www.pudn.com > QuadTreeLOD4cs.rar > Frustum.cpp, change:2003-08-04,size:18441b
// Frustum.cpp: implementation of the CFrustum class.
//
//////////////////////////////////////////////////////////////////////
#include "Frustum.h"
#include "gamehead.h"
//////////////////////////////////////////////////////////////////////
// Construction/Destruction
//////////////////////////////////////////////////////////////////////
CFrustum::CFrustum()
{
}
CFrustum::~CFrustum()
{
}
// 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.
///////////////////////////////// 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;
}
bool CFrustum::CuboidInFrustum( float x, float y, float z, SIZE 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.cx) + m_Frustum[i][B] * (y - size.cy) + m_Frustum[i][C] * (z - size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x + size.cx) + m_Frustum[i][B] * (y - size.cy) + m_Frustum[i][C] * (z - size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x - size.cx) + m_Frustum[i][B] * (y + size.cy) + m_Frustum[i][C] * (z - size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x + size.cx) + m_Frustum[i][B] * (y + size.cy) + m_Frustum[i][C] * (z - size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x - size.cx) + m_Frustum[i][B] * (y - size.cy) + m_Frustum[i][C] * (z + size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x + size.cx) + m_Frustum[i][B] * (y - size.cy) + m_Frustum[i][C] * (z + size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x - size.cx) + m_Frustum[i][B] * (y + size.cy) + m_Frustum[i][C] * (z + size.cx) + m_Frustum[i][D] > 0)
continue;
if(m_Frustum[i][A] * (x + size.cx) + m_Frustum[i][B] * (y + size.cy) + m_Frustum[i][C] * (z + size.cx) + 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
//
//