483 lines
15 KiB
C
483 lines
15 KiB
C
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// Copyright (c) 2015 INRIA Sophia-Antipolis (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org).
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// You can redistribute it and/or modify it under the terms of the GNU
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// General Public License as published by the Free Software Foundation,
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// either version 3 of the License, or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: GPL-3.0+
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//
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//
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// Author(s) : Sven Oesau, Yannick Verdie, Clément Jamin, Pierre Alliez
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//
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#ifndef CGAL_SHAPE_DETECTION_3_CONE_H
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#define CGAL_SHAPE_DETECTION_3_CONE_H
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#include <CGAL/license/Point_set_shape_detection_3.h>
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#include <CGAL/Shape_detection_3/Shape_base.h>
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#include <CGAL/number_utils.h>
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#include <cmath>
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/*!
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\file Cone.h
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*/
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namespace CGAL {
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namespace Shape_detection_3 {
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/*!
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\brief Cone implements Shape_base.
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The cone is represented by its apex, the axis and the opening angle.
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This representation models an open infinite single-cone.
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\tparam Traits a model of `EfficientRANSACTraits`
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\ingroup PkgPointSetShapeDetection3Shapes
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*/
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template <class Traits>
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class Cone : public Shape_base<Traits> {
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using Shape_base<Traits>::update_label;
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public:
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/// \cond SKIP_IN_MANUAL
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typedef typename Traits::Point_map Point_map;
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///< property map to access the location of an input point.
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typedef typename Traits::Normal_map Normal_map;
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///< property map to access the unoriented normal of an input point.
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typedef typename Traits::FT FT; ///< number type.
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typedef typename Traits::Point_3 Point_3;///< point type.
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typedef typename Traits::Vector_3 Vector_3;///< vector type.
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/// \endcond
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Cone() : Shape_base<Traits>(), m_wrap(false) {}
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/*!
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The opening angle between the axis and the surface of the cone.
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*/
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FT angle() const {
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return m_angle;
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}
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/*!
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The apex of the cone.
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*/
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Point_3 apex() const {
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return m_apex;
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}
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/*!
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The axis points from the apex into the cone.
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*/
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Vector_3 axis() const {
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return m_axis;
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}
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/*!
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Helper function to write apex, axis and angle of the cone and
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number of assigned points into a string.
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*/
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/// \cond SKIP_IN_MANUAL
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std::string info() const {
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std::stringstream sstr;
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sstr << "Type: cone apex: (" << this->get_x(m_apex) << ", " << this->get_y(m_apex);
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sstr << ", " << this->get_z(m_apex) << ") axis: (" << this->get_x(m_axis) << ", ";
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sstr << this->get_y(m_axis) << ", " << this->get_z(m_axis) << ") angle:" << m_angle;
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sstr << " #Pts: " << this->m_indices.size();
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return sstr.str();
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}
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/*!
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Computes squared Euclidean distance from query point to the shape.
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*/
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FT squared_distance(const Point_3 &p) const {
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Vector_3 toApex = this->constr_vec(m_apex, p);
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FT a = this->sqlen(toApex);
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// projection on axis
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FT b = this->scalar_pdct(toApex, m_axis);
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// distance to axis
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if (a - b * b <= 0)
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return 0;
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FT l = CGAL::sqrt(a - b * b);
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FT c = m_cos_ang * l;
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FT d = m_neg_sin_ang * b;
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// far on other side?
