View Frustum Culling

FrustumVisibilityTester.java

/*
 * Frustum.java
 *
 * Created on 24 oktober 2003, 13:36
 */

package org.codejive.utils4gl;

import javax.media.opengl.GL;

/**
 * Port from digiben tutorial on www.gametutorials.com
 * See below class for more info
 * @version $Revision: 297 $
 */
public class FrustumVisibilityTester {

	// We create an enum of the sides so we don't have to call each side 0 or 1.
	// This way it makes it more understandable and readable when dealing with frustum sides.
	public static final int RIGHT	= 0;		// The RIGHT side of the frustum
	public static final int LEFT	= 1;		// The LEFT	 side of the frustum
	public static final int BOTTOM	= 2;		// The BOTTOM side of the frustum
	public static final int TOP		= 3;		// The TOP side of the frustum
	public static final int BACK	= 4;		// The BACK	side of the frustum
	public static final int FRONT	= 5;		// The FRONT side of the frustum
	// Like above, instead of saying a number for the ABC and D of the plane, we
	// want to be more descriptive.
	public static final int A = 0;	// The X value of the plane's normal
	public static final int B = 1;	// The Y value of the plane's normal
	public static final int C = 2;	// The Z value of the plane's normal
	public static final int D = 3;	// The distance the plane is from the origin
	
	
	private float[][] m_Frustum = new float[6][4];

	
	///////////////////////////////// NORMALIZE PLANE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
	/////
	/////	This normalizes a plane (A side) from a given frustum.
	/////
	///////////////////////////////// NORMALIZE PLANE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

	private void normalizePlane(float[][] _frustum, int _side) {
		// Here we calculate the magnitude of the normal to the plane (point A B C)
		// Remember that (A, B, C) is that same thing as the normal's (X, Y, Z).
		// To calculate magnitude you use the equation:  magnitude = sqrt( x^2 + y^2 + z^2)
		float magnitude = (float)Math.sqrt( 
			_frustum[_side][A] * _frustum[_side][A] + 
			_frustum[_side][B] * _frustum[_side][B] + 
			_frustum[_side][C] * _frustum[_side][C] 
		);
		// Then we divide the plane's values by it's magnitude.
		// This makes it easier to work with.
		_frustum[_side][A] /= magnitude;
		_frustum[_side][B] /= magnitude;
		_frustum[_side][C] /= magnitude;
		_frustum[_side][D] /= magnitude; 
	}


	///////////////////////////////// CALCULATE FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
	/////
	/////	This extracts our frustum from the projection and modelview matrix.
	/////
	///////////////////////////////// CALCULATE FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

	public void calculateFrustum(GL _gl) {    
		float[] proj = new float[16];								// This will hold our projection matrix
		float[] modl = new float[16];								// This will hold our modelview matrix
		float[] clip = new float[16];								// This will hold the clipping planes

		// glGetFloatv() is used to extract information about our OpenGL world.
		// Below, we pass in GL_PROJECTION_MATRIX to abstract our projection matrix.
		// It then stores the matrix into an array of [16].
		_gl.glGetFloatv( GL.GL_PROJECTION_MATRIX, proj, 0 );

		// By passing in GL_MODELVIEW_MATRIX, we can abstract our model view matrix.
		// This also stores it in an array of [16].
		_gl.glGetFloatv( GL.GL_MODELVIEW_MATRIX, modl, 0 );

		// Now that we have our modelview and projection matrix, if we combine these 2 matrices,
		// it will give us our clipping planes.  To combine 2 matrices, we multiply them.

		clip[ 0] = modl[ 0] * proj[ 0] + modl[ 1] * proj[ 4] + modl[ 2] * proj[ 8] + modl[ 3] * proj[12];
		clip[ 1] = modl[ 0] * proj[ 1] + modl[ 1] * proj[ 5] + modl[ 2] * proj[ 9] + modl[ 3] * proj[13];
		clip[ 2] = modl[ 0] * proj[ 2] + modl[ 1] * proj[ 6] + modl[ 2] * proj[10] + modl[ 3] * proj[14];
		clip[ 3] = modl[ 0] * proj[ 3] + modl[ 1] * proj[ 7] + modl[ 2] * proj[11] + modl[ 3] * proj[15];

		clip[ 4] = modl[ 4] * proj[ 0] + modl[ 5] * proj[ 4] + modl[ 6] * proj[ 8] + modl[ 7] * proj[12];
		clip[ 5] = modl[ 4] * proj[ 1] + modl[ 5] * proj[ 5] + modl[ 6] * proj[ 9] + modl[ 7] * proj[13];
		clip[ 6] = modl[ 4] * proj[ 2] + modl[ 5] * proj[ 6] + modl[ 6] * proj[10] + modl[ 7] * proj[14];
		clip[ 7] = modl[ 4] * proj[ 3] + modl[ 5] * proj[ 7] + modl[ 6] * proj[11] + modl[ 7] * proj[15];

		clip[ 8] = modl[ 8] * proj[ 0] + modl[ 9] * proj[ 4] + modl[10] * proj[ 8] + modl[11] * proj[12];
		clip[ 9] = modl[ 8] * proj[ 1] + modl[ 9] * proj[ 5] + modl[10] * proj[ 9] + modl[11] * proj[13];
		clip[10] = modl[ 8] * proj[ 2] + modl[ 9] * proj[ 6] + modl[10] * proj[10] + modl[11] * proj[14];
		clip[11] = modl[ 8] * proj[ 3] + modl[ 9] * proj[ 7] + modl[10] * proj[11] + modl[11] * proj[15];

		clip[12] = modl[12] * proj[ 0] + modl[13] * proj[ 4] + modl[14] * proj[ 8] + modl[15] * proj[12];
		clip[13] = modl[12] * proj[ 1] + modl[13] * proj[ 5] + modl[14] * proj[ 9] + modl[15] * proj[13];
		clip[14] = modl[12] * proj[ 2] + modl[13] * proj[ 6] + modl[14] * proj[10] + modl[15] * proj[14];
		clip[15] = modl[12] * proj[ 3] + modl[13] * proj[ 7] + modl[14] * proj[11] + modl[15] * proj[15];

		// Now we actually want to get the sides of the frustum.  To do this we take
		// the clipping planes we received above and extract the sides from them.

		// This will extract the RIGHT side of the frustum
		m_Frustum[RIGHT][A] = clip[ 3] - clip[ 0];
		m_Frustum[RIGHT][B] = clip[ 7] - clip[ 4];
		m_Frustum[RIGHT][C] = clip[11] - clip[ 8];
		m_Frustum[RIGHT][D] = clip[15] - clip[12];

		// Now that we have a normal (A,B,C) and a distance (D) to the plane,
		// we want to normalize that normal and distance.

		// Normalize the RIGHT side
		normalizePlane(m_Frustum, RIGHT);

		// This will extract the LEFT side of the frustum
		m_Frustum[LEFT][A] = clip[ 3] + clip[ 0];
		m_Frustum[LEFT][B] = clip[ 7] + clip[ 4];
		m_Frustum[LEFT][C] = clip[11] + clip[ 8];
		m_Frustum[LEFT][D] = clip[15] + clip[12];

		// Normalize the LEFT side
		normalizePlane(m_Frustum, LEFT);

		// This will extract the BOTTOM side of the frustum
		m_Frustum[BOTTOM][A] = clip[ 3] + clip[ 1];
		m_Frustum[BOTTOM][B] = clip[ 7] + clip[ 5];
		m_Frustum[BOTTOM][C] = clip[11] + clip[ 9];
		m_Frustum[BOTTOM][D] = clip[15] + clip[13];

		// Normalize the BOTTOM side
		normalizePlane(m_Frustum, BOTTOM);

		// This will extract the TOP side of the frustum
		m_Frustum[TOP][A] = clip[ 3] - clip[ 1];
		m_Frustum[TOP][B] = clip[ 7] - clip[ 5];
		m_Frustum[TOP][C] = clip[11] - clip[ 9];
		m_Frustum[TOP][D] = clip[15] - clip[13];

		// Normalize the TOP side
		normalizePlane(m_Frustum, TOP);

		// This will extract the BACK side of the frustum
		m_Frustum[BACK][A] = clip[ 3] - clip[ 2];
		m_Frustum[BACK][B] = clip[ 7] - clip[ 6];
		m_Frustum[BACK][C] = clip[11] - clip[10];
		m_Frustum[BACK][D] = clip[15] - clip[14];

		// Normalize the BACK side
		normalizePlane(m_Frustum, BACK);

		// This will extract the FRONT side of the frustum
		m_Frustum[FRONT][A] = clip[ 3] + clip[ 2];
		m_Frustum[FRONT][B] = clip[ 7] + clip[ 6];
		m_Frustum[FRONT][C] = clip[11] + clip[10];
		m_Frustum[FRONT][D] = clip[15] + clip[14];

		// Normalize the FRONT side
		normalizePlane(m_Frustum, FRONT);
	}

	// The code below will allow us to make checks within the frustum.  For example,
	// if we want to see if a point, a sphere, or a cube lies inside of the frustum.
	// Because all of our planes point INWARDS (The normals are all pointing inside the frustum)
	// we then can assume that if a point is in FRONT of all of the planes, it's inside.

