dust3d/third_party/libigl/include/igl/segment_segment_intersect.cpp

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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2016 Francisca Gil Ureta <gilureta@cs.nyu.edu>
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#include "segment_segment_intersect.h"
#include <Eigen/Geometry>
template<typename DerivedSource, typename DerivedDir>
IGL_INLINE bool igl::segment_segment_intersect(
const Eigen::PlainObjectBase <DerivedSource> &p,
const Eigen::PlainObjectBase <DerivedDir> &r,
const Eigen::PlainObjectBase <DerivedSource> &q,
const Eigen::PlainObjectBase <DerivedDir> &s,
double &a_t,
double &a_u,
double eps
)
{
// http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
// Search intersection between two segments
// p + t*r : t \in [0,1]
// q + u*s : u \in [0,1]
// p + t * r = q + u * s // x s
// t(r x s) = (q - p) x s
// t = (q - p) x s / (r x s)
// (r x s) ~ 0 --> directions are parallel, they will never cross
Eigen::RowVector3d rxs = r.cross(s);
if (rxs.norm() <= eps)
return false;
int sign;
double u;
// u = (q p) × r / (r × s)
Eigen::RowVector3d u1 = (q - p).cross(r);
sign = ((u1.dot(rxs)) > 0) ? 1 : -1;
u = u1.norm() / rxs.norm();
u = u * sign;
double t;
// t = (q - p) x s / (r x s)
Eigen::RowVector3d t1 = (q - p).cross(s);
sign = ((t1.dot(rxs)) > 0) ? 1 : -1;
t = t1.norm() / rxs.norm();
t = t * sign;
a_t = t;
a_u = u;
if ((u - 1.) > eps || u < -eps)
return false;
if ((t - 1.) > eps || t < -eps)
return false;
return true;
};
#ifdef IGL_STATIC_LIBRARY
template bool igl::segment_segment_intersect<Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3> >(Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, double&, double&, double);
#endif