src/2geom/d2-sbasis.cpp

/**
 * \file
 * \brief Some two-dimensional SBasis operations
 *//*
 * Authors:
 *   MenTaLguy <mental@rydia.net>
 *   Jean-François Barraud <jf.barraud@gmail.com>
 *   Johan Engelen <j.b.c.engelen@alumnus.utwente.nl>
 *
 * Copyright 2007-2012 Authors
 *
 * This library is free software; you can redistribute it and/or
 * modify it either under the terms of the GNU Lesser General Public
 * License version 2.1 as published by the Free Software Foundation
 * (the "LGPL") or, at your option, under the terms of the Mozilla
 * Public License Version 1.1 (the "MPL"). If you do not alter this
 * notice, a recipient may use your version of this file under either
 * the MPL or the LGPL.
 *
 * You should have received a copy of the LGPL along with this library
 * in the file COPYING-LGPL-2.1; if not, output to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 * You should have received a copy of the MPL along with this library
 * in the file COPYING-MPL-1.1
 *
 * The contents of this file are subject to the Mozilla Public License
 * Version 1.1 (the "License"); you may not use this file except in
 * compliance with the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
 * OF ANY KIND, either express or implied. See the LGPL or the MPL for
 * the specific language governing rights and limitations.
 *
 */

#include <2geom/d2.h>
#include <2geom/piecewise.h>

namespace Geom {

SBasis L2(D2<SBasis> const & a, unsigned k) { return sqrt(dot(a, a), k); }

D2<SBasis> multiply(Linear const & a, D2<SBasis> const & b) {
    return D2<SBasis>(multiply(a, b[X]), multiply(a, b[Y]));
}

D2<SBasis> multiply(SBasis const & a, D2<SBasis> const & b) {
    return D2<SBasis>(multiply(a, b[X]), multiply(a, b[Y]));
}

D2<SBasis> truncate(D2<SBasis> const & a, unsigned terms) {
    return D2<SBasis>(truncate(a[X], terms), truncate(a[Y], terms));
}

unsigned sbasis_size(D2<SBasis> const & a) {
    return std::max((unsigned) a[0].size(), (unsigned) a[1].size());
}

//TODO: Is this sensical? shouldn't it be like pythagorean or something?
double tail_error(D2<SBasis> const & a, unsigned tail) {
    return std::max(a[0].tailError(tail), a[1].tailError(tail));
}

Piecewise<D2<SBasis> > sectionize(D2<Piecewise<SBasis> > const &a) {
    Piecewise<SBasis> x = partition(a[0], a[1].cuts), y = partition(a[1], a[0].cuts);
    assert(x.size() == y.size());
    Piecewise<D2<SBasis> > ret;
    for(unsigned i = 0; i < x.size(); i++)
        ret.push_seg(D2<SBasis>(x[i], y[i]));
    ret.cuts.insert(ret.cuts.end(), x.cuts.begin(), x.cuts.end());
    return ret;
}

D2<Piecewise<SBasis> > make_cuts_independent(Piecewise<D2<SBasis> > const &a) {
    D2<Piecewise<SBasis> > ret;
    for(unsigned d = 0; d < 2; d++) {
        for(unsigned i = 0; i < a.size(); i++)
            ret[d].push_seg(a[i][d]);
        ret[d].cuts.insert(ret[d].cuts.end(), a.cuts.begin(), a.cuts.end());
    }
    return ret;
}

Piecewise<D2<SBasis> > rot90(Piecewise<D2<SBasis> > const &M){
  Piecewise<D2<SBasis> > result;
  if (M.empty()) return M;
  result.push_cut(M.cuts[0]);
  for (unsigned i=0; i<M.size(); i++){
    result.push(rot90(M[i]),M.cuts[i+1]);
  }
  return result;
}

/** @brief Calculates the 'dot product' or 'inner product' of \c a and \c b
 * @return  \f[
 *      f(t) \rightarrow \left\{
 *      \begin{array}{c}
 *      a_1 \bullet b_1 \\
 *      a_2 \bullet b_2 \\
 *      \ldots \\
 *      a_n \bullet b_n \\
 *      \end{array}\right.
 * \f]
 * @relates Piecewise */
Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b)
{
  Piecewise<SBasis > result;
  if (a.empty() || b.empty()) return result;
  Piecewise<D2<SBasis> > aa = partition(a,b.cuts);
  Piecewise<D2<SBasis> > bb = partition(b,a.cuts);

  result.push_cut(aa.cuts.front());
  for (unsigned i=0; i<aa.size(); i++){
    result.push(dot(aa.segs[i],bb.segs[i]),aa.cuts[i+1]);
  }
  return result;
}

