COMPUTER GRAPHICS Hochiminh city University of Technology Faculty of Computer Science and...

COMPUTER GRAPHICS

Hochiminh city University of TechnologyFaculty of Computer Science and Engineering

CHAPTER 02:

Graphics Programming

Faculty of Computer Science and Engineering - HCMUT

OUTLINE IntroductionOpenGL LibrariesWindows-based programmingA simple programStructure of the programViewingViewportPrimitivesDraw ObjectThe Sierpinski GasketHidden-Surface RemovalMore Examples

IntroductionProgramming Environment

– Hardware: display, graphics card

– Software: OS (Windows), programming language (MS VC++), graphics library (OpenGL, DirectX)

OpenGL

– Platform-independent API

– Easy to use

– Close enough to the hardware to get excellent performance

– Treat 2D and 3D in the same way

OpenGL LibrariesOpenGL core library

– OpenGL32 on Windows

– GL on most unix/linux systems (libGL.a)OpenGL Utility Library (GLU)

– Provides functionality in OpenGL core but avoids having to rewrite code

Links with window system

– GLX for X window systems

– WGL for Windows

– AGL for Macintosh

OpenGL LibrariesOpenGL Utility Toolkit (GLUT)

– Provides functionality common to all window systems

• Open a window

• Get input from mouse and keyboard

• Menus

• Event-driven

– Code is portable but GLUT lacks the functionality of a good toolkit for a specific platform

• No slide bars

OpenGL Libraries

OpenGL LibrariesOpenGL Functions

– Primitives• Points• Line Segments• Polygons

– Attributes– Transformations

• Modeling• Viewing

– Control (GLUT)– Input (GLUT)– Query

Windows-based programmingEvent-driven programmingEvent queueCallback functionRegister callback function

• glutDisplayFunc(myDisplay)

• glutReshapeFunc(myReshape)

• glutMouseFunc(myMouse)

• glutKeyboardFunc(myKeyboard)

A simple programGenerate a square on a solid background

A simple program#include <GL/glut.h>void mydisplay(){

glClear(GL_COLOR_BUFFER_BIT);glBegin(GL_POLYGON);

glVertex2f(-0.5, -0.5);glVertex2f(-0.5, 0.5);glVertex2f(0.5, 0.5);glVertex2f(0.5, -0.5);

glEnd();glFlush();

}int main(int argc, char** argv){

glutCreateWindow("simple");glutDisplayFunc(mydisplay);glutMainLoop();

A simple program

– Objects

– Viewer

– Light Source(s)

– Materials

Structure of the program Most OpenGL programs have a similar structure that consists of the

following functions

– main():

• defines the callback functions

• opens one or more windows with the required properties

• enters event loop (last executable statement)

– init(): sets the state variables

• Viewing

• Attributes

– Callbacks

• Display function

• Input and window functions

Structure of the program

Structure of the programglutInit allows application to get command line

arguments and initializes systemgluInitDisplayMode requests properties for the window

(the rendering context)– RGB color– Single buffering– Properties logically ORed together

glutWindowSize in pixelsglutWindowPosition from top-left corner of displayglutCreateWindow create window with title “simple”glutDisplayFunc display callbackglutMainLoop enter infinite event loop

– Objects

– Viewer

– Light Source(s)

– Materials

ViewingOpenGL places a camera at the origin in object space

pointing in the negative z directionThe default viewing volume is a box centered at the

origin with a side of length 2

ViewingPerspective projections:

all projectors meet at the center of projection

Parallel projection: projectors are parallel, center of projection is replaced by a direction of projection

Viewing In the default orthographic view, points are projected

forward along the z axis onto the plane z=0

Viewing

glBegin(GL_POLYGON);

glVertex2f(-0.5, -0.5);

glVertex2f(-0.5, 0.5);

glVertex2f(0.5, 0.5);

glVertex2f(0.5, -0.5);

glEnd();

Viewing

glEnd();

Viewing

glEnd();

ViewingglMatrixMode (GL_PROJECTION)

glLoadIdentity();

glOrtho(-1.0, 1.0, -1.0, 1.0, -1.0, 1.0);glMatrixMode (GL_PROJECTION)

glLoadIdentity();

glOrtho(-1.0, 1.0, -1.0, 1.0)glOrtho(left, right, bottom, top, near, far)gluOrtho2D(left, right,bottom,top)

Viewing

ViewingglBegin(GL_POLYGON);

glVertex2f(-2.0, 0.0);glVertex2f(-2.0, 2.0);glVertex2f(0.0, 2.0);glVertex2f(0.0, 0.0);

glEnd();

glBegin(GL_POLYGON);glVertex2f( 0.0, -4.0);glVertex2f( 2.0, 0.0);glVertex2f( 4.0, -4.0);

glEnd();

ViewingHow to get the picture of triangle and square?

