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Java™ Binding for the OpenGL® API
/**
* Copyright 2010 JogAmp Community. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice, this list
* of conditions and the following disclaimer in the documentation and/or other materials
* provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY JogAmp Community ``AS IS'' AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL JogAmp Community OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are those of the
* authors and should not be interpreted as representing official policies, either expressed
* or implied, of JogAmp Community.
*/
package com.jogamp.opengl.math.geom;
import com.jogamp.common.os.Platform;
/**
* Providing frustum {@link #getPlanes() planes} derived by different inputs
* ({@link #updateByPMV(float[], int) P*MV}, ..)
* used to {@link #classifySphere(float[], float) classify objects} and to test
* whether they are {@link #isOutside(AABBox) outside}.
*
*
* Extracting the world-frustum planes from the P*Mv:
*
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix
* Gil Gribb
* Klaus Hartmann
* http://graphics.cs.ucf.edu/cap4720/fall2008/plane_extraction.pdf
*
* Classifying Point, Sphere and AABBox:
*
* Efficient View Frustum Culling
* Daniel Sýkora
* Josef Jelínek
* http://www.cg.tuwien.ac.at/hostings/cescg/CESCG-2002/DSykoraJJelinek/index.html
*
*
* Lighthouse3d.com
* http://www.lighthouse3d.com/tutorials/view-frustum-culling/
*
*
* Fundamentals about Planes, Half-Spaces and Frustum-Culling:
*
* Planes and Half-Spaces, Max Wagner
* http://www.emeyex.com/site/tuts/PlanesHalfSpaces.pdf
*
*
* Frustum Culling, Max Wagner
* http://www.emeyex.com/site/tuts/FrustumCulling.pdf
*
*
*/
public class Frustum {
/** Normalized planes[l, r, b, t, n, f] */
protected Plane[] planes = new Plane[6];
/**
* Creates an undefined instance w/o calculating the frustum.
*
* Use one of the update(..) methods to set the {@link #getPlanes() planes}.
*
* @see #updateByPlanes(Plane[])
* @see #updateByPMV(float[], int)
*/
public Frustum() {
for (int i = 0; i < 6; ++i) {
planes[i] = new Plane();
}
}
/**
* Plane equation := dot(n, x - p) = 0 -> ax + bc + cx + d == 0
*
* In order to work w/ {@link Frustum#isOutside(AABBox) isOutside(..)} methods,
* the normals have to point to the inside of the frustum.
*
*/
public static class Plane {
/** Normal of the plane */
public final float[] n = new float[3];
/** Distance to origin */
public float d;
/**
* Return signed distance of plane to given point.
*
* - If dist < 0 , then the point p lies in the negative halfspace.
* - If dist = 0 , then the point p lies in the plane.
* - If dist > 0 , then the point p lies in the positive halfspace.
*
* A plane cuts 3D space into 2 half spaces.
*
* Positive halfspace is where the plane’s normals vector points into.
*
*
* Negative halfspace is the other side of the plane, i.e. *-1
*
**/
public final float distanceTo(float x, float y, float z) {
return n[0] * x + n[1] * y + n[2] * z + d;
}
/** Return distance of plane to given point, see {@link #distanceTo(float, float, float)}. */
public final float distanceTo(float[] p) {
return n[0] * p[0] + n[1] * p[1] + n[2] * p[2] + d;
}
@Override
public String toString() {
return "Plane[ [ " + n[0] + ", " + n[1] + ", " + n[2] + " ], " + d + "]";
}
}
/** Index for left plane: {@value} */
public static final int LEFT = 0;
/** Index for right plane: {@value} */
public static final int RIGHT = 1;
/** Index for bottom plane: {@value} */
public static final int BOTTOM = 2;
/** Index for top plane: {@value} */
public static final int TOP = 3;
/** Index for near plane: {@value} */
public static final int NEAR = 4;
/** Index for far plane: {@value} */
public static final int FAR = 5;
/**
* {@link Plane}s are ordered in the returned array as follows:
*
* - {@link #LEFT}
* - {@link #RIGHT}
* - {@link #BOTTOM}
* - {@link #TOP}
* - {@link #NEAR}
* - {@link #FAR}
*
*
* {@link Plane}'s normals are pointing to the inside of the frustum
* in order to work w/ {@link #isOutside(AABBox) isOutside(..)} methods.
*
*
* @return array of normalized {@link Plane}s, order see above.
*/
public final Plane[] getPlanes() { return planes; }
/**
* Copy the given src planes into this this instance's planes.
* @param src the 6 source planes
*/
public final void updateByPlanes(Plane[] src) {
for (int i = 0; i < 6; ++i) {
final Plane p0 = planes[i];
final float[] p0_n = p0.n;
final Plane p1 = src[i];
final float[] p1_n = p1.n;
p0_n[0] = p1_n[0];
p0_n[1] = p1_n[1];
p0_n[2] = p1_n[2];
p0.d = p1.d;
}
}
/**
* Calculate the frustum planes in world coordinates
* using the passed float[16] as premultiplied P*MV (column major order).