	///////////////////////////////// POINT IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
	/////
	/////	This determines if a point is inside of the frustum
	/////
	///////////////////////////////// POINT IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

	public boolean isPointInFrustum(float _x, float _y, float _z) {
		// If you remember the plane equation (A*x + B*y + C*z + D = 0), then the rest
		// of this code should be quite obvious and easy to figure out yourself.
		// In case don't know the plane equation, it might be a good idea to look
		// at our Plane Collision tutorial at www.GameTutorials.com in OpenGL Tutorials.
		// I will briefly go over it here.  (A,B,C) is the (X,Y,Z) of the normal to the plane.
		// They are the same thing... but just called ABC because you don't want to say:
		// (x*x + y*y + z*z + d = 0).  That would be wrong, so they substitute them.
		// the (x, y, z) in the equation is the point that you are testing.  The D is
		// The distance the plane is from the origin.  The equation ends with "= 0" because
		// that is true when the point (x, y, z) is ON the plane.  When the point is NOT on
		// the plane, it is either a negative number (the point is behind the plane) or a
		// positive number (the point is in front of the plane).  We want to check if the point
		// is in front of the plane, so all we have to do is go through each point and make
		// sure the plane equation goes out to a positive number on each side of the frustum.
		// The result (be it positive or negative) is the distance the point is front the plane.

		// Go through all the sides of the frustum
		for (int i = 0; i < 6; i++) {
			// Calculate the plane equation and check if the point is behind a side of the frustum
			if (m_Frustum[i][A] * _x + m_Frustum[i][B] * _y + m_Frustum[i][C] * _z + m_Frustum[i][D] <= 0) {
				// The point was behind a side, so it ISN'T in the frustum
				return false;
			}
		}

		// The point was inside of the frustum (In front of ALL the sides of the frustum)
		return true;
	}


	///////////////////////////////// SPHERE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
	/////
	/////	This determines if a sphere is inside of our frustum by it's center and radius.
	/////
	///////////////////////////////// SPHERE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

	public boolean isSphereInFrustum(float _x, float _y, float _z, float _radius) {
		// Now this function is almost identical to the PointInFrustum(), except we
		// now have to deal with a radius around the point.  The point is the center of
		// the radius.  So, the point might be outside of the frustum, but it doesn't
		// mean that the rest of the sphere is.  It could be half and half.  So instead of
		// checking if it's less than 0, we need to add on the radius to that.  Say the
		// equation produced -2, which means the center of the sphere is the distance of
		// 2 behind the plane.  Well, what if the radius was 5?  The sphere is still inside,
		// so we would say, if(-2 < -5) then we are outside.  In that case it's false,
		// so we are inside of the frustum, but a distance of 3.  This is reflected below.

		// Go through all the sides of the frustum
		for (int i = 0; i < 6; i++)	{
			// If the center of the sphere is farther away from the plane than the radius
			if (m_Frustum[i][A] * _x + m_Frustum[i][B] * _y + m_Frustum[i][C] * _z + m_Frustum[i][D] <= -_radius) {
				// The distance was greater than the radius so the sphere is outside of the frustum
				return false;
			}
		}

		// The sphere was inside of the frustum!
		return true;
	}


	///////////////////////////////// CUBE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
	/////
	/////	This determines if a cube is in or around our frustum by it's center and 1/2 it's length
	/////
	///////////////////////////////// CUBE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

	public boolean isCubeInFrustum(float _x, float _y, float _z, float _size) {
		// This test is a bit more work, but not too much more complicated.
		// Basically, what is going on is, that we are given the center of the cube,
		// and half the length.  Think of it like a radius.  Then we checking each point
		// in the cube and seeing if it is inside the frustum.  If a point is found in front
		// of a side, then we skip to the next side.  If we get to a plane that does NOT have
		// a point in front of it, then it will return false.

