update 2geom to rev 1114 and fix error.

(bzr r3624)

4 files changed, 223 insertions, 388 deletions

diff --git a/src/2geom/Makefile_insert b/src/2geom/Makefile_insert
index 4a87c1a93..4e8fb13d8 100644
--- a/src/2geom/Makefile_insert
+++ b/src/2geom/Makefile_insert
@@ -24,7 +24,6 @@
 	2geom/crossing.cpp	\

 	2geom/d2-sbasis.cpp	\

 	2geom/d2-sbasis.h	\

-	2geom/d2.cpp	\

 	2geom/d2.h	\

 	2geom/geom.cpp	\

 	2geom/geom.h	\

diff --git a/src/2geom/d2-sbasis.cpp b/src/2geom/d2-sbasis.cpp
index b68e3e6c5..c5c005c24 100644
--- a/src/2geom/d2-sbasis.cpp
+++ b/src/2geom/d2-sbasis.cpp
@@ -4,145 +4,155 @@
  * This is due to the trickinesses of template submatching. */
 
 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_independant(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;

-}

-

-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;

-}

-

-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;

-}

-

+
+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_independant(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;
+}
+
+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;
+}
+
+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, Matrix 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;
+}
+
 /* Replaced by remove_short_cuts in piecewise.h
-//this recursively removes the shortest cut interval until none is shorter than tol.

-//TODO: code this in a more efficient way!

-Piecewise<D2<SBasis> > remove_short_cuts(Piecewise<D2<SBasis> > const &f, double tol){

-    double min = tol;

-    unsigned idx = f.size();

-    for(unsigned i=0; i<f.size(); i++){

-        if (min > f.cuts[i+1]-f.cuts[i]){

-            min = f.cuts[i+1]-f.cuts[i];

-            idx = int(i);

-        }

-    }

-    if (idx==f.size()){

-        return f;

-    }

-    if (f.size()==1) {

-        //removing this seg would result in an empty pw<d2<sb>>...

-        return f;

-    }

-    Piecewise<D2<SBasis> > new_f=f;

-    for (int dim=0; dim<2; dim++){

-        double v = Hat(f.segs.at(idx)[dim][0]);

-        //TODO: what about closed curves?

-        if (idx>0 && f.segs.at(idx-1).at1()==f.segs.at(idx).at0()) 

-            new_f.segs.at(idx-1)[dim][0][1] = v;

-        if (idx<f.size() && f.segs.at(idx+1).at0()==f.segs.at(idx).at1()) 

-            new_f.segs.at(idx+1)[dim][0][0] = v;

-    }

-    double t = (f.cuts.at(idx)+f.cuts.at(idx+1))/2;

-    new_f.cuts.at(idx+1) = t;    

-    

-    new_f.segs.erase(new_f.segs.begin()+idx);

-    new_f.cuts.erase(new_f.cuts.begin()+idx);        

-    return remove_short_cuts(new_f, tol);

-}

+//this recursively removes the shortest cut interval until none is shorter than tol.
+//TODO: code this in a more efficient way!
+Piecewise<D2<SBasis> > remove_short_cuts(Piecewise<D2<SBasis> > const &f, double tol){
+    double min = tol;
+    unsigned idx = f.size();
+    for(unsigned i=0; i<f.size(); i++){
+        if (min > f.cuts[i+1]-f.cuts[i]){
+            min = f.cuts[i+1]-f.cuts[i];
+            idx = int(i);
+        }
+    }
+    if (idx==f.size()){
+        return f;
+    }
+    if (f.size()==1) {
+        //removing this seg would result in an empty pw<d2<sb>>...
+        return f;
+    }
+    Piecewise<D2<SBasis> > new_f=f;
+    for (int dim=0; dim<2; dim++){
+        double v = Hat(f.segs.at(idx)[dim][0]);
+        //TODO: what about closed curves?
+        if (idx>0 && f.segs.at(idx-1).at1()==f.segs.at(idx).at0()) 
+            new_f.segs.at(idx-1)[dim][0][1] = v;
+        if (idx<f.size() && f.segs.at(idx+1).at0()==f.segs.at(idx).at1()) 
+            new_f.segs.at(idx+1)[dim][0][0] = v;
+    }
+    double t = (f.cuts.at(idx)+f.cuts.at(idx+1))/2;
+    new_f.cuts.at(idx+1) = t;    
+    
+    new_f.segs.erase(new_f.segs.begin()+idx);
+    new_f.cuts.erase(new_f.cuts.begin()+idx);        
+    return remove_short_cuts(new_f, tol);
+}
 */
-

-//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++){

-                result.segs[prev][dim][0][1]=pt0[dim];

-                result.segs[cur ][dim][0][0]=pt0[dim];

-            }

-        }

-        prev = cur++;

-    }

-    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++){
+                result.segs[prev][dim][0][1]=pt0[dim];
+                result.segs[cur ][dim][0][0]=pt0[dim];
+            }
+        }
+        prev = cur++;
+    }
+    return result;
+}
 }
diff --git a/src/2geom/d2-sbasis.h b/src/2geom/d2-sbasis.h
index dab2559ca..95f1ca0dd 100644
--- a/src/2geom/d2-sbasis.h
+++ b/src/2geom/d2-sbasis.h
@@ -4,82 +4,85 @@
 #ifndef __2GEOM_SBASIS_CURVE_H
 #define __2GEOM_SBASIS_CURVE_H
 
-#include "sbasis.h"

-#include "sbasis-2d.h"

+#include "sbasis.h"
+#include "sbasis-2d.h"
 #include "piecewise.h"
+#include "matrix.h"
 
 //TODO: implement intersect
 
 namespace Geom {
-

-inline D2<SBasis> compose(D2<SBasis> const & a, SBasis const & b) {

-    return D2<SBasis>(compose(a[X], b), compose(a[Y], b));

-}

-

-SBasis L2(D2<SBasis> const & a, unsigned k);

-double L2(D2<double> const & a);

-

-D2<SBasis> multiply(Linear const & a, D2<SBasis> const & b);

-inline D2<SBasis> operator*(Linear const & a, D2<SBasis> const & b) { return multiply(a, b); }

-D2<SBasis> multiply(SBasis const & a, D2<SBasis> const & b);

-inline D2<SBasis> operator*(SBasis const & a, D2<SBasis> const & b) { return multiply(a, b); }

-D2<SBasis> truncate(D2<SBasis> const & a, unsigned terms);

-

-unsigned sbasis_size(D2<SBasis> const & a);

-double tail_error(D2<SBasis> const & a, unsigned tail);

-

-//Piecewise<D2<SBasis> > specific decls:

-

-Piecewise<D2<SBasis> > sectionize(D2<Piecewise<SBasis> > const &a);

-D2<Piecewise<SBasis> > make_cuts_independant(Piecewise<D2<SBasis> > const &a);

-Piecewise<D2<SBasis> > rot90(Piecewise<D2<SBasis> > const &a);

-Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b);

-Piecewise<SBasis> cross(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b);

-

-Piecewise<D2<SBasis> > force_continuity(Piecewise<D2<SBasis> > const &f, 

-                                        double tol=0,

-                                        bool closed=false);

-

-class CoordIterator

-: public std::iterator<std::input_iterator_tag, SBasis const>

-{

-public:

-  CoordIterator(std::vector<D2<SBasis> >::const_iterator const &iter, unsigned d) : impl_(iter), ix_(d) {}

-

-  inline bool operator==(CoordIterator const &other) { return other.impl_ == impl_; }

-  inline bool operator!=(CoordIterator const &other) { return other.impl_ != impl_; }

-

-  inline SBasis operator*() const {

-        return (*impl_)[ix_];

-  }

-

-  inline CoordIterator &operator++() {

-    ++impl_;

-    return *this;

-  }

-  inline CoordIterator operator++(int) {

-    CoordIterator old=*this;

-    ++(*this);

-    return old;

-  }

-

-private:

-  std::vector<D2<SBasis> >::const_iterator impl_;

-  unsigned ix_;

-};

-

-inline CoordIterator iterateCoord(Piecewise<D2<SBasis> > const &a, unsigned d) {

-    return CoordIterator(a.segs.begin(), d);

-}

-

-//bounds specializations with order

-inline Rect bounds_fast(D2<SBasis> const & s, unsigned order=0) {

-    return Rect(bounds_fast(s[X], order),

-                bounds_fast(s[Y], order));

-}

-inline Rect bounds_local(D2<SBasis> const & s, Interval i, unsigned order=0) {

-    return Rect(bounds_local(s[X], i, order),

-                bounds_local(s[Y], i, order));

+
+inline D2<SBasis> compose(D2<SBasis> const & a, SBasis const & b) {
+    return D2<SBasis>(compose(a[X], b), compose(a[Y], b));
+}
+
+SBasis L2(D2<SBasis> const & a, unsigned k);
+double L2(D2<double> const & a);
+
+D2<SBasis> multiply(Linear const & a, D2<SBasis> const & b);
+inline D2<SBasis> operator*(Linear const & a, D2<SBasis> const & b) { return multiply(a, b); }
+D2<SBasis> multiply(SBasis const & a, D2<SBasis> const & b);
+inline D2<SBasis> operator*(SBasis const & a, D2<SBasis> const & b) { return multiply(a, b); }
+D2<SBasis> truncate(D2<SBasis> const & a, unsigned terms);
+
+unsigned sbasis_size(D2<SBasis> const & a);
+double tail_error(D2<SBasis> const & a, unsigned tail);
+
+//Piecewise<D2<SBasis> > specific decls:
+
+Piecewise<D2<SBasis> > sectionize(D2<Piecewise<SBasis> > const &a);
+D2<Piecewise<SBasis> > make_cuts_independant(Piecewise<D2<SBasis> > const &a);
+Piecewise<D2<SBasis> > rot90(Piecewise<D2<SBasis> > const &a);
+Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b);
+Piecewise<SBasis> cross(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b);
+
+Piecewise<D2<SBasis> > operator*(Piecewise<D2<SBasis> > const &a, Matrix const &m);
+
+Piecewise<D2<SBasis> > force_continuity(Piecewise<D2<SBasis> > const &f, 
+                                        double tol=0,
+                                        bool closed=false);
+
+class CoordIterator
+: public std::iterator<std::input_iterator_tag, SBasis const>
+{
+public:
+  CoordIterator(std::vector<D2<SBasis> >::const_iterator const &iter, unsigned d) : impl_(iter), ix_(d) {}
+
+  inline bool operator==(CoordIterator const &other) { return other.impl_ == impl_; }
+  inline bool operator!=(CoordIterator const &other) { return other.impl_ != impl_; }
+
+  inline SBasis operator*() const {
+        return (*impl_)[ix_];
+  }
+
+  inline CoordIterator &operator++() {
+    ++impl_;
+    return *this;
+  }
+  inline CoordIterator operator++(int) {
+    CoordIterator old=*this;
+    ++(*this);
+    return old;
+  }
+
+private:
+  std::vector<D2<SBasis> >::const_iterator impl_;
+  unsigned ix_;
+};
+
+inline CoordIterator iterateCoord(Piecewise<D2<SBasis> > const &a, unsigned d) {
+    return CoordIterator(a.segs.begin(), d);
+}
+
+//bounds specializations with order
+inline Rect bounds_fast(D2<SBasis> const & s, unsigned order=0) {
+    return Rect(bounds_fast(s[X], order),
+                bounds_fast(s[Y], order));
+}
+inline Rect bounds_local(D2<SBasis> const & s, Interval i, unsigned order=0) {
+    return Rect(bounds_local(s[X], i, order),
+                bounds_local(s[Y], i, order));
 }
 
 }
diff --git a/src/2geom/d2.cpp b/src/2geom/d2.cpp
deleted file mode 100644
index 86538062b..000000000
--- a/src/2geom/d2.cpp
+++ /dev/null
@@ -1,177 +0,0 @@
-/*

- * d2.cpp - Lifts one dimensional objects into 2d 

- *

- * Copyright 2007 Michael Sloan <mgsloan@gmail.com>

- *

- * 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 "d2.h"

-

-namespace Geom {

-

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

-double L2(D2<double> const & a) { return hypot(a[0], a[1]); }

-

-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_independant(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;

-}

-

-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;

-}

-

-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;

-}

-

-/* Replaced by remove_short_cuts in piecewise.h
-//this recursively removes the shortest cut interval until none is shorter than tol.

-//TODO: code this in a more efficient way!

-Piecewise<D2<SBasis> > remove_short_cuts(Piecewise<D2<SBasis> > const &f, double tol){

-    double min = tol;

-    unsigned idx = f.size();

-    for(unsigned i=0; i<f.size(); i++){

-        if (min > f.cuts[i+1]-f.cuts[i]){

-            min = f.cuts[i+1]-f.cuts[i];

-            idx = int(i);

-        }

-    }

-    if (idx==f.size()){

-        return f;

-    }

-    if (f.size()==1) {

-        //removing this seg would result in an empty pw<d2<sb>>...

-        return f;

-    }

-    Piecewise<D2<SBasis> > new_f=f;

-    for (int dim=0; dim<2; dim++){

-        double v = Hat(f.segs.at(idx)[dim][0]);

-        //TODO: what about closed curves?

-        if (idx>0 && f.segs.at(idx-1).at1()==f.segs.at(idx).at0()) 

-            new_f.segs.at(idx-1)[dim][0][1] = v;

-        if (idx<f.size() && f.segs.at(idx+1).at0()==f.segs.at(idx).at1()) 

-            new_f.segs.at(idx+1)[dim][0][0] = v;

-    }

-    double t = (f.cuts.at(idx)+f.cuts.at(idx+1))/2;

-    new_f.cuts.at(idx+1) = t;    

-    

-    new_f.segs.erase(new_f.segs.begin()+idx);

-    new_f.cuts.erase(new_f.cuts.begin()+idx);        

-    return remove_short_cuts(new_f, tol);

-}

-*/
-

-//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++){

-                result.segs[prev][dim][0][1]=pt0[dim];

-                result.segs[cur ][dim][0][0]=pt0[dim];

-            }

-        }

-        prev = cur++;

-    }

-    return result;

-}

-  

-};