*
* Frustum plane's normals will point to the inside of the viewing frustum,
* as required by this class.
*
*/
public void updateByPMV(float[] pmv, int pmv_off) {
// Left: a = m41 + m11, b = m42 + m12, c = m43 + m13, d = m44 + m14 - [1..4] row-major
// Left: a = m30 + m00, b = m31 + m01, c = m32 + m02, d = m33 + m03 - [0..3] row-major
{
final Plane p = planes[LEFT];
final float[] p_n = p.n;
p_n[0] = pmv[ pmv_off + 3 + 0 * 4 ] + pmv[ pmv_off + 0 + 0 * 4 ];
p_n[1] = pmv[ pmv_off + 3 + 1 * 4 ] + pmv[ pmv_off + 0 + 1 * 4 ];
p_n[2] = pmv[ pmv_off + 3 + 2 * 4 ] + pmv[ pmv_off + 0 + 2 * 4 ];
p.d = pmv[ pmv_off + 3 + 3 * 4 ] + pmv[ pmv_off + 0 + 3 * 4 ];
}
// Right: a = m41 - m11, b = m42 - m12, c = m43 - m13, d = m44 - m14 - [1..4] row-major
// Right: a = m30 - m00, b = m31 - m01, c = m32 - m02, d = m33 - m03 - [0..3] row-major
{
final Plane p = planes[RIGHT];
final float[] p_n = p.n;
p_n[0] = pmv[ pmv_off + 3 + 0 * 4 ] - pmv[ pmv_off + 0 + 0 * 4 ];
p_n[1] = pmv[ pmv_off + 3 + 1 * 4 ] - pmv[ pmv_off + 0 + 1 * 4 ];
p_n[2] = pmv[ pmv_off + 3 + 2 * 4 ] - pmv[ pmv_off + 0 + 2 * 4 ];
p.d = pmv[ pmv_off + 3 + 3 * 4 ] - pmv[ pmv_off + 0 + 3 * 4 ];
}
// Bottom: a = m41 + m21, b = m42 + m22, c = m43 + m23, d = m44 + m24 - [1..4] row-major
// Bottom: a = m30 + m10, b = m31 + m11, c = m32 + m12, d = m33 + m13 - [0..3] row-major
{
final Plane p = planes[BOTTOM];
final float[] p_n = p.n;
p_n[0] = pmv[ pmv_off + 3 + 0 * 4 ] + pmv[ pmv_off + 1 + 0 * 4 ];
p_n[1] = pmv[ pmv_off + 3 + 1 * 4 ] + pmv[ pmv_off + 1 + 1 * 4 ];
p_n[2] = pmv[ pmv_off + 3 + 2 * 4 ] + pmv[ pmv_off + 1 + 2 * 4 ];
p.d = pmv[ pmv_off + 3 + 3 * 4 ] + pmv[ pmv_off + 1 + 3 * 4 ];
}
// Top: a = m41 - m21, b = m42 - m22, c = m43 - m23, d = m44 - m24 - [1..4] row-major
// Top: a = m30 - m10, b = m31 - m11, c = m32 - m12, d = m33 - m13 - [0..3] row-major
{
final Plane p = planes[TOP];
final float[] p_n = p.n;
p_n[0] = pmv[ pmv_off + 3 + 0 * 4 ] - pmv[ pmv_off + 1 + 0 * 4 ];
p_n[1] = pmv[ pmv_off + 3 + 1 * 4 ] - pmv[ pmv_off + 1 + 1 * 4 ];
p_n[2] = pmv[ pmv_off + 3 + 2 * 4 ] - pmv[ pmv_off + 1 + 2 * 4 ];
p.d = pmv[ pmv_off + 3 + 3 * 4 ] - pmv[ pmv_off + 1 + 3 * 4 ];
}
// Near: a = m41 + m31, b = m42 + m32, c = m43 + m33, d = m44 + m34 - [1..4] row-major
// Near: a = m30 + m20, b = m31 + m21, c = m32 + m22, d = m33 + m23 - [0..3] row-major
{
final Plane p = planes[NEAR];
final float[] p_n = p.n;
p_n[0] = pmv[ pmv_off + 3 + 0 * 4 ] + pmv[ pmv_off + 2 + 0 * 4 ];
p_n[1] = pmv[ pmv_off + 3 + 1 * 4 ] + pmv[ pmv_off + 2 + 1 * 4 ];
p_n[2] = pmv[ pmv_off + 3 + 2 * 4 ] + pmv[ pmv_off + 2 + 2 * 4 ];
p.d = pmv[ pmv_off + 3 + 3 * 4 ] + pmv[ pmv_off + 2 + 3 * 4 ];
}
// Far: a = m41 - m31, b = m42 - m32, c = m43 - m33, d = m44 - m34 - [1..4] row-major
// Far: a = m30 - m20, b = m31 - m21, c = m32 + m22, d = m33 + m23 - [0..3] row-major
{
final Plane p = planes[FAR];
final float[] p_n = p.n;
p_n[0] = pmv[ pmv_off + 3 + 0 * 4 ] - pmv[ pmv_off + 2 + 0 * 4 ];
p_n[1] = pmv[ pmv_off + 3 + 1 * 4 ] - pmv[ pmv_off + 2 + 1 * 4 ];
p_n[2] = pmv[ pmv_off + 3 + 2 * 4 ] - pmv[ pmv_off + 2 + 2 * 4 ];
p.d = pmv[ pmv_off + 3 + 3 * 4 ] - pmv[ pmv_off + 2 + 3 * 4 ];
}
// Normalize all planes
for (int i = 0; i < 6; ++i) {
final Plane p = planes[i];
final float[] p_n = p.n;
final double invl = Math.sqrt(p_n[0] * p_n[0] + p_n[1] * p_n[1] + p_n[2] * p_n[2]);
p_n[0] /= invl;
p_n[1] /= invl;
p_n[2] /= invl;
p.d /= invl;
}
}
private static final boolean isOutsideImpl(Plane p, AABBox box) {
final float[] low = box.getLow();
final float[] high = box.getHigh();
if ( p.distanceTo(low[0], low[1], low[2]) > 0.0f ||
p.distanceTo(high[0], low[1], low[2]) > 0.0f ||
p.distanceTo(low[0], high[1], low[2]) > 0.0f ||
p.distanceTo(high[0], high[1], low[2]) > 0.0f ||
p.distanceTo(low[0], low[1], high[2]) > 0.0f ||
p.distanceTo(high[0], low[1], high[2]) > 0.0f ||
p.distanceTo(low[0], high[1], high[2]) > 0.0f ||
p.distanceTo(high[0], high[1], high[2]) > 0.0f ) {
return false;
}
return true;
}
/**
* Check to see if an axis aligned bounding box is completely outside of the frustum.
*
* Note: If method returns false, the box may only be partially inside.
*
*/
public final boolean isAABBoxOutside(AABBox box) {
for (int i = 0; i < 6; ++i) {
if ( isOutsideImpl(planes[i], box) ) {
// fully outside
return true;
}
}
// We make no attempt to determine whether it's fully inside or not.
return false;
}
public static enum Location { OUTSIDE, INSIDE, INTERSECT };
/**
* Check to see if a point is outside, inside or on a plane of the frustum.
*
* @param p the point
* @return {@link Location} of point related to frustum planes
*/
public final Location classifyPoint(float[] p) {
Location res = Location.INSIDE;
for (int i = 0; i < 6; ++i) {
final float d = planes[i].distanceTo(p);
if ( d < 0.0f ) {
return Location.OUTSIDE;
} else if ( d == 0.0f ) {
res = Location.INTERSECT;
}
}
return res;
}
/**
* Check to see if a point is outside of the frustum.
*
* @param p the point
* @return true if outside of the frustum, otherwise inside or on a plane
*/
public final boolean isPointOutside(float[] p) {
return Location.OUTSIDE == classifyPoint(p);
}
/**
* Check to see if a sphere is outside, intersecting or inside of the frustum.
*
* @param p center of the sphere
* @param radius radius of the sphere
* @return {@link Location} of point related to frustum planes
*/
public final Location classifySphere(float[] p, float radius) {
Location res = Location.INSIDE; // fully inside
for (int i = 0; i < 6; ++i) {
final float d = planes[i].distanceTo(p);
if ( d < -radius ) {
// fully outside
return Location.OUTSIDE;
} else if (d < radius ) {
// intersecting
res = Location.INTERSECT;
}
}
return res;
}
/**
* Check to see if a sphere is outside of the frustum.
*
* @param p center of the sphere
* @param radius radius of the sphere
* @return true if outside of the frustum, otherwise inside or intersecting
*/
public final boolean isSphereOutside(float[] p, float radius) {
return Location.OUTSIDE == classifySphere(p, radius);
}
public StringBuilder toString(StringBuilder sb) {
if( null == sb ) {
sb = new StringBuilder();
}
sb.append("Frustum[ Planes[ ").append(Platform.NEWLINE)
.append(" L: ").append(planes[0]).append(", ").append(Platform.NEWLINE)
.append(" R: ").append(planes[1]).append(", ").append(Platform.NEWLINE)
.append(" B: ").append(planes[2]).append(", ").append(Platform.NEWLINE)
.append(" T: ").append(planes[3]).append(", ").append(Platform.NEWLINE)
.append(" N: ").append(planes[4]).append(", ").append(Platform.NEWLINE)
.append(" F: ").append(planes[5]).append("], ").append(Platform.NEWLINE)
.append("]");
return sb;
}
@Override
public String toString() {
return toString(null).toString();
}
}