Lecture 3/2

OpenGL: Math on transformation

• How does a pixel get its color

  • Direct Color Mode: specify vertex color by glColor*().
  • Lighting Mode: specify material color by glMaterial*().
  • Texture Mapping: get color by table looking into the the rectangle image.

    // Of the 3 methods, only one of the first two can be used, but the third one can be
    // used either by replacing either of the first two, or modulating with it.
    

  • How to transform a point by the current model view transformation

      // Transform a point by the current model view transformation matrix
      // The given initial space point is not changed, the new position of the transformed point is returned.
      Point TP(Point const& p)
      {
        static float mtr[16];
    
        glGetFloatv(GL_MODELVIEW_MATRIX, mtr);
        
        float *col0 = mtr, *col1 = mtr + 4, *col2 = mtr + 8, *col3 = mtr + 12;
    
        Point ret = Point(0., 0., 0.);
        ret += Point(col0) * p.x;
        ret += Point(col1) * p.y;
        ret += Point(col2) * p.z;
        ret += Point(col3);
    
        return  ret / (p.x * col0[3] + p.y * col1[3] + p.z * col2[3] + col3[3]);
      }
    

  • How to multiply transform matrix directly

        glMatrixMode(GL_MODELVIEW);
        glLoadIdentity();
    
        // perhaps some transformation here
    
        // some transformation here.  In the example below, we get the matrix of it, and multiply it directly to matrix stack.
    
        // draw geometry
    

    The following code has the same effect as the above one.

        glMatrixMode(GL_MODELVIEW);
        glLoadIdentity();
    
        // perhaps transformation here
    
        static float mtr[16];
        glPushMatrix();
        {
           glLoadIdentity();
           // some some transformation here.
           glGetFloatv(GL_MODELVIEW_MATRIX, mtr);
        }
        glPopMatrix();
    
        glMultMatrixf( rotationMatrix );
        // draw geometry
    

  • How to use special keyboard callback

        // define a special key callback function.
        void specialKey(int key, int x, int y) 
        {
            switch(key)
            {
               case : action1(); break;
               case : action2(); break;
               case : action3(); break;
               case : action4(); break;
            }
            glutPostRedisplay();
        }
    
        // register it with glut (in main()).
        glutSpecialFunc(specialKey);     // like glutKeyboardFunc(keyboard), deals some with non-ascii keys.
    

  • How to use alpaha channel to render transparent objects

        /*
          Draw all opaque geometries here.
         */
    
    
        // Draw a transparent object.
    
        glEnable (GL_BLEND);
        {
          glDepthMask (GL_FALSE);              // this object is not drawn if it is blocked by others, however it does not block any other objects.
    
          glBlendFunc (GL_DST_ALPHA, GL_ONE_MINUS_SRC_COLOR); // specify blend function here.
    
          // specify alpha value using glMaterial*() if lighting is enabled.
          GLfloat mat_transparent[] = { 0.0, 0.8, 0.8, 0.6 };
          glMaterialfv(GL_FRONT, GL_DIFFUSE, mat_transparent);
    
          // or using glColor*() if lighting is disabled.
          glColor4f(.0, .8, .8, .6);
    
          // draw transparent geometry here
    
          glDepthMask (GL_TRUE);              // restore z-buffer mask
        }
        glDisable (GL_BLEND);
    

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