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#include <2geom/d2.h>
/* One would think that we would include d2-sbasis.h, however,
* you cannot actually include it in anything - only d2 may import it.
* 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_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.empty()) {
prev_sb = SBasis(Linear(0.0, c));
} else {
prev_sb[0][1] = c;
}
if (cur_sb.empty()) {
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;
}
static void set_first_point(Piecewise<D2<SBasis> > &f, Point a){
if ( f.empty() ){
f.concat(Piecewise<D2<SBasis> >(D2<SBasis>(Linear(a[X]),Linear(a[Y]))));
return;
}
for (unsigned dim=0; dim<2; dim++){
if (f.segs.front()[dim].size() == 0){