303 lines
15 KiB
C++
303 lines
15 KiB
C++
#include <cmath>
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#include <SDL_opengl.h>
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#include "gl_frustum.h"
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namespace Util {
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// We create an enum of the sides so we don't have to call each side 0 or 1.
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// This way it makes it more understandable and readable when dealing with frustum sides.
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enum FrustumSide
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{
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RIGHT = 0, // The RIGHT side of the frustum
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LEFT = 1, // The LEFT side of the frustum
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BOTTOM = 2, // The BOTTOM side of the frustum
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TOP = 3, // The TOP side of the frustum
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BACK = 4, // The BACK side of the frustum
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FRONT = 5 // The FRONT side of the frustum
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};
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// Like above, instead of saying a number for the ABC and D of the plane, we
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// want to be more descriptive.
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enum PlaneData
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{
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A = 0, // The X value of the plane's normal
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B = 1, // The Y value of the plane's normal
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C = 2, // The Z value of the plane's normal
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D = 3 // The distance the plane is from the origin
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};
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///////////////////////////////// NORMALIZE PLANE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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/////
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///// This normalizes a plane (A side) from a given frustum.
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/////
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///////////////////////////////// NORMALIZE PLANE \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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void NormalizePlane(float frustum[6][4], int side)
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{
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// Here we calculate the magnitude of the normal to the plane (point A B C)
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// Remember that (A, B, C) is that same thing as the normal's (X, Y, Z).
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// To calculate magnitude you use the equation: magnitude = sqrt( x^2 + y^2 + z^2)
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float magnitude = (float)sqrt( frustum[side][A] * frustum[side][A] +
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frustum[side][B] * frustum[side][B] +
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frustum[side][C] * frustum[side][C] );
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// Then we divide the plane's values by it's magnitude.
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// This makes it easier to work with.
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frustum[side][A] /= magnitude;
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frustum[side][B] /= magnitude;
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frustum[side][C] /= magnitude;
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frustum[side][D] /= magnitude;
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}
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///////////////////////////////// CALCULATE FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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/////
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///// This extracts our frustum from the projection and modelview matrix.
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/////
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///////////////////////////////// CALCULATE FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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void CFrustum::CalculateFrustum()
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{
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float proj[16]; // This will hold our projection matrix
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float modl[16]; // This will hold our modelview matrix
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float clip[16]; // This will hold the clipping planes
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// glGetFloatv() is used to extract information about our OpenGL world.
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// Below, we pass in GL_PROJECTION_MATRIX to abstract our projection matrix.
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// It then stores the matrix into an array of [16].
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glGetFloatv( GL_PROJECTION_MATRIX, proj );
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// By passing in GL_MODELVIEW_MATRIX, we can abstract our model view matrix.
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// This also stores it in an array of [16].
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glGetFloatv( GL_MODELVIEW_MATRIX, modl );
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// Now that we have our modelview and projection matrix, if we combine these 2 matrices,
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// it will give us our clipping planes. To combine 2 matrices, we multiply them.
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clip[ 0] = modl[ 0] * proj[ 0] + modl[ 1] * proj[ 4] + modl[ 2] * proj[ 8] + modl[ 3] * proj[12];
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clip[ 1] = modl[ 0] * proj[ 1] + modl[ 1] * proj[ 5] + modl[ 2] * proj[ 9] + modl[ 3] * proj[13];
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clip[ 2] = modl[ 0] * proj[ 2] + modl[ 1] * proj[ 6] + modl[ 2] * proj[10] + modl[ 3] * proj[14];
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clip[ 3] = modl[ 0] * proj[ 3] + modl[ 1] * proj[ 7] + modl[ 2] * proj[11] + modl[ 3] * proj[15];
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clip[ 4] = modl[ 4] * proj[ 0] + modl[ 5] * proj[ 4] + modl[ 6] * proj[ 8] + modl[ 7] * proj[12];
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clip[ 5] = modl[ 4] * proj[ 1] + modl[ 5] * proj[ 5] + modl[ 6] * proj[ 9] + modl[ 7] * proj[13];
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clip[ 6] = modl[ 4] * proj[ 2] + modl[ 5] * proj[ 6] + modl[ 6] * proj[10] + modl[ 7] * proj[14];
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clip[ 7] = modl[ 4] * proj[ 3] + modl[ 5] * proj[ 7] + modl[ 6] * proj[11] + modl[ 7] * proj[15];
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clip[ 8] = modl[ 8] * proj[ 0] + modl[ 9] * proj[ 4] + modl[10] * proj[ 8] + modl[11] * proj[12];
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clip[ 9] = modl[ 8] * proj[ 1] + modl[ 9] * proj[ 5] + modl[10] * proj[ 9] + modl[11] * proj[13];
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clip[10] = modl[ 8] * proj[ 2] + modl[ 9] * proj[ 6] + modl[10] * proj[10] + modl[11] * proj[14];
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clip[11] = modl[ 8] * proj[ 3] + modl[ 9] * proj[ 7] + modl[10] * proj[11] + modl[11] * proj[15];
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clip[12] = modl[12] * proj[ 0] + modl[13] * proj[ 4] + modl[14] * proj[ 8] + modl[15] * proj[12];
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clip[13] = modl[12] * proj[ 1] + modl[13] * proj[ 5] + modl[14] * proj[ 9] + modl[15] * proj[13];
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clip[14] = modl[12] * proj[ 2] + modl[13] * proj[ 6] + modl[14] * proj[10] + modl[15] * proj[14];
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clip[15] = modl[12] * proj[ 3] + modl[13] * proj[ 7] + modl[14] * proj[11] + modl[15] * proj[15];
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// Now we actually want to get the sides of the frustum. To do this we take
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// the clipping planes we received above and extract the sides from them.
