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