/*
* (C) Copyright 2015-2017 Kai Burjack
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*/
package org.joml;
/**
* Provides methods to compute rays through an arbitrary perspective transformation defined by a {@link Matrix4fc}.
* <p>
* This can be used to compute the eye-rays in simple software-based raycasting/raytracing.
* <p>
* To obtain the origin of the rays call {@link #origin(Vector3f)}.
* Then to compute the directions of subsequent rays use {@link #dir(float, float, Vector3f)}.
*
* @author Kai Burjack
*/
public class FrustumRayBuilder {
private float nxnyX, nxnyY, nxnyZ;
private float pxnyX, pxnyY, pxnyZ;
private float pxpyX, pxpyY, pxpyZ;
private float nxpyX, nxpyY, nxpyZ;
private float cx, cy, cz;
/**
* Create a new {@link FrustumRayBuilder} with an undefined frustum.
* <p>
* Before obtaining ray directions, make sure to define the frustum using {@link #set(Matrix4fc)}.
*/
public FrustumRayBuilder() {
}
/**
* Create a new {@link FrustumRayBuilder} from the given {@link Matrix4fc matrix} by extracing the matrix's frustum.
*
* @param m
* the {@link Matrix4fc} to create the frustum from
*/
public FrustumRayBuilder(Matrix4fc m) {
set(m);
}
/**
* Update the stored frustum corner rays and origin of <code>this</code> {@link FrustumRayBuilder} with the given {@link Matrix4fc matrix}.
* <p>
* Reference: <a href="http://gamedevs.org/uploads/fast-extraction-viewing-frustum-planes-from-world-view-projection-matrix.pdf">
* Fast Extraction of Viewing Frustum Planes from the World-View-Projection Matrix</a>
* <p>
* Reference: <a href="http://geomalgorithms.com/a05-_intersect-1.html">http://geomalgorithms.com</a>
*
* @param m
* the {@link Matrix4fc matrix} to update the frustum corner rays and origin with
* @return this
*/
public FrustumRayBuilder set(Matrix4fc m) {
float nxX = m.m03() + m.m00(), nxY = m.m13() + m.m10(), nxZ = m.m23() + m.m20(), d1 = m.m33() + m.m30();
float pxX = m.m03() - m.m00(), pxY = m.m13() - m.m10(), pxZ = m.m23() - m.m20(), d2 = m.m33() - m.m30();
float nyX = m.m03() + m.m01(), nyY = m.m13() + m.m11(), nyZ = m.m23() + m.m21();
float pyX = m.m03() - m.m01(), pyY = m.m13() - m.m11(), pyZ = m.m23() - m.m21(), d3 = m.m33() - m.m31();
// bottom left
nxnyX = nyY * nxZ - nyZ * nxY;
nxnyY = nyZ * nxX - nyX * nxZ;
nxnyZ = nyX * nxY - nyY * nxX;
// bottom right
pxnyX = pxY * nyZ - pxZ * nyY;
pxnyY = pxZ * nyX - pxX * nyZ;
pxnyZ = pxX * nyY - pxY * nyX;
// top left
nxpyX = nxY * pyZ - nxZ * pyY;
nxpyY = nxZ * pyX - nxX * pyZ;
nxpyZ = nxX * pyY - nxY * pyX;
// top right
pxpyX = pyY * pxZ - pyZ * pxY;
pxpyY = pyZ * pxX - pyX * pxZ;
pxpyZ = pyX * pxY - pyY * pxX;
// compute origin
float pxnxX, pxnxY, pxnxZ;
pxnxX = pxY * nxZ - pxZ * nxY;
pxnxY = pxZ * nxX - pxX * nxZ;
pxnxZ = pxX * nxY - pxY * nxX;
float invDot = 1.0f / (nxX * pxpyX + nxY * pxpyY + nxZ * pxpyZ);
cx = (-pxpyX * d1 - nxpyX * d2 - pxnxX * d3) * invDot;
cy = (-pxpyY * d1 - nxpyY * d2 - pxnxY * d3) * invDot;
cz = (-pxpyZ * d1 - nxpyZ * d2 - pxnxZ * d3) * invDot;
return this;
}
/**
* Store the eye/origin of the perspective frustum in the given <code>origin</code>.
*
* @param origin
* will hold the perspective origin
* @return the <code>origin</code> vector
*/
public Vector3fc origin(Vector3f origin) {
origin.x = cx;
origin.y = cy;
origin.z = cz;
return origin;
}
/**
* Obtain the normalized direction of a ray starting at the center of the coordinate system and going
* through the near frustum plane.
* <p>
* The parameters <code>x</code> and <code>y</code> are used to interpolate the generated ray direction
* from the bottom-left to the top-right frustum corners.
*
* @param x
* the interpolation factor along the left-to-right frustum planes, within <tt>[0..1]</tt>
* @param y
* the interpolation factor along the bottom-to-top frustum planes, within <tt>[0..1]</tt>
* @param dir
* will hold the normalized ray direction
* @return the <code>dir</code> vector
*/
public Vector3fc dir(float x, float y, Vector3f dir) {
float y1x = nxnyX + (nxpyX - nxnyX) * y;
float y1y = nxnyY + (nxpyY - nxnyY) * y;
float y1z = nxnyZ + (nxpyZ - nxnyZ) * y;
float y2x = pxnyX + (pxpyX - pxnyX) * y;
float y2y = pxnyY + (pxpyY - pxnyY) * y;
float y2z = pxnyZ + (pxpyZ - pxnyZ) * y;
float dx = y1x + (y2x - y1x) * x;
float dy = y1y + (y2y - y1y) * x;
float dz = y1z + (y2z - y1z) * x;
// normalize the vector
float invLen = (float) (1.0 / Math.sqrt(dx * dx + dy * dy + dz * dz));
dir.x = dx * invLen;
dir.y = dy * invLen;
dir.z = dz * invLen;
return dir;
}
}