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// This will extract the RIGHT side of the frustum
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m_Frustum[RIGHT][A] = clip[ 3] - clip[ 0];
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m_Frustum[RIGHT][B] = clip[ 7] - clip[ 4];
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m_Frustum[RIGHT][C] = clip[11] - clip[ 8];
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m_Frustum[RIGHT][D] = clip[15] - clip[12];
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// Now that we have a normal (A,B,C) and a distance (D) to the plane,
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// we want to normalize that normal and distance.
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// Normalize the RIGHT side
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NormalizePlane(m_Frustum, RIGHT);
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// This will extract the LEFT side of the frustum
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m_Frustum[LEFT][A] = clip[ 3] + clip[ 0];
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m_Frustum[LEFT][B] = clip[ 7] + clip[ 4];
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m_Frustum[LEFT][C] = clip[11] + clip[ 8];
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m_Frustum[LEFT][D] = clip[15] + clip[12];
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// Normalize the LEFT side
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NormalizePlane(m_Frustum, LEFT);
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// This will extract the BOTTOM side of the frustum
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m_Frustum[BOTTOM][A] = clip[ 3] + clip[ 1];
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m_Frustum[BOTTOM][B] = clip[ 7] + clip[ 5];
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m_Frustum[BOTTOM][C] = clip[11] + clip[ 9];
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m_Frustum[BOTTOM][D] = clip[15] + clip[13];
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// Normalize the BOTTOM side
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NormalizePlane(m_Frustum, BOTTOM);
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// This will extract the TOP side of the frustum
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m_Frustum[TOP][A] = clip[ 3] - clip[ 1];
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m_Frustum[TOP][B] = clip[ 7] - clip[ 5];
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m_Frustum[TOP][C] = clip[11] - clip[ 9];
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m_Frustum[TOP][D] = clip[15] - clip[13];
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// Normalize the TOP side
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NormalizePlane(m_Frustum, TOP);
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// This will extract the BACK side of the frustum
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m_Frustum[BACK][A] = clip[ 3] - clip[ 2];
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m_Frustum[BACK][B] = clip[ 7] - clip[ 6];
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m_Frustum[BACK][C] = clip[11] - clip[10];
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m_Frustum[BACK][D] = clip[15] - clip[14];
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// Normalize the BACK side
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NormalizePlane(m_Frustum, BACK);
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// This will extract the FRONT side of the frustum
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m_Frustum[FRONT][A] = clip[ 3] + clip[ 2];
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m_Frustum[FRONT][B] = clip[ 7] + clip[ 6];
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m_Frustum[FRONT][C] = clip[11] + clip[10];
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m_Frustum[FRONT][D] = clip[15] + clip[14];
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// Normalize the FRONT side
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NormalizePlane(m_Frustum, FRONT);
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}
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// The code below will allow us to make checks within the frustum. For example,
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// if we want to see if a point, a sphere, or a cube lies inside of the frustum.
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// Because all of our planes point INWARDS (The normals are all pointing inside the frustum)
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// we then can assume that if a point is in FRONT of all of the planes, it's inside.
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///////////////////////////////// POINT IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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/////
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///// This determines if a point is inside of the frustum
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/////
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///////////////////////////////// POINT IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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bool CFrustum::PointInFrustum( float x, float y, float z )
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{
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// If you remember the plane equation (A*x + B*y + C*z + D = 0), then the rest
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// of this code should be quite obvious and easy to figure out yourself.
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// In case don't know the plane equation, it might be a good idea to look
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// at our Plane Collision tutorial at www.GameTutorials.com in OpenGL Tutorials.
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// I will briefly go over it here. (A,B,C) is the (X,Y,Z) of the normal to the plane.
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// They are the same thing... but just called ABC because you don't want to say:
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// (x*x + y*y + z*z + d = 0). That would be wrong, so they substitute them.
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// the (x, y, z) in the equation is the point that you are testing. The D is
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// The distance the plane is from the origin. The equation ends with "= 0" because
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// that is true when the point (x, y, z) is ON the plane. When the point is NOT on
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// the plane, it is either a negative number (the point is behind the plane) or a
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// positive number (the point is in front of the plane). We want to check if the point
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// is in front of the plane, so all we have to do is go through each point and make
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// sure the plane equation goes out to a positive number on each side of the frustum.
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// The result (be it positive or negative) is the distance the point is front the plane.
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// Go through all the sides of the frustum
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for(int i = 0; i < 6; i++ )
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{
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// Calculate the plane equation and check if the point is behind a side of the frustum
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if(m_Frustum[i][A] * x + m_Frustum[i][B] * y + m_Frustum[i][C] * z + m_Frustum[i][D] <= 0)
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{
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// The point was behind a side, so it ISN'T in the frustum
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return false;
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}
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}
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// The point was inside of the frustum (In front of ALL the sides of the frustum)
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return true;
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}
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///////////////////////////////// SPHERE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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/////
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///// This determines if a sphere is inside of our frustum by it's center and radius.
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/////
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///////////////////////////////// SPHERE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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bool CFrustum::SphereInFrustum( float x, float y, float z, float radius )
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{
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// Now this function is almost identical to the PointInFrustum(), except we
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// now have to deal with a radius around the point. The point is the center of
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// the radius. So, the point might be outside of the frustum, but it doesn't
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// mean that the rest of the sphere is. It could be half and half. So instead of
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// checking if it's less than 0, we need to add on the radius to that. Say the
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// equation produced -2, which means the center of the sphere is the distance of
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// 2 behind the plane. Well, what if the radius was 5? The sphere is still inside,
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// so we would say, if(-2 < -5) then we are outside. In that case it's false,
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// so we are inside of the frustum, but a distance of 3. This is reflected below.
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// Go through all the sides of the frustum
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for(int i = 0; i < 6; i++ )
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{
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// If the center of the sphere is farther away from the plane than the radius
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if( m_Frustum[i][A] * x + m_Frustum[i][B] * y + m_Frustum[i][C] * z + m_Frustum[i][D] <= -radius )
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{
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// The distance was greater than the radius so the sphere is outside of the frustum
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return false;
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}
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}
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// The sphere was inside of the frustum!
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return true;
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}
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///////////////////////////////// CUBE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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/////
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///// This determines if a cube is in or around our frustum by it's center and 1/2 it's length
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/////
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///////////////////////////////// CUBE IN FRUSTUM \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\*
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bool CFrustum::CubeInFrustum( float x, float y, float z, float size )
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{
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// This test is a bit more work, but not too much more complicated.
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// Basically, what is going on is, that we are given the center of the cube,
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// and half the length. Think of it like a radius. Then we checking each point
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// in the cube and seeing if it is inside the frustum. If a point is found in front
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// of a side, then we skip to the next side. If we get to a plane that does NOT have
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// a point in front of it, then it will return false.
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// *Note* - This will sometimes say that a cube is inside the frustum when it isn't.
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// This happens when all the corners of the bounding box are not behind any one plane.
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// This is rare and shouldn't effect the overall rendering speed.
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for(int i = 0; i < 6; i++ )
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{
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * (y - size) + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * (y - size) + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * (y + size) + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * (y + size) + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * (y - size) + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * (y - size) + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * (y + size) + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * (y + size) + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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// If we get here, it isn't in the frustum
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return false;
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}
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return true;
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}
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bool CFrustum::BlockInFrustum(float x, float z, float size) {
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const float b_height = 6.0f;
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for(int i = 0; i < 6; i++ )
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{
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * 0.0f + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * 0.0f + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * b_height + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * b_height + m_Frustum[i][C] * (z - size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * 0.0f + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * 0.0f + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x - size) + m_Frustum[i][B] * b_height + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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if(m_Frustum[i][A] * (x + size) + m_Frustum[i][B] * b_height + m_Frustum[i][C] * (z + size) + m_Frustum[i][D] > 0)
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continue;
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// If we get here, it isn't in the frustum
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return false;
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}
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return true;
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}
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}
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