDisplayMode(GLUT_RGB| GLUT_DEPTH | GLUT_DOUBLE);
GLUT_RGB: define RGB color mode
GLUT_DEPTH: a depth buffer for hidden-surface removal
GLUT_DOUBLE: number of buffer Double/Single
default:
RGB color, no hidden surface removal, single buffering
glutInitWindowSize(480, 640);
glutInitWindowPosition(0,0)

Aspect ratio
 Ratio of rectangle’s width to its height
 If glOrtho and glutInitWindowSize are not
specified the same size, object are distort.

View port
 A rectangular area of the display window
 Setting a view port
void glViewport(GLint x, GLint y, GLsizei w, GLsizei h);

Service function: main, display and myinit
 glutMainLoop(); /* begin an event-processing loop, let the
window waiting for kill process */
 void glutDisplayFunc(void *(func)(void));
/* call to the redisplay function name func */
#include <GL/glut.h>
void main(int argc, char **argv){
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB );
glutInitWindowSize(500, 500);
glutInitWindowPosition(0, 0);
glutCreateWindow("Simple OpenGL example");
glutDisplayFunc(display);
myinit();
glutMainLoop();
}
Program template

Program structure consisting
 myinit :
setup user options to state variables dealing with viewing
and attributes-parameters

Example program:
Sierspinski Gasket
Proceeding of Sierspinski
1. Pick a random initial point in triangle
2. Select vertex
3. Finding the halfway point between initial point and
random vertex
4. Mark and display new point
5. Replace the initial point with this new point
6. Return to step 2

Pseudo code
main() {
Initialize_the_system();
for(some_number_of_points) {
pt = generate_a_point();
display_the_point(pt);
}
cleanup();
}
Sierpinski gasket

Array with OpenGL
// For 3D vertex, 2D is a special case
GLfloat vertex[3]; /* define array */
// Then we can use
glVertex3fv(vertex);/* pass by reference */
// Defining geometric object in Begin and End fn. statement
glBegin(GL_LINES);
glVertex2f(x1, y1);
glVertex2f(x2, y2);
glEnd();

The same data able to define another object
// define a pair of points
glBegin(GL_POINTS);
glVertex2f(x1, y1);
glVertex2f(x2, y2);
geEnd();

Using a 2 elements array to carry a point
// By defining new data type with 2 element array
typedef GLfloat point2[2];
// point2[0] carry x data
// point2[1] carry y data
when use
point2 vertices[3] ; // that means
vertices[0][0], vertices[1][0], vertices[2][0] // carry x value
vertices[0][1], vertices[1][1], vertices[2][1] // carry y value
point2 vertices[3] = {{0.0, 0.0}, {250.0, 500.0}, {500,0}}

Graphics Example Sierspinski
 Thing need to do
 Coloring
 Locate the image
 Define size
 Window creating
 Image clipping
 Image duration
5000 random point 2D Sierspinski

Triangular gasket
 There is no point in the middle triangle
 The same observation can be applied to the other 3 triangles and so
on
 Another method to fill the area is use triangle polygon instead of
point
 Strategy
 Start with a triangle which subdivide the area to 4 triangles
 Remove the middle one
 Repeat to other triangles until the size of the removing triangle is small
enough. Let say 1 pixel
 This is the recursive program
 See program

typedef float point2[2]; /* initial triangle */
point2 v[]={{-1.0, -0.58}, {1.0, -0.58}, {0.0, 1.15}};
void triangle( point2 a, point2 b, point2 c) { /* display one triangle */
glBegin(GL_TRIANGLES);
glVertex2fv(a);
glVertex2fv(b);
glVertex2fv(c);
glEnd();
}
void divide_triangle(point2 a, point2 b, point2 c, int m) {
/* triangle subdivision using vertex numbers */
point2 v0, v1, v2;
int j;
if (m>0) {
for(j=0; j<2; j++) v0[j]=(a[j]+b[j])/2;
for(j=0; j<2; j++) v1[j]=(a[j]+c[j])/2;
for(j=0; j<2; j++) v2[j]=(b[j]+c[j])/2;
divide_triangle(a, v0, v1, m-1);
divide_triangle(c, v1, v2, m-1);
divide_triangle(b, v2, v0, m-1);
}
else /* draw triangle at end of recursion */
triangle(a,b,c);
}

void display(void) {
glClear(GL_COLOR_BUFFER_BIT);
divide_triangle(v[0], v[1], v[2], n);
glFlush();
}
with 4 level recursion with 5 level recursion

3D Sierspinski gasket
 Begin with tetrahedron instead
triangle
 Use 3D point
point v[]={ { 0.0, 0.0, 1.0},
{ 0.0, 0.942809, -0.33333},
{-0.816497, -0.471405, -0.333333},
{ 0.816497, -0.471405, -0.333333}
};

The hidden surface removal
 Problem may happen if there is no relation between
surface
 Close opaque object should mask the far object
 The part of far object which overlap with close object
should remove
 Z-buffer algorithm is a method to manipulate.

Exercises
1. Write a part of C program to define a unit circle object at position (1,1) using
OpenGL command
1. Explain the algorithm that you use to draw
Hint: you may use primitive such as TRIANGLE_FANS, or others
2. Write 2 unit circles, one at (1,1) and the other at (-1,-1). The (1,1) circle use full
surface shaded with red color and the other display in wire frame.
3. Space-filling curves have interested mathematicians for centuries. In the limit, these
curves have infinite length, but they are confined to a finite rectangle and never cross
themselves. Many of these curves can be generated iteratively. Consider the “rule”
pictured in shown below that replaces a single line segment with four shorter
segments. Write a program that starts with a triangle and iteratively applies the
replacement rule to all the line segments. The object that you generate is called the
Koch snowflake.

Computer Graphics involves technology to access. The Process transforms and presents information in a visual form. The role of computer graphics insensible.

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Computer Graphics involves technology to access. The Process transforms and presents information in a visual form. The role of computer graphics insensible.