Frustum.cpp

//***********************************************************************//
//																		 //
//		- "Talk to me like I'm a 3 year old!" Programming Lessons -		 //
//                                                                       //
//		$Author:		DigiBen		digiben@gametutorials.com			 //
//																		 //
//		$Program:		Frustum Culling									 //
//																		 //
//		$Description:	Demonstrates checking if shapes are in view		 //
//																		 //
//		$Date:			8/28/01											 //
//																		 //
//***********************************************************************//

#include "main.h"

// 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.
enum FrustumSide
{
	RIGHT	= 0,		// The RIGHT side of the frustum
	LEFT	= 1,		// The LEFT	 side of the frustum
	BOTTOM	= 2,		// The BOTTOM side of the frustum
	TOP		= 3,		// The TOP side of the frustum
	BACK	= 4,		// The BACK	side of the frustum
	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.
enum PlaneData
{
	A = 0,				// The X value of the plane's normal
	B = 1,				// The Y value of the plane's normal
	C = 2,				// The Z value of the plane's normal
	D = 3				// The distance the plane is from the origin
};

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

void NormalizePlane(float frustum[6][4], 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)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 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

void CFrustum::CalculateFrustum()
{    
	float   proj[16];								// This will hold our projection matrix
	float   modl[16];								// This will hold our modelview matrix
	float   clip[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].
	glGetFloatv( GL_PROJECTION_MATRIX, proj );

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

	// 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 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

bool CFrustum::PointInFrustum( 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 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

bool CFrustum::SphereInFrustum( 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 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*

bool CFrustum::CubeInFrustum( 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
//
//