– glMatrixMode (GL_PROJECTION);

– glLoadIdentity();

– gluOrtho2D(-2.0, 4.0, -4.0, 2.0);How to get the picture of the square?How to get the picture of the triangle?

ViewportDo not have use the entire window for the image:

glViewport(x,y,w,h)Values in pixels (screen coordinates)

ViewportSize of the graphics window

– glutInitWindowSize(cx, cy);

glutInitWindowSize(640, 480);

ViewportglViewport(320, 240, 320, 240)

ViewportglViewport(320, 240, 240, 240)

ViewportHow to draw picture in the second quadrant?

– glViewport(0, 240, 320, 240);How to draw picture in the third quadrant?How to draw picture in the fourth quadrant?How to draw picture in all quadrant?

ViewportHow to draw picture in all quadrant?

Viewport glViewport(320, 240, 320, 240);

glBegin() //draw square

………………

glEnd()

glBegin() //draw triangle

………………

glEnd() glViewport(0, 240, 320, 240);

…………………………………. glViewport(0, 0, 320, 240);

…………………………………. glViewport(320, 0, 320, 240);

………………………………….

Primitives

– Objects

– Viewer

– Light Source(s)

– MaterialsPolylineTextFilled regionRaster image

PrimitivesPolyline

– A polyline is a connected sequence of straight lines

– A polyline can be used to approximated a smooth curve

– Functions:

• Draw Point: drawDot(x1, y1)

• Draw Line: drawLine(x1, y1, x2, y2)

• Draw Polyline: drawPolyline(poly)

PrimitivesPolyline

– Polygon: polyline if the first and the last points are connected by an edge

– Polygon type: simple, convex

PrimitivesPolyline

– Attributes: Color, thickness, type (solid, dash), join points

PrimitivesText:

– Display mode: text mode, graphics mode– Attributes: Font, color, size, orientation, space

PrimitivesFilled region

– Filled region is a shape filled with some color or pattern. The boundary is often a polygon

PrimitivesUse filled region to shade the different faces of a three-

dimensional object

PrimitivesRaster Image

– Raster image is made up of many pixels.

– Stored as an array of numerical values

How are raster images created?

– Hand-designed, Computed Images, Scanned ImagesRaster image can be processed

Draw Object

glBegin(parameter)

glVertex2f(…) //or glVertex3f(…)

glVertex2f(…)

………………

glEnd()Parameter

– GL_POINTS, GL_LINES, GL_TRIANGLES, v.v

Draw Object

glBegin(GL_POINTS);

glVertex2f( 0.5, 1.0);

glVertex2f(-0.5, -1.0);

glVertex2f( 0.5, -1.0);

glEnd();

Draw Object

glBegin(GL_LINES);

glVertex2f(-0.5, -1.0);

glVertex2f( 0.5, -1.0);

glEnd();

Draw Object

glBegin(GL_LINE_STRIP);

glVertex2f(-0.5, -1.0);

glVertex2f( 0.5, -1.0);

glEnd();

Draw Object

glBegin(GL_LINE_LOOP);

glVertex2f(-0.5, -1.0);

glVertex2f( 0.5, -1.0);

glEnd();

Draw Object

glBegin(GL_TRIANGLES);

glVertex2f(-0.5, -1.0);

glVertex2f( 0.5, -1.0);

glEnd();

Draw ObjectglPolygonMode(GL_FRONT_AND_BACK, GL_LINE);glColor3f(1.0, 0.0, 0.0);glLineWidth(3.0);

Draw ObjectglPolygonMode(GL_FRONT_AND_BACK, GL_POINT);glColor3f(1.0, 1.0, 0.0);glPointSize(5);

