213 lines
6.5 KiB
C++
213 lines
6.5 KiB
C++
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
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/*************************************************************************
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*
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* Copyright 2000, 2010 Oracle and/or its affiliates.
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*
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* OpenOffice.org - a multi-platform office productivity suite
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*
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* This file is part of OpenOffice.org.
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*
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* OpenOffice.org is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License version 3
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* only, as published by the Free Software Foundation.
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*
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* OpenOffice.org is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License version 3 for more details
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* (a copy is included in the LICENSE file that accompanied this code).
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*
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* You should have received a copy of the GNU Lesser General Public License
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* version 3 along with OpenOffice.org. If not, see
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* <http://www.openoffice.org/license.html>
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* for a copy of the LGPLv3 License.
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*
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************************************************************************/
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#include <algorithm>
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#include <functional>
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#include <vector>
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#include "bezierclip.hxx"
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// -----------------------------------------------------------------------------
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/* Implements the theta function from Sedgewick: Algorithms in XXX, chapter 24 */
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template <class PointType> double theta( const PointType& p1, const PointType& p2 )
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{
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typename PointType::value_type dx, dy, ax, ay;
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double t;
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dx = p2.x - p1.x; ax = absval( dx );
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dy = p2.y - p1.y; ay = absval( dy );
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t = (ax+ay == 0) ? 0 : (double) dy/(ax+ay);
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if( dx < 0 )
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t = 2-t;
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else if( dy < 0 )
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t = 4+t;
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return t*90.0;
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}
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/* Model of LessThanComparable for theta sort.
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* Uses the theta function from Sedgewick: Algorithms in XXX, chapter 24
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*/
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template <class PointType> class ThetaCompare : public ::std::binary_function< const PointType&, const PointType&, bool >
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{
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public:
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ThetaCompare( const PointType& rRefPoint ) : maRefPoint( rRefPoint ) {}
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bool operator() ( const PointType& p1, const PointType& p2 )
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{
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// return true, if p1 precedes p2 in the angle relative to maRefPoint
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return theta(maRefPoint, p1) < theta(maRefPoint, p2);
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}
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double operator() ( const PointType& p ) const
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{
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return theta(maRefPoint, p);
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}
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private:
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PointType maRefPoint;
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};
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/* Implementation of the predicate 'counter-clockwise' for three points, from Sedgewick: Algorithms in XXX, chapter 24 */
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template <class PointType, class CmpFunctor> typename PointType::value_type ccw( const PointType& p0, const PointType& p1, const PointType& p2, CmpFunctor& thetaCmp )
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{
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typename PointType::value_type dx1, dx2, dy1, dy2;
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typename PointType::value_type theta0( thetaCmp(p0) );
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typename PointType::value_type theta1( thetaCmp(p1) );
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typename PointType::value_type theta2( thetaCmp(p2) );
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#if 0
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if( theta0 == theta1 ||
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theta0 == theta2 ||
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theta1 == theta2 )
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{
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// cannot reliably compare, as at least two points are
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// theta-equal. See bug description below
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return 0;
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}
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#endif
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dx1 = p1.x - p0.x; dy1 = p1.y - p0.y;
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dx2 = p2.x - p0.x; dy2 = p2.y - p0.y;
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if( dx1*dy2 > dy1*dx2 )
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return +1;
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if( dx1*dy2 < dy1*dx2 )
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return -1;
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if( (dx1*dx2 < 0) || (dy1*dy2 < 0) )
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return -1;
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if( (dx1*dx1 + dy1*dy1) < (dx2*dx2 + dy2*dy2) )
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return +1;
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return 0;
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}
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/*
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Bug
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===
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Sometimes, the resulting polygon is not the convex hull (see below
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for an edge configuration to reproduce that problem)
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Problem analysis:
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=================
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The root cause of this bug is the fact that the second part of
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the algorithm (the 'wrapping' of the point set) relies on the
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previous theta sorting. Namely, it is required that the
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generated point ordering, when interpreted as a polygon, is not
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self-intersecting. This property, although, cannot be
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guaranteed due to limited floating point accuracy. For example,
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for two points very close together, and at the same time very
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far away from the theta reference point p1, can appear on the
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same theta value (because floating point accuracy is limited),
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although on different rays to p1 when inspected locally.
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Example:
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/
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P3 /
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|\ /
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|/ \
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P2 \
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\
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...____________\
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P1
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Here, P2 and P3 are theta-equal relative to P1, but the local
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ccw measure always says 'left turn'. Thus, the convex hull is
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wrong at this place.
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Solution:
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=========
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If two points are theta-equal and checked via ccw, ccw must
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also classify them as 'equal'. Thus, the second stage of the
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convex hull algorithm sorts the first one out, effectively
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reducing a cluster of theta-equal points to only one. This
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single point can then be treated correctly.
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*/
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/* Implementation of Graham's convex hull algorithm, see Sedgewick: Algorithms in XXX, chapter 25 */
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Polygon2D convexHull( const Polygon2D& rPoly )
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{
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const Polygon2D::size_type N( rPoly.size() );
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Polygon2D result( N + 1 );
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::std::copy(rPoly.begin(), rPoly.end(), result.begin()+1 );
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Polygon2D::size_type min, i;
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// determine safe point on hull (smallest y value)
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for( min=1, i=2; i<=N; ++i )
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{
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if( result[i].y < result[min].y )
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min = i;
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}
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// determine safe point on hull (largest x value)
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for( i=1; i<=N; ++i )
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{
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if( result[i].y == result[min].y &&
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result[i].x > result[min].x )
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{
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min = i;
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}
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}
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// TODO: add inner elimination optimization from Sedgewick: Algorithms in XXX, chapter 25
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// TODO: use radix sort instead of ::std::sort(), calc theta only once and store
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// setup first point and sort
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::std::swap( result[1], result[min] );
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ThetaCompare<Point2D> cmpFunc(result[1]);
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::std::sort( result.begin()+1, result.end(), cmpFunc );
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// setup sentinel
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result[0] = result[N];
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// generate convex hull
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Polygon2D::size_type M;
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for( M=3, i=4; i<=N; ++i )
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{
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while( ccw(result[M], result[M-1], result[i], cmpFunc) >= 0 )
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--M;
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++M;
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::std::swap( result[M], result[i] );
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}
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// copy range [1,M] to output
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return Polygon2D( result.begin()+1, result.begin()+M+1 );
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}
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/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
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