		// *Note* - This will sometimes say that a cube is inside the frustum when it isn't.
		// This happens when all the corners of the bounding box are not behind any one plane.
		// This is rare and shouldn't effect the overall rendering speed.

		for (int i = 0; i < 6; i++) {
			if(m_Frustum[i][A] * (_x - _size) + m_Frustum[i][B] * (_y - _size) + m_Frustum[i][C] * (_z - _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x + _size) + m_Frustum[i][B] * (_y - _size) + m_Frustum[i][C] * (_z - _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x - _size) + m_Frustum[i][B] * (_y + _size) + m_Frustum[i][C] * (_z - _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x + _size) + m_Frustum[i][B] * (_y + _size) + m_Frustum[i][C] * (_z - _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x - _size) + m_Frustum[i][B] * (_y - _size) + m_Frustum[i][C] * (_z + _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x + _size) + m_Frustum[i][B] * (_y - _size) + m_Frustum[i][C] * (_z + _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x - _size) + m_Frustum[i][B] * (_y + _size) + m_Frustum[i][C] * (_z + _size) + m_Frustum[i][D] > 0)
			   continue;
			if(m_Frustum[i][A] * (_x + _size) + m_Frustum[i][B] * (_y + _size) + m_Frustum[i][C] * (_z + _size) + m_Frustum[i][D] > 0)
			   continue;

			// If we get here, it isn't in the frustum
			return false;
		}

		return true;
	}
}

/////////////////////////////////////////////////////////////////////////////////
//
// * QUICK NOTES * 
//
// WOZZERS!  That seemed like an incredible amount to look at, but if you break it
// down, it's not.  Frustum culling is a VERY useful thing when it comes to 3D.
// If you want a large world, there is no way you are going to send it down the
// 3D pipeline every frame and let OpenGL take care of it for you.  That would
// give you a 0.001 frame rate.  If you hit '+' and bring the sphere count up to
// 1000, then take off culling, you will see the HUGE difference it makes.  
// Also, you wouldn't really be rendering 1000 spheres.  You would most likely
// use the sphere code for larger objects.  Let me explain.  Say you have a bunch
// of objects, well... all you need to do is give the objects a radius, and then
// test that radius against the frustum.  If that sphere is in the frustum, then you
// render that object.  Also, you won't be rendering a high poly sphere so it won't
// be so slow.  This goes for bounding box's too (Cubes).  If you don't want to
// do a cube, it is really easy to convert the code for rectangles.  Just pass in
// a width and height, instead of just a length.  Remember, it's HALF the length of
// the cube, not the full length.  So it would be half the width and height for a rect.
// 
// This is a perfect starter for an octree tutorial.  Wrap you head around the concepts
// here and then see if you can apply this to making an octree.  Hopefully we will have
// a tutorial up and running for this subject soon.  Once you have frustum culling,
// the next step is getting space partitioning.  Either it being a BSP tree of an Octree.
// 
// Let's go over a brief overview of the things we learned here:
//
// 1) First we need to abstract the frustum from OpenGL.  To do that we need the
//    projection and modelview matrix.  To get the projection matrix we use:
//
//			glGetFloatv( GL_PROJECTION_MATRIX, /* An Array of 16 floats */ );
//    Then, to get the modelview matrix we use:
//
//			glGetFloatv( GL_MODELVIEW_MATRIX, /* An Array of 16 floats */ );
//    
//	  These 2 functions gives us an array of 16 floats (The matrix).
//
// 2) Next, we need to combine these 2 matrices.  We do that by matrix multiplication.
//
// 3) Now that we have the 2 matrixes combined, we can abstract the sides of the frustum.
//    This will give us the normal and the distance from the plane to the origin (ABC and D).
//
// 4) After abstracting a side, we want to normalize the plane data.  (A B C and D).
//
// 5) Now we have our frustum, and we can check points against it using the plane equation.
//    Once again, the plane equation (A*x + B*y + C*z + D = 0) says that if, point (X,Y,Z)
//    times the normal of the plane (A,B,C), plus the distance of the plane from origin,
//    will equal 0 if the point (X, Y, Z) lies on that plane.  If it is behind the plane
//    it will be a negative distance, if it's in front of the plane (the way the normal is facing)
//    it will be a positive number.
//
//
// If you need more help on the plane equation and why this works, download our
// Ray Plane Intersection Tutorial at www.GameTutorials.com.
//
// That's pretty much it with frustums.  There is a lot more we could talk about, but
// I don't want to complicate this tutorial more than I already have.
//
// I want to thank Mark Morley for his tutorial on frustum culling.  Most of everything I got
// here comes from his teaching.  If you want more in-depth, visit his tutorial at:
//
// http://www.markmorley.com/opengl/frustumculling.html
//
// Good luck!
//
//
// Ben Humphrey (DigiBen)
// Game Programmer
// DigiBen@GameTutorials.com
// Co-Web Host of www.GameTutorials.com
//
//

/*
 * $Log$
 * Revision 1.3  2003/11/17 10:49:59  tako
 * Added CVS macros for revision and log.
 *
 */