Draw ObjectglPolygonMode(GL_FRONT_AND_BACK, GL_FILL);glColor3f(0.0, 1.0, 0.0);glClearColor(1.0, 1.0, 1.0, 1.0);

Draw Object

Draw ObjectglPolygonMode(GL_FRONT_AND_BACK, GL_FILL);glColor3f(0.0, 1.0, 0.0);glClearColor(1.0, 1.0, 1.0, 1.0);glBegin(GL_TRIANGLES);

……………………..glEnd();glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);glColor3f(1.0, 0.0, 0.0);glLineWidth(3);glBegin(GL_TRIANGLES);

……………………..glEnd();

Draw ObjectglBegin(GL_TRIANGLES);

glVertex2f(-0.5, 1.0);glVertex2f( 0.5, 1.0);glVertex2f(-0.5, 0.0);glVertex2f(-0.5, 0.0);glVertex2f( 0.5, 1.0);glVertex2f( 0.5, 0.0);glVertex2f(-0.5, -1.0);glVertex2f(-0.5, 0.0);glVertex2f( 0.5, 0.0);glVertex2f( 0.5, 0.0);glVertex2f(-0.5, -1.0);glVertex2f( 0.5, -1.0);

glEnd();

Draw Object

glBegin(GL_TRIANGLE_STRIP);

glVertex2f(-0.5, -1.0);

glVertex2f( 0.5, -1.0);

glEnd();

Draw Object

GL_QUADSGL_QUAD_STRIPGL_TRIANGLE_FAN

Draw Object

void drawPoint(GLint x, GLint y) {

glBegin(GL_POINTS);

glVertex2i(x, y);

glEnd();

void drawLine(GLint x1, GLint y1, GLint x2, GLint y2){

glBegin(GL_LINES);

glVertex2i(x1, y1);

glVertex2i(x2, y2);

glEnd();

Draw Objectclass GLintPointArray {

const int MAX_NUM = 100;

public:

int num ;

GLintPoint pt[MAX_NUM] ;

void drawPolyLine(GLintPointArray poly,int closed) {

glBegin(closed ? GL_LINE_LOOP : GL_LINE_STRIP);

for(int i=0;i<poly.num;i++)

glVertex2i(poly.pt[i].x, poly.pt[i].y);

glEnd();

glFlush();

The Sierpinski Gasket

1. Pick an initial point (x, y, z) at random inside the triangle

2. Select one of the three vertices at random

3. Find the location halfway between the initial point and the randomly selected vertex

4. Display this new point by putting some sort of marker, such as a small circle at the corresponding location on the display

5. Replace the point at (x, y, z) with this new point

6. Return to step 2

main()

Initialize_the_system();

for(some_number_of_points)

pt = generate_a_point();

Display_the_point(pt);

void myinit()

glClearColor(1.0, 1.0, 1.0, 1.0); /* white background */

glColor3f(1.0, 0.0, 0.0); /* draw in red */

glMatrixMode(GL_PROJECTION);

glLoadIdentity();

gluOrtho2D(0.0, 50.0, 0.0, 50.0);

glMatrixMode(GL_MODELVIEW);

The Sierpinski Gasketvoid display( void ){ GLfloat vertices[3][2]={{0.0,0.0},{25.0,50.0},{50.0,0.0}}; /* A triangle */ int j, k; int rand(); /* standard random number generator */ GLfloat p[2] ={7.5,5.0}; /* An arbitrary initial point inside traingle */

glClear(GL_COLOR_BUFFER_BIT); /*clear the window */ glBegin(GL_POINTS); for( k=0; k<5000; k++) { j = rand()%3; /* pick a vertex at random */

p[0] = (p[0]+vertices[j][0])/2.0; p[1] = (p[1]+vertices[j][1])/2.0;

glVertex2fv(p); }

glEnd();glFlush(); /* clear buffers */

The Sierpinski GasketStart with a triangle

Connect bisectors of sides and remove central triangle

Repeat

The Sierpinski GasketFive subdivisions

The Sierpinski GasketGLfloat v[3][2]={{-1.0, -0.58}, {1.0, -0.58}, {0.0, 1.15}};int n;

void triangle( GLfloat *a, GLfloat *b, GLfloat *c)

/* display one triangle */{ glVertex2fv(a); glVertex2fv(b); glVertex2fv(c);}

The Sierpinski Gasketvoid divide_triangle(GLfloat *a, GLfloat *b,

GLfloat *c, int m){ 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(triangle(a,b,c));}

The Sierpinski Gasketvoid display(){ glClear(GL_COLOR_BUFFER_BIT); glBegin(GL_TRIANGLES); divide_triangle(v[0], v[1], v[2], n); glEnd(); glFlush();}

void myinit(){ glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(-2.0, 2.0, -2.0, 2.0); glMatrixMode(GL_MODELVIEW); glClearColor (1.0, 1.0, 1.0,1.0) glColor3f(0.0,0.0,0.0);}

The Sierpinski Gasketint main(int argc, char **argv){ n=4; glutInit(&argc, argv); glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB); glutInitWindowSize(500, 500); glutCreateWindow(“2D Gasket"); glutDisplayFunc(display); myinit();

glutMainLoop();}

The Sierpinski GasketWe can easily make the program three-dimensional by

using– GLfloat v[4][3]– glVertex3f– glOrtho

But that would not be very interesting Instead, we can start with a tetrahedron

The Sierpinski GasketWe can subdivide each of the four faces

Appears as if we remove a solid tetrahedron from the center leaving four smaller tetrahedra

The Sierpinski Gasketvoid triangle( GLfloat *a, GLfloat *b, GLfloat *c){ glVertex3fv(a); glVertex3fv(b); glVertex3fv(c);}

void tetra(GLfloat *a, GLfloat *b, GLfloat *c, GLfloat *d){ glColor3fv(colors[0]); triangle(b, d, c); glColor3fv(colors[1]); triangle(a, b, c); glColor3fv(colors[2]); triangle(a, c, d); glColor3fv(colors[3]); triangle(a, d, b);}

The Sierpinski Gasketvoid divide_tetra(GLfloat *a, GLfloat *b, GLfloat *c, GLfloat *d, int m){

GLfloat mid[6][3];

int j;

if(m>0) {

for(j=0; j<3; j++) mid[0][j]=(a[j]+b[j])/2;

…………………………………………….

divide_tetra(a, mid[0], mid[1], mid[2], m-1);

…………………………………………….

else(tetra(a,b,c,d)); /* draw tetrahedron at end of recursion */

The Sierpinski GasketBecause the triangles are drawn in the order they are

defined in the program, the front triangles are not always rendered in front of triangles behind them

Hidden-Surface RemovalWe want to see only those surfaces in front of other

surfacesOpenGL uses a hidden-surface method called the z-

buffer algorithm that saves depth information as objects are rendered so that only the front objects appear in the image

Hidden-Surface RemovalThe algorithm uses an extra buffer, the z-buffer, to

store depth information as geometry travels down the pipeline

It must be– Requested in main()

•glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH)

– Enabled •glEnable(GL_DEPTH_TEST)

– Cleared in the display callback•glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

More Examples void hardwirededHouse(){ glBegin(GL_LINE_LOOP);//vẽ khung ngôi nhà glVertex2i(40, 40); glVertex2i(40, 90); glVertex2i(70, 120); glVertex2i(100, 90); glVertex2i(100, 40); glEnd(); glBegin(GL_LINE_STRIP);//vẽ ống khói glVertex2i(50, 100); glVertex2i(50, 120); glVertex2i(60, 120); glVertex2i(60, 110); glEnd(); . . . // vẽ cửa ra vào

. . . // vẽ cửa sổ}

More Examples void parameterizedHouse(GLintPoint peak,GLint width,GLint

height)// tọa độ của nóc nhà là peak, // chiều cao, chiều rộng của ngôi nhà là height và width{ glBegin(GL_LINE_LOOP); glVertex2i(peak.x, peak.y); glVertex2i(peak.x + width/2,peak.y – 3*height/8); glVertex2i(peak.x + width/2,peak.y – height); glVertex2i(peak.x - width/2,peak.y – height); glVertex2i(peak.x - width/2,peak.y – 3*height/8); glEnd(); vẽ ống khói vẽ cửa ra vào vẽ cửa sổ}

More Examples

More ExamplesSpherical coordinate system

– x = r*sin(theta)*cos(phi);

– z = r*cos(theta)*cos(phi);

– y = r*sin(phi);

More Examples

More Examplesfor(float phi = -80; phi<=80; phi+=20){

phir = c*phi;phir20 = c*(phi+20);glBegin(GL_QUAD_STRIP);for(float theta = -180; theta<=180; theta+=20) {

thetar = c*theta;x = sin(thetar)*cos(phir); z = cos(thetar)*cos(phir);y = sin(phir);glVertex3d(x, y, z);x = sin(thetar)*cos(phir20);z =

cos(thetar)*cos(phir20);y = sin(phir20);glVertex3d(x, y, z);

}glEnd();

More ExamplesglBegin(GL_TRIANGLE_FAN);

glVertex3d(0, 1, 0);c80 = c*80;y = sin(c80);for(float theta = 180; theta>=-180; theta-=20){

thetar = c*theta;x = sin(thetar)*cos(c80);z = cos(thetar)*cos(c80);glVertex3d(x, y, z);

}glEnd();

More Examples

Modeling Shapes with Polygonal Meshes

Polygonal meshes are simply collections of polygons, or “faces,” that together form the “skin” of an object. They have become a standard way of representing a broad class of solid shapes in graphics.

Easy to represent (by a sequence of vertices) and transform, have simple properties (a single normal vector, sequence of vertices) and transform, have simple properties (a single normal vector, a well-defined inside and outside, etc.), and are easy to draw (using a polygon-fill routine or by mapping texture onto the polygon).

glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);

glVertex3f(-1, 1, 1);

glVertex3f( 1, 1, 1);

glVertex3f( 1, 1, -1);

glVertex3f( -1, 1, -1);

glEnd();

……………………………….

glPolygonMode(GL_FRONT_AND_BACK, GL_FILL);

glColor3f(0, 0, 1);

glVertex3f(-1, 1, 1);

glVertex3f( 1, 1, 1);

glVertex3f( 1, 1, -1);

glVertex3f( -1, 1, -1);

glEnd();

……………………………….

Data Structureclass Mesh {

Face faceArr[];

class Face {

Point3 vertexArr[];

Vector3 normArr[];

Defining a Polygonal Mesh

- A more efficient approach uses three separate lists : a vertex list, a normal list, and a face list

- The three lists work together : The vertex list contains locational or geometric information, the normal list contains orientation information, and the face list contains connectivity or topological information.

class VertexID{

public:

int vertIndex; //index of this vertex in the vertex list

int normIndex; // index of this vertex's normal

class Face{

public:

int nVerts; // number of vertice in this face

VertexID* vert; // the list of vertex and normal index

Face() { nVerts = 0; vert = NULL; }

~Face() { delete[] vert; nVerts = 0; }

class Mesh { private: int numVerts; // number of vertices in the mesh Point3* pt; // array of 3D vertices int numNormals; // number of normal vectors for the mesh Vector3* norm; // array of normals int numFaces; // number of faces in the mesh Face* face; // array of face data // ... others to be added later public: Mesh(); ~Mesh();

// ... others };

void Mesh::DrawWireframe(){

glPolygonMode(GL_FRONT_AND_BACK, GL_LINE);

for (int f = 0; f < numFaces; f++) {

for (int v = 0; v < face[f].nVerts; v++){

int iv = face[f].vert[v].vertIndex;

glVertex3f(pt[iv].x, pt[iv].y, pt[iv].z);

glEnd();

void Mesh::CreateTetrahedron()

numVerts=4;

pt = new Point3[numVerts];

pt[0].set(0, 0, 0);

pt[1].set(1, 0, 0);

pt[2].set(0, 1, 0);

pt[3].set(0, 0, 1);

numFaces= 4;

face = new Face[numFaces];

face[0].nVerts = 3;

face[0].vert = new VertexID[face[0].nVerts];

face[0].vert[0].vertIndex = 1;

face[0].vert[0].normIndex = 0;

Further Reading “Interactive Computer Graphics: A Topdown

Approach Using OpenGL”, Edward Angel

– Chapter 2: Graphics Programming “Đồ họa máy tính trong không gian hai chiều”, Trần

Giang Sơn

– Chương 2: Bước đầu tạo hình ảnh “Đồ họa máy tính trong không gian ba chiều”, Trần Giang

– Chương 1: Mô hình hóa đối tượng ba chiều bằng lưới đa giác

COMPUTER GRAPHICS Hochiminh city University of Technology Faculty of Computer Science and...

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