/** @brief Calculates the 'dot product' or 'inner product' of \c a and \c b
 * @return  \f[
 *      f(t) \rightarrow \left\{
 *      \begin{array}{c}
 *      a_1 \bullet b \\
 *      a_2 \bullet b \\
 *      \ldots \\
 *      a_n \bullet b \\
 *      \end{array}\right.
 * \f]
 * @relates Piecewise */
Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a, Point const &b)
{
  Piecewise<SBasis > result;
  if (a.empty()) return result;

  result.push_cut(a.cuts.front());
  for (unsigned i = 0; i < a.size(); ++i){
    result.push(dot(a.segs[i],b), a.cuts[i+1]);
  }
  return result;
}


Piecewise<SBasis> cross(Piecewise<D2<SBasis> > const &a,
            Piecewise<D2<SBasis> > const &b){
  Piecewise<SBasis > result;
  if (a.empty() || b.empty()) return result;
  Piecewise<D2<SBasis> > aa = partition(a,b.cuts);
  Piecewise<D2<SBasis> > bb = partition(b,a.cuts);

  result.push_cut(aa.cuts.front());
  for (unsigned i=0; i<a.size(); i++){
    result.push(cross(aa.segs[i],bb.segs[i]),aa.cuts[i+1]);
  }
  return result;
}

Piecewise<D2<SBasis> > operator*(Piecewise<D2<SBasis> > const &a, Affine const &m) {
  Piecewise<D2<SBasis> > result;
  if(a.empty()) return result;
  result.push_cut(a.cuts[0]);
  for (unsigned i = 0; i < a.size(); i++) {
    result.push(a[i] * m, a.cuts[i+1]);
  }
  return result;
}

//if tol>0, only force continuity where the jump is smaller than tol.
Piecewise<D2<SBasis> > force_continuity(Piecewise<D2<SBasis> > const &f, double tol, bool closed)
{
    if (f.size()==0) return f;
    Piecewise<D2<SBasis> > result=f;
    unsigned cur   = (closed)? 0:1;
    unsigned prev  = (closed)? f.size()-1:0;
    while(cur<f.size()){
        Point pt0 = f.segs[prev].at1();
        Point pt1 = f.segs[cur ].at0();
        if (tol<=0 || L2sq(pt0-pt1)<tol*tol){
            pt0 = (pt0+pt1)/2;
            for (unsigned dim=0; dim<2; dim++){
                SBasis &prev_sb=result.segs[prev][dim];
                SBasis &cur_sb =result.segs[cur][dim];
                Coord const c=pt0[dim];
                if (prev_sb.isZero(0)) {
                  prev_sb = SBasis(Linear(0.0, c));
                } else {
                  prev_sb[0][1] = c;
                }
                if (cur_sb.isZero(0)) {
                  cur_sb = SBasis(Linear(c, 0.0));
                } else {
                  cur_sb[0][0] = c;
                }
            }
        }
        prev = cur++;
    }
    return result;
}

std::vector<Geom::Piecewise<Geom::D2<Geom::SBasis> > >
split_at_discontinuities (Geom::Piecewise<Geom::D2<Geom::SBasis> > const & pwsbin, double tol)
{
    using namespace Geom;
    std::vector<Piecewise<D2<SBasis> > > ret;
    unsigned piece_start = 0;
    for (unsigned i=0; i<pwsbin.segs.size(); i++){
        if (i==(pwsbin.segs.size()-1) || L2(pwsbin.segs[i].at1()- pwsbin.segs[i+1].at0()) > tol){
            Piecewise<D2<SBasis> > piece;
            piece.cuts.push_back(pwsbin.cuts[piece_start]);
            for (unsigned j = piece_start; j<i+1; j++){
                piece.segs.push_back(pwsbin.segs[j]);
                piece.cuts.push_back(pwsbin.cuts[j+1]);
            }
            ret.push_back(piece);
            piece_start = i+1;
        }
    }
    return ret;
}

