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/*
This file is part of the Boson game
Copyright (C) 2005 Andreas Beckermann (b_mann@gmx.de)
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#include "math/boplane.h"
#include <math.h>
#include <stdio.h>
void BoPlane::debugPlane(const BoVector3Float& normal, float distance)
{
printf("((%f %f %f) %f\n", normal[0], normal[1], normal[2], distance);
}
bool BoPlane::intersectPlane(const BoPlane& plane1, const BoPlane& plane2, BoVector3Float* intersectionPoint, BoVector3Float* intersectionVector)
{
const BoVector3Float& n1 = plane1.normal();
const BoVector3Float& n2 = plane2.normal();
BoVector3Float cross = BoVector3Float::crossProduct(n1, n2);
if (cross.isEqual(0.0f, 0.0f, 0.0f)) {
// AB: note that intersections are still possible, if planes are equal
// -> see isEqual()
return false;
}
*intersectionVector = cross;
// AB: the cross product is already 50% of the work.
// The cross product gives a vector that is perpendicular to both, n1 and n2.
// -> cross is perpendicular to n1, meaning it is on plane1.
// -> cross is perpendicular to n2, meaning it is on plane2.
// => cross is a vector that describes the direction of a line that is on both,
// plane1 and plane2. it is that line that we want.
// Now all we need is the starting point of the line.
// A 3d plane can be described in several ways - e.g. using a normal vector "n"
// and a point "p0" on the plane (p0 can be retrieved from our planes using
// n*distanceFromOrigin).
// Another way is the equation "n * ((x,y,z) - p0) = 0", where the plane is the
// set of all solutions to that equation. Note that by "*" we mean
// dotproduct here.
//
// What we have: 2 equations of the form "n * ((x,y,z) - p0) = 0" (i.e. 2 planes)
// What we want: one solution to these equations, i.e. one point that is on both
// planes. This is also one point of the intersection line.
//
// 2 equations and 3 variables.
// -> the vector "cross" describes the direction of the intersection line.
// It must also intersect at least one of the x-/y-/z-planes.
// If a component of "cross" is non-zero, the line must intersect with the
// corresponding plane, so if e.g. the z component is non-zero, we can
// assume z=0 and have only 2 equations and 2 variables left.
// However due to rounding errors with float variables, we cannot safely
// check for a component "!= 0.0f", so we just pick the one with the largest
// absolute value (which is of course guaranteed to be non-zero, as the
// vector is non-zero).
// AB: note that our normals are directed to the _inside_ of the frustum,
// therefore we need to multiply be the negative normal (or by the negative
// distance) to get a point on the plane
//
// (this is because this code is intended for use in conjunction with
// viewFrustum planes)
BoVector3Float p0Plane1 = n1 * (-plane1.distanceFromOrigin());
BoVector3Float p0Plane2 = n2 * (-plane2.distanceFromOrigin());
float absx = fabsf(cross[0]);
float absy = fabsf(cross[1]);
float absz = fabsf(cross[2]);
// "n1 * p0Plane1" and "n2 * p0Plane2" is used in all three cases below
float n1DotP0Plane1 = BoVector3Float::dotProduct(n1, p0Plane1);
float n2DotP0Plane2 = BoVector3Float::dotProduct(n2, p0Plane2);
if (absx >= absy && absx >= absz) {
// "n * ((x,y,z) - p0) = 0" simplifies to "n * ((0,y,z) - p0) = 0" for
// both planes, i.e.
// "n1 * ((x,y,0) - p0Plane1) = 0" and "n2 * ((0,y,z) - p0Plane2) = 0"
// this is a 2 equations with 2 variables which is solved below.
intersectionPoint->setX(0.0f);
intersectionPoint->setY((n2DotP0Plane2 * n1.z() - n1DotP0Plane1 * n2.z()) / (n1.z() * n2.y() - n2.z() * n1.y()));
intersectionPoint->setZ((n2DotP0Plane2 * n1.y() - n1DotP0Plane1 * n2.y()) / (n1.y() * n2.z() - n2.y() * n1.z()));
} else if (absy >= absx && absy >= absz) {
intersectionPoint->setY(0.0f);
intersectionPoint->setX((n2DotP0Plane2 * n1.z() - n1DotP0Plane1 * n2.z()) / (n1.z() * n2.x() - n2.z() * n1.x()));
intersectionPoint->setZ((n2DotP0Plane2 * n1.x() - n1DotP0Plane1 * n2.x()) / (n1.x() * n2.z() - n2.x() * n1.z()));
} else {
intersectionPoint->setZ(0.0f);
intersectionPoint->setX((n2DotP0Plane2 * n1.y() - n1DotP0Plane1 * n2.y()) / (n1.y() * n2.x() - n2.y() * n1.x()));
intersectionPoint->setY((n2DotP0Plane2 * n1.x() - n1DotP0Plane1 * n2.x()) / (n1.x() * n2.y() - n2.x() * n1.y()));
}
return true;
}
bool BoPlane::intersectLine(const BoVector3Float& linePoint, const BoVector3Float& lineVector, BoVector3Float* intersection) const
{
float factor;
if (!intersectLineInternal(linePoint, lineVector, &factor)) {
return false;
}
*intersection = linePoint + lineVector * factor;
return true;
}
bool BoPlane::intersectLineSegment(const BoVector3Float& linePoint1, const BoVector3Float& linePoint2, BoVector3Float* intersection) const
{
float factor;
BoVector3Float lineVector = (linePoint2 - linePoint1);
if (!intersectLineInternal(linePoint1, lineVector, &factor)) {
return false;
}
if (factor < 0.0f || factor > 1.0f) {
return false;
}
*intersection = linePoint1 + lineVector * factor;
return true;
}
bool BoPlane::intersectLineInternal(const BoVector3Float& linePoint, const BoVector3Float& lineVector, float* factor) const
{
// http://geometryalgorithms.com/Archive/algorithm_0104/algorithm_0104B.htm#intersect3D_SegPlane()
// provides a nice explanation of the maths in here
float NdotLine = BoVector3Float::dotProduct(normal(), lineVector);
if (fabsf(NdotLine) <= 0.001) {
// intersection still possible, if the line is on the plane.
return false;
}
// now we know the line _does_ intersect with the plane (let's call the point p)
// the vector from a point on the plane to p is perpendicular to the plane
// normal.
// That means their dot product is 0.
//
// i.e. normal * (point_on_plane - p) = 0
// "p" can also be written as linePoint + a * lineVector, with a being a
// certain real number. this makes:
// normal * (point_on_plane - (linePoint + a * lineVector)) = 0
// =>
// normal * (point_on_plane - linePoint) + a * normal * lineVector = 0
// =>
// a = (normal * (point_on_plane - linePoint)) / (normal * lineVector)
float foo = BoVector3Float::dotProduct(normal(), pointOnPlane() - linePoint);
float a = foo / NdotLine;
*factor = a;
return true;
}
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