Additional Clipping Planes

In addition to the six clipping planes of the viewing volume (left, right, bottom, top, near, and far), you can define up to six additional clipping planes to further restrict the viewing volume, as shown in Figure 3-22. This is useful for removing extraneous objects in a scene - for example, if you want to display a cutaway view of an object.

Each plane is specified by the coefficients of its equation: Ax+By+Cz+D = 0. The clipping planes are automatically transformed appropriately by modeling and viewing transformations. The clipping volume becomes the intersection of the viewing volume and all half-spaces defined by the additional clipping planes. Remember that polygons that get clipped automatically have their edges reconstructed appropriately by OpenGL.


Figure 3-22 : Additional Clipping Planes and the Viewing Volume

void glClipPlane(GLenum plane, const GLdouble *equation);

Defines a clipping plane. The equation argument points to the four coefficients of the plane equation, Ax+By+Cz+D = 0. All points with eye coordinates (xe, ye, ze, we) that satisfy (A B C D)M-1 (xe ye ze we)T >= 0 lie in the half-space defined by the plane, where M is the current modelview matrix at the time glClipPlane() is called. All points not in this half-space are clipped away. The plane argument is GL_CLIP_PLANEi, where i is an integer specifying which of the available clipping planes to define. i is a number between 0 and one less than the maximum number of additional clipping planes.

You need to enable each additional clipping plane you define:


You can disable a plane with


All implementations of OpenGL must support at least six additional clipping planes, although some implementations may allow more. You can use glGetIntegerv() with GL_MAX_CLIP_PLANES to find how many clipping planes are supported.

Note: Clipping performed as a result of glClipPlane() is done in eye coordinates, not in clip coordinates. This difference is noticeable if the projection matrix is singular (that is, a real projection matrix that flattens three-dimensional coordinates to two-dimensional ones). Clipping performed in eye coordinates continues to take place in three dimensions even when the projection matrix is singular.

A Clipping Plane Code Example

Example 3-5 renders a wireframe sphere with two clipping planes that slice away three-quarters of the original sphere, as shown in Figure 3-23.


Figure 3-23 : Clipped Wireframe Sphere

Example 3-5 : Wireframe Sphere with Two Clipping Planes: clip.c

#include <GL/gl.h>
#include <GL/glu.h>
#include <GL/glut.h>
void init(void)
   glClearColor (0.0, 0.0, 0.0, 0.0);
   glShadeModel (GL_FLAT);
void display(void)
   GLdouble eqn[4] = {0.0, 1.0, 0.0, 0.0};
   GLdouble eqn2[4] = {1.0, 0.0, 0.0, 0.0};
   glColor3f (1.0, 1.0, 1.0);
   glTranslatef (0.0, 0.0, -5.0);
/*    clip lower half -- y < 0          */
   glClipPlane (GL_CLIP_PLANE0, eqn);
   glEnable (GL_CLIP_PLANE0);
/*    clip left half -- x < 0           */
   glClipPlane (GL_CLIP_PLANE1, eqn2);
   glEnable (GL_CLIP_PLANE1);
   glRotatef (90.0, 1.0, 0.0, 0.0);
   glutWireSphere(1.0, 20, 16);
   glFlush ();
void reshape (int w, int h)
   glViewport (0, 0, (GLsizei) w, (GLsizei) h);
   glMatrixMode (GL_PROJECTION);
   glLoadIdentity ();
   gluPerspective(60.0, (GLfloat) w/(GLfloat) h, 1.0, 20.0);
   glMatrixMode (GL_MODELVIEW);
int main(int argc, char** argv)
   glutInit(&argc, argv);
   glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB);
   glutInitWindowSize (500, 500);
   glutInitWindowPosition (100, 100);
   glutCreateWindow (argv[0]);
   init ();
   return 0;

Try This

  • Try changing the coefficients that describe the clipping planes in Example 3-5.
  • Try calling a modeling transformation, such as glRotate*(), to affect glClipPlane(). Make the clipping plane move independently of the objects in the scene.