Transformations

Objectives

To perform transformations on 2D objects using OpenGL programming

OpenGL transformation functions

OpenGL maintains a 4x4 transformation matrix that is multiplied by every (x,y,z) value sent to glVertex(). This is sometimes referred to as the CT (current transform). The CT can be modified by the following functions:

• glLoadIdentity();
• glTranslate{fd}( dx, dy, dz );
• glScale{fd}( sx, sy, sz);
• glRotate{fd}( angleInDegrees, axisXvalue, axisYvalue, axisZvalue);

How to use the OpenGL transformation functions

There are two different 4x4 matrices used by OpenGL to produce an image. They are:

• Projection matrix - used to "project" a 3D image onto a 2D plane to create an image.
• ModelView matrix - used to transform objects and the camera to create the desired scene and view.

Commands like glTranslate, glRotate, and glScale will modify the active matrix. It is the programmer's responsibility to make sure the appropriate matrix is "active." The active matrix is determined by calls to glMatrixMode(), such as:

• glMatrixMode(GL_PROJECTION); // make the projection matrix active
• glMatrixMode(GL_MODELVIEW); // make the modelview matrix active

2) The transformations caused by glRotate, glTranslate, and glScale are applied to the CT (current transform). They will accumulate continually unless you reset the matrix back to the Identity matrix. If you want to start a new set of transformations, then call glLoadIdentity(), as in the following example:

  glMatrixMode(GL_MODELVIEW);

  glLoadIdentity();               // start a new sequence of transforms

  glTranslatef(-3.0, -4.0, 0.0);

  glRotatef(90.0, 1.0, 0.0, 0.0);

  drawObject1();

  glLoadIdentity();               // start a new sequence of transforms

  glTranslatef(4.0, 2.0, 1.0);

  glScalef(2.0, 1.0, 1.0);

  drawObject2();

Programming Exercises

1.      Implement an Opengl interactive graphics program that draws a triangle which can be translated by pressing 'l', 'r', 'u', or 'd' keys.

You can draw a triangle with equal side 1 unit:

//-------------------------------------------------------------------

float midX = 0.5;

float midY = sqrt(3)/2.0;

void drawTriangle(void)

{

  glBegin(GL_POLYGON);

    glColor3f ( 1.0, 0.0, 0.0);

    glVertex2f( 0.0, 0.0);

    glColor3f ( 0.0, 1.0, 0.0);

    glVertex2f( midX, midY);

    glColor3f ( 0.0, 0.0, 1.0);

    glVertex2f( 1.0, 0.0);

  glEnd();

}

//-------------------------------------------------------------------

2.      Modify your programs from the previous questions so that the triangle now will translate and rotate when the user presses the 'l', 'r', 'u', or 'd' keys (for translation) and 'c' (for clockwise rotation),'a' (for anti-clockwise rotation),

.................

#include <glut.h>

#include <math.h>

float midX = 0.5;

float midY = sqrt(3.0)/2.0;

float PI=3.1415;

//------------------------------------------------------------------- 

void drawTriangle(void) 

{ 

  glBegin(GL_POLYGON); 

    glColor3f ( 1.0, 0.0, 0.0); 

    glVertex2f( 0.0, 0.0); 

    glColor3f ( 0.0, 1.0, 0.0); 

    glVertex2f( midX, midY); 

    glColor3f ( 0.0, 0.0, 1.0); 

    glVertex2f( 1.0, 0.0); 

  glEnd();

} 

//------------------------------------------------------------------- 

void Transform(GLfloat tx, GLfloat ty)

{

 glMatrixMode(GL_MODELVIEW);

 glClear(GL_COLOR_BUFFER_BIT);

 glTranslatef(tx, ty, 0.0);

 drawTriangle();

 glFlush();

 glutSwapBuffers();

}

//------------------------------------------------------------------- 

void myDisplay(void)

{

  glClear( GL_COLOR_BUFFER_BIT );

  drawTriangle();

  glFlush();

  glutSwapBuffers();

}

//-------------------------------------------------------------------

void mySpecialKey(int key, int x, int y)

{

 GLfloat tx = 0.0, ty = 0.0;

 switch(key)

 {

 case GLUT_KEY_UP       : ty += 0.05; break;

 case GLUT_KEY_DOWN : ty -= 0.05; break;

 case GLUT_KEY_RIGHT : tx += 0.05; break;

 case GLUT_KEY_LEFT : tx -= 0.05; break;

 case GLUT_KEY_HOME : glLoadIdentity();

  // drawTriangle();

   break;

 }

 Transform(tx, ty);

 glutPostRedisplay();

}

//-------------------------------------------------------------------

void myInit(void)

{

  glClearColor(0.0, 0.0, 0.0, 0.0); // set the background to black

  glColor3f(1.0f, 1.0f, 1.0f);      // set the drawing color to white

  

  glMatrixMode(GL_PROJECTION);

  glLoadIdentity();

  gluOrtho2D(0.0, 3.0, 0.0, 3.0);

}

//-------------------------------------------------------------------

void main( int argc, char **argv)

{

  glutInit(&argc, argv);

  glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB ); 

  glutInitWindowSize(450,450);

  glutInitWindowPosition(0,0);

  glutCreateWindow("One Triangle");

  

  glutDisplayFunc(myDisplay);

  glutSpecialFunc(mySpecialKey);

  myInit();

  

  glutMainLoop();

}