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return (b < 0 && c - d < 0) ? a : CGAL::abs(c + d) * CGAL::abs(c + d);
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}
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/// \endcond
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protected:
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/// \cond SKIP_IN_MANUAL
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virtual void create_shape(const std::vector<std::size_t> &indices) {
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Point_3 p1 = this->point(indices[0]);
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Point_3 p2 = this->point(indices[1]);
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Point_3 p3 = this->point(indices[2]);
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Vector_3 n1 = this->normal(indices[0]);
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Vector_3 n2 = this->normal(indices[1]);
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Vector_3 n3 = this->normal(indices[2]);
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// first calculate intersection of three planes -> apex
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Vector_3 lineDir = this->cross_pdct(n1, n2);
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FT length = CGAL::sqrt(this->sqlen(lineDir));
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if (length == 0)
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return;
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lineDir = this->scale(lineDir, (FT)1.0 / length);
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// lineDir not normalized direction of intersection lines
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// of two planes (p1, n1) and (p2, n2)
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// get point on line by moving point p1 onto line
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Vector_3 orthLineInPlane = this->cross_pdct(n1, lineDir);
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length = CGAL::sqrt(this->sqlen(orthLineInPlane));
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if (length == 0)
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return;
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orthLineInPlane = this->scale(orthLineInPlane, (FT)1.0 / length);
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// distance of p1 to (p2, n2)
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FT d = this->scalar_pdct(this->constr_vec(CGAL::ORIGIN, p1), n2)
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- this->scalar_pdct(this->constr_vec(CGAL::ORIGIN, p2), n2);
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// projection of orthLineInPlane onto p2
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FT l = this->scalar_pdct(orthLineInPlane, n2);
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if (l == 0)
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return;
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Point_3 pointOnLine = this->transl(
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p1, this->scale(orthLineInPlane, -d/l));
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// distance of pLineDir to (p3, n3)
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d = this->scalar_pdct(this->constr_vec(CGAL::ORIGIN, pointOnLine), n3)
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- this->scalar_pdct(this->constr_vec(CGAL::ORIGIN, p3), n3);
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l = this->scalar_pdct(lineDir, n3);
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if (l == 0)
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return;
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m_apex = this->transl(pointOnLine, this->scale(lineDir, -d/l));
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// 2. find axis
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Vector_3 v1 = this->constr_vec(m_apex, p1);
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length = CGAL::sqrt(this->sqlen(v1));
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if (length == 0)
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return;
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v1 = this->scale(v1, (FT)1.0 / length);
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Point_3 c1 = this->transl(m_apex, v1);
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Vector_3 v2 = this->constr_vec(m_apex, p2);
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length = CGAL::sqrt(this->sqlen(v2));
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if (length == 0)
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return;
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v2 = this->scale(v2, (FT)1.0 / length);
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Point_3 c2 = this->transl(m_apex, v2);
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Vector_3 v3 = this->constr_vec(m_apex, p3);
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length = CGAL::sqrt(this->sqlen(v3));
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if (length == 0)
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return;
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v3 = this->scale(v3, (FT)1.0 / length);
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Point_3 c3 = this->transl(m_apex, v3);
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m_axis = this->cross_pdct(this->constr_vec(c2, c1), this->constr_vec(c3, c1));
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m_axis = (this->scalar_pdct(orthLineInPlane, m_axis) < 0) ?
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this->scale(m_axis, FT(-1)) : m_axis;
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length = CGAL::sqrt(this->sqlen(m_axis));
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if (length == 0)
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return;
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m_axis = this->scale(m_axis, (FT)1.0 / length);
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m_angle = acos(this->scalar_pdct(v1, m_axis)) + acos(this->scalar_pdct(v2, m_axis)) + acos(this->scalar_pdct(v3, m_axis));
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m_angle /= (FT)3.0;
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if (m_angle < 0 || m_angle > CGAL_PI / (FT)2.12)
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return;
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m_neg_sin_ang = -sin(m_angle);
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m_cos_ang = cos(m_angle);
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this->m_is_valid = true;
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}
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virtual void squared_distance(const std::vector<std::size_t> &indices,