Point unitTangentAt(D2<SBasis> const & a, Coord t, unsigned n)
{
    std::vector<Point> derivs = a.valueAndDerivatives(t, n);
    for (unsigned deriv_n = 1; deriv_n < derivs.size(); deriv_n++) {
        Coord length = derivs[deriv_n].length();
        if ( ! are_near(length, 0) ) {
            // length of derivative is non-zero, so return unit vector
            return derivs[deriv_n] / length;
        }
    }
    return Point (0,0);
}

static void set_first_point(Piecewise<D2<SBasis> > &f, Point const &a){
    if ( f.empty() ){
        f.concat(Piecewise<D2<SBasis> >(D2<SBasis>(SBasis(Linear(a[X])), SBasis(Linear(a[Y])))));
        return;
    }
    for (unsigned dim=0; dim<2; dim++){
        f.segs.front()[dim][0][0] = a[dim];
    }
}
static void set_last_point(Piecewise<D2<SBasis> > &f, Point const &a){
    if ( f.empty() ){
        f.concat(Piecewise<D2<SBasis> >(D2<SBasis>(SBasis(Linear(a[X])), SBasis(Linear(a[Y])))));
        return;
    }
    for (unsigned dim=0; dim<2; dim++){
        f.segs.back()[dim][0][1] = a[dim];
    }
}

std::vector<Piecewise<D2<SBasis> > > fuse_nearby_ends(std::vector<Piecewise<D2<SBasis> > > const &f, double tol){

    if ( f.empty()) return f;
    std::vector<Piecewise<D2<SBasis> > > result;
    std::vector<std::vector<unsigned> > pre_result;
    for (unsigned i=0; i<f.size(); i++){
        bool inserted = false;
        Point a = f[i].firstValue();
        Point b = f[i].lastValue();
        for (unsigned j=0; j<pre_result.size(); j++){
            Point aj = f.at(pre_result[j].back()).lastValue();
            Point bj = f.at(pre_result[j].front()).firstValue();
            if ( L2(a-aj) < tol ) {
                pre_result[j].push_back(i);
                inserted = true;
                break;
            }
            if ( L2(b-bj) < tol ) {
                pre_result[j].insert(pre_result[j].begin(),i);
                inserted = true;
                break;
            }
        }
        if (!inserted) {
            pre_result.push_back(std::vector<unsigned>());
            pre_result.back().push_back(i);
        }
    }
    for (unsigned i=0; i<pre_result.size(); i++){
        Piecewise<D2<SBasis> > comp;
        for (unsigned j=0; j<pre_result[i].size(); j++){
            Piecewise<D2<SBasis> > new_comp = f.at(pre_result[i][j]);
            if ( j>0 ){
                set_first_point( new_comp, comp.segs.back().at1() );
            }
            comp.concat(new_comp);
        }
        if ( L2(comp.firstValue()-comp.lastValue()) < tol ){
            //TODO: check sizes!!!
            set_last_point( comp, comp.segs.front().at0() );
        }
        result.push_back(comp);
    }
    return result;
}

/*
 *  Computes the intersection of two sets given as (ordered) union of intervals.
 */
static std::vector<Interval> intersect( std::vector<Interval> const &a, std::vector<Interval> const &b){
    std::vector<Interval> result;
    //TODO: use order!
    for (unsigned i=0; i < a.size(); i++){
        for (unsigned j=0; j < b.size(); j++){
            OptInterval c( a[i] );
            c &= b[j];
            if ( c ) {
                result.push_back( *c );
            }
        }
    }
    return result;
}

std::vector<Interval> level_set( D2<SBasis> const &f, Rect region){
    std::vector<Rect> regions( 1, region );
    return level_sets( f, regions ).front();
}
std::vector<Interval> level_set( D2<SBasis> const &f, Point p, double tol){
    Rect region(p, p);
    region.expandBy( tol );
    return level_set( f, region );
}
std::vector<std::vector<Interval> > level_sets( D2<SBasis> const &f, std::vector<Rect> regions){
    std::vector<Interval> regsX (regions.size(), Interval() );
    std::vector<Interval> regsY (regions.size(), Interval() );
    for ( unsigned i=0; i < regions.size(); i++ ){
        regsX[i] = regions[i][X];
        regsY[i] = regions[i][Y];
    }
    std::vector<std::vector<Interval> > x_in_regs = level_sets( f[X], regsX );
    std::vector<std::vector<Interval> > y_in_regs = level_sets( f[Y], regsY );
    std::vector<std::vector<Interval> >result(regions.size(), std::vector<Interval>() );
    for (unsigned i=0; i<regions.size(); i++){
        result[i] = intersect ( x_in_regs[i], y_in_regs[i] );
    }
    return result;
}
std::vector<std::vector<Interval> > level_sets( D2<SBasis> const &f, std::vector<Point> pts, double tol){
    std::vector<Rect> regions( pts.size(), Rect() );
    for (unsigned i=0; i<pts.size(); i++){
        regions[i] = Rect( pts[i], pts[i] );
        regions[i].expandBy( tol );
    }
    return level_sets( f, regions );
}


}  // namespace Geom


/*
  Local Variables:
  mode:c++
  c-file-style:"stroustrup"
  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
  indent-tabs-mode:nil
  fill-column:99
  End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :