# Lab (4) - Graphics

Reminder: Exam (1) - March 2, 2005

Objectives:
To create different views of a cube
To create a rotating cube

Following is a program that creates a cube.

#include <GL/glut.h>
#include <math.h>
typedef GLfloat point3[3];
double PI;
point3 p[8]={
{0,0,0},  //black
{0,0,1},  //blue
{1,0,1},  //magenta
{1,0,0},  //red
{0,1,0},  //green
{0,1,1},  //green+blue
{1,1,1},  //white
{1,1,0}   //yellow
};

void drawPoint(int i){
glVertex3fv(p[i]);
}
void drawFace(int i1,int i2,int i3,int i4){
glBegin(GL_POLYGON);
glColor3fv(p[i1]);
drawPoint(i1);
drawPoint(i2);
drawPoint(i3);
drawPoint(i4);
glEnd();
}

void myinit(void)
{

/* attributes */
glClearColor(1.0, 1.0, 1.0, 1.0); /* white background */
glColor3f(0.0, 0.0, 0.0); /* draw in black */
/* set up viewing */
glMatrixMode(GL_PROJECTION);
glOrtho(-1, 1, -1, 1,-10,10);
glMatrixMode(GL_MODELVIEW);
glEnable(GL_DEPTH_TEST);
PI=3.141592654;
}
void drawCube(){
drawFace(0,3,2,1); //bottom = black,
drawFace(1,2,6,5); //front = blue
drawFace(2,3,7,6); //right side = magenta
drawFace(3,0,4,7); //back side = red
drawFace(4,5,6,7); //top = green
drawFace(5,4,0,1); //left side = green + blue
}

void display( void )
{
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);  /*clear the window */
glMatrixMode(GL_MODELVIEW);
glTranslatef(-.5,-.5,-.5);
drawCube();
glFlush(); /* clear buffers */
}

void main(int argc, char** argv)
{
/* Standard GLUT initialization */
glutInit(&argc,argv);
glutInitDisplayMode (GLUT_SINGLE| GLUT_RGB|GLUT_DEPTH);

glutInitWindowSize(500,500); /* 500 x 500 pixel window */
glutInitWindowPosition(0,0); /* place window top left on display */
glutCreateWindow("Cube"); /* window title */
glutDisplayFunc(display); /* display callback invoked when window opened */
myinit(); /* set attributes */
myinit(); /* set attributes */
glutMainLoop(); /* enter event loop */
}

Activity (1)
Cut and paste the program into your .Net VC++ screen.  Before you compile and run, take a guess on what shape you will see on the screen, then compile and run the program to see whether your were correct.

If you said a square you are right.  If you said a cube that is seen from its front side (only front face) that is better.

Activity (2)
The rotation of cube can be done using the glRotatef(theta, x, y, z); where theta is the angle of rotation and x, y, z determine the axis around which you will rotate the cube.  For example:

glRotatef(45, 1, 0, 0);

will rotate the cube by 45 degree around the x axis, because the  y and z  components are set to 0.

Make changes in the program (one rotation at the time) to create the following view of the cube.

Note that this image can be created by rotating the cube about the x axis by 45 and then about the y axis by 45.

Activity (3)
The above view is not an "isogonal view" of the cube.  To create the correct view the rotation about y axis must be 45 but rotation about x axis must be computed.  The angle of rotation around x axis must be:

Tetha = sin-1 (sqrt(3)/3)  OR Tetha = cos-1 (sqrt(2)/sqrt(3) )

Note that this angle must be in Radian.   We will talk about different views in class very soon.  For now, take this from me that the above rotation angle around x axis will produce an isogonal view shown below.  Try to figure out why the angle is Theta and not 45.

Make changes in your program to create the correct "isogonal view" of the cube as shown below.

Activity (4)
Here is what I want you to experiment with next.  In the function:
void drawCube(){
drawFace(0,3,2,1); //bottom = black,
drawFace(1,2,6,5); //front = blue
drawFace(2,3,7,6); //right side = magenta
drawFace(3,0,4,7); //back side = red
drawFace(4,5,6,7); //top = green
drawFace(5,4,0,1); //left side = green + blue
}
First figure out which set of numbers (function call above) produces the left blue side.  Note that the comment on the code may not be accurate.  Once you find out which one, try to reorder the vertices in that set ONLY to see what the effect of the reordering of the points is on the output.  For example, assuming that the line:
drawFace(1,2,6,5); //front = blue
is indeed for the blue side in the above image, then find out what the result is when you use:
drawFace(5,1,2,6); //front = blue
But more importantly, find out what the would be the outcome if you try something like:
drawFace(5, 6, 2, 1); //front = blue

Activity (5)
Make changes so your program such that it creates and spins a color cube in a cumulative direction. In order to do this, you can use the Idle call back function.  Your program should do different things based on the following list:

1) if 'x' or 'X' is pressed, it rotates about x axis
2) if 'y' or 'Y' is pressed, it rotates about y axis
3) if 'z' or 'Z' is pressed, it rotates about z axis
4) if '+' is pressed, it increases the speed of rotation
5) if '-' is pressed, it decreases the speed of rotation
6) if '  ' spacebar is pressed, everything is reset
7) if 'q' or 'Q' is pressed, it terminates A hint for rotation: Hint

Post-Lab