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std::vector<FT> &dists) const {
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for (std::size_t i = 0;i<indices.size();i++) {
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Vector_3 to_apex = this->constr_vec(m_apex, this->point(indices[i]));
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FT a = this->sqlen(to_apex);
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// projection on axis
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FT b = this->scalar_pdct(to_apex, m_axis);
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// distance to axis
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FT l = CGAL::sqrt(a - b * b);
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FT c = m_cos_ang * l;
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FT d = m_neg_sin_ang * b;
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// far on other side?
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dists[i] =
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(b < 0 && c - d < 0) ? a : CGAL::abs(c + d) * CGAL::abs(c + d);
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}
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}
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virtual void cos_to_normal(const std::vector<std::size_t> &indices,
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std::vector<FT> &angles) const {
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for (std::size_t i = 0;i<indices.size();i++) {
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// construct vector orthogonal to axis in direction of the point
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Vector_3 a = this->constr_vec(m_apex, this->point(indices[i]));
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Vector_3 b = this->cross_pdct(m_axis,
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this->cross_pdct(m_axis, a));
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b = (this->scalar_pdct(a, b) < 0) ? this->scale(b, FT(-1)) : b;
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FT length = CGAL::sqrt(this->sqlen(b));
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if (length == 0) {
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angles[i] = (FT)1.0;
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continue;
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}
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b = this->scale(b, (FT)1.0 / length);
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b = this->sum_vectors(
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this->scale(b, m_cos_ang),
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this->scale(m_axis, m_neg_sin_ang));
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angles[i] = CGAL::abs(this->scalar_pdct(this->normal(indices[i]), b));
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}
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}
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virtual FT cos_to_normal(const Point_3 &p, const Vector_3 &n) const {
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// construct vector orthogonal to axis in direction of the point
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Vector_3 a = this->constr_vec(m_apex, p);
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Vector_3 b = this->cross_pdct(m_axis, this->cross_pdct(m_axis, a));
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b = (this->scalar_pdct(a, b) < 0) ? this->scale(b, FT(-1)) : b;
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FT length = CGAL::sqrt(this->sqlen(b));
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if (length == 0) {
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return (FT)1.0;
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}
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b = this->scale(b, (FT)1.0 / length);
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b = this->sum_vectors(
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this->scale(b, m_cos_ang),
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this->scale(m_axis, m_neg_sin_ang));
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return CGAL::abs(this->scalar_pdct(n, b));
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}
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virtual std::size_t minimum_sample_size() const {
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return 3;
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}
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virtual void post_wrap(const std::vector<unsigned int> &bitmap,
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const std::size_t &u_extent,
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const std::size_t &v_extent,
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std::vector<unsigned int> &labels) const {
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if (!m_wrap)
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return;
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// handle top index separately
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unsigned int nw = bitmap[u_extent - 1];
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unsigned int l = bitmap[0];
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// Special case v_extent is just 1
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if (v_extent == 1) {
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if (nw && nw != l) {
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l = (std::min<unsigned int>)(nw, l);
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update_label(labels, (std::max<unsigned int>)(nw, l), l);
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}
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return;
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}
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unsigned int w = bitmap[2 * u_extent - 1];
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unsigned int sw;
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if (l) {
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if (nw && nw != l) {
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l = (std::min<unsigned int>)(nw, l);
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update_label(labels, (std::max<unsigned int>)(nw, l), l);
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}
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else if (w && w != l) {
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l = (std::min<unsigned int>)(w, l);
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update_label(labels, (std::max<unsigned int>)(w, l), l);
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}
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}
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// handle mid indices
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for (std::size_t y = 1;y<v_extent - 1;y++) {
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l = bitmap[y * u_extent];
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if (!l)
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continue;
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nw = bitmap[y * u_extent - 1];
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w = bitmap[(y + 1) * u_extent - 1];
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sw = bitmap[(y + 2) * u_extent - 1];
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if (nw && nw != l) {
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l = (std::min<unsigned int>)(nw, l);
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update_label(labels, (std::max<unsigned int>)(nw, l), l);
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}
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if (w && w != l) {
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l = (std::min<unsigned int>)(w, l);
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update_label(labels, (std::max<unsigned int>)(w, l), l);
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}
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else if (sw && sw != l) {
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l = (std::min<unsigned int>)(sw, l);
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update_label(labels, (std::max<unsigned int>)(sw, l), l);
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}
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}
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// handle last index
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l = bitmap[(v_extent - 1) * u_extent];
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if (!l)
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return;
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nw = bitmap[(v_extent - 1) * u_extent - 1];
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w = bitmap[u_extent * v_extent - 1];
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if (nw && nw != l) {
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l = (std::min<unsigned int>)(nw, l);
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update_label(labels, (std::max<unsigned int>)(nw, l), l);
|
||
|
|
}
|
||
|
|
else if (w && w != l) {
|
||
|
|
l = (std::min<unsigned int>)(w, l);
|
||
|
|
update_label(labels, (std::max<unsigned int>)(w, l), l);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
virtual void parameters(const std::vector<std::size_t> &indices,
|
||
|
|
std::vector<std::pair<FT, FT> > ¶meterSpace,
|
||
|
|
FT &cluster_epsilon,
|
||
|
|
FT min[2],
|
||
|
|
FT max[2]) const {
|
||
|
|
|
||
|
|
// Create basis d1, d2
|
||
|
|
Vector_3 d1 = this->constr_vec(
|
||
|
|
ORIGIN, this->constr_pt(FT(0), FT(0), FT(1)));
|
||
|
|
Vector_3 d2 = this->cross_pdct(m_axis, d1);
|
||
|
|
FT l = this->sqlen(d2);
|
||
|
|
if (l < (FT)0.0001) {
|
||
|
|
d1 = this->constr_vec(ORIGIN, this->constr_pt(FT(1), FT(0), FT(0)));
|
||
|
|
d2 = this->cross_pdct(m_axis, d1);
|
||
|
|
l = this->sqlen(d2);
|
||
|
|
}
|
||
|
|
d2 = this->scale(d2, FT(1) / CGAL::sqrt(l));
|
||
|
|
|
||
|
|
d1 = this->cross_pdct(m_axis, d2);
|
||
|
|
l = CGAL::sqrt(this->sqlen(d1));
|
||
|
|
if (l == 0)
|
||
|
|
return;
|
||
|
|
|
||
|
|
d1 = this->scale(d1, (FT)1.0 / l);
|
||
|
|
|
||
|
|
if (m_angle > CGAL_M_PI_4) {
|
||
|
|
// Projection onto a disk preserving distance to apex
|
||
|
|
|
||
|
|
m_wrap = false;
|
||
|
|
|
||
|
|
// First index separately to initialize min/max
|
||
|
|
Vector_3 d = this->constr_vec(m_apex, this->point(indices[0]));
|
||
|
|
FT l = this->scalar_pdct(d, m_axis) / m_cos_ang;
|
||
|
|
FT u = this->scalar_pdct(d, d1);
|
||
|
|
FT v = this->scalar_pdct(d, d2);
|
||
|
|
FT l2 = CGAL::sqrt(u * u + v * v);
|
||
|
|
u = u * l/l2;
|
||
|
|
v = v * l/l2;
|
||
|
|
min[0] = max[0] = u;
|
||
|
|
min[1] = max[1] = v;
|
||
|
|
parameterSpace[0] = std::pair<FT, FT>(u, v);
|
||
|
|
|
||
|
|
for (std::size_t i = 1;i<indices.size();i++) {
|
||
|
|
d = this->constr_vec(m_apex, this->point(indices[i]));
|
||
|
|
l = this->scalar_pdct(d, m_axis) / m_cos_ang;
|
||
|
|
u = this->scalar_pdct(d, d1);
|
||
|
|
v = this->scalar_pdct(d, d2);
|
||
|
|
l2 = CGAL::sqrt(u * u + v * v);
|
||
|
|
u = u * l/l2;
|
||
|
|
v = v * l/l2;
|
||
|
|
|
||
|
|
min[0] = (std::min<FT>)(min[0], u);
|
||
|
|
max[0] = (std::max<FT>)(max[0], u);
|
||
|
|
|
||
|
|
min[1] = (std::min<FT>)(min[1], v);
|
||
|
|
max[1] = (std::max<FT>)(max[1], v);
|
||
|
|
|
||
|
|
parameterSpace[i] = std::pair<FT, FT>(u, v);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
// Map onto triangle.
|
||
|
|
// u coordinate is arclength
|
||
|
|
// v coordinate is distance to apex
|
||
|
|
|
||
|
|
Vector_3 d = this->constr_vec(m_apex, this->point(indices[0]));
|
||
|
|
FT v = this->scalar_pdct(d, m_axis) / m_cos_ang;
|
||
|
|
FT phi = atan2(this->scalar_pdct(d, d2), this->scalar_pdct(d, d1));
|
||
|
|
FT u = FT(phi + CGAL_PI);
|
||
|
|
FT avg_v = v;
|
||
|
|
|
||
|
|
min[0] = max[0] = u;
|
||
|
|
min[1] = max[1] = v;
|
||
|
|
parameterSpace[0] = std::pair<FT, FT>(u, v);
|
||
|
|
for (std::size_t i = 1;i<indices.size();i++) {
|
||
|
|
d = this->constr_vec(m_apex, this->point(indices[i]));
|
||
|
|
v = this->scalar_pdct(d, m_axis) / m_cos_ang;
|
||
|
|
phi = atan2(this->scalar_pdct(d, d2), this->scalar_pdct(d, d1));
|
||
|
|
u = FT(phi + CGAL_PI);
|
||
|
|
|
||
|
|
min[0] = (std::min<FT>)(min[0], u);
|
||
|
|
max[0] = (std::max<FT>)(max[0], u);
|
||
|
|
|
||
|
|
min[1] = (std::min<FT>)(min[1], v);
|
||
|
|
max[1] = (std::max<FT>)(max[1], v);
|
||
|
|
|
||
|
|
avg_v += v;
|
||
|
|
|
||
|
|
parameterSpace[i] = std::pair<FT, FT>(u, v);
|
||
|
|
}
|
||
|
|
|
||
|
|
// Scale u parameter by average circumference to arc length
|
||
|
|
avg_v /= indices.size();
|
||
|
|
const FT scale = -m_neg_sin_ang * avg_v;
|
||
|
|
|
||
|
|
m_wrap = (min[0] + 2 * CGAL_PI - max[0]) * scale < cluster_epsilon;
|
||
|
|
|
||
|
|
for (std::size_t i = 0;i<parameterSpace.size();i++) {
|
||
|
|
std::pair<FT, FT> p = parameterSpace[i];
|
||
|
|
parameterSpace[i] = std::pair<FT, FT>(p.first * scale, p.second);
|
||
|
|
}
|
||
|
|
|
||
|
|
min[0] *= scale;
|
||
|
|
max[0] *= scale;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
virtual bool supports_connected_component() const {
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
private:
|
||
|
|
FT m_angle;
|
||
|
|
Point_3 m_apex;
|
||
|
|
Vector_3 m_axis;
|
||
|
|
FT m_neg_sin_ang, m_cos_ang;
|
||
|
|
mutable bool m_wrap;
|
||
|
|
/// \endcond
|
||
|
|
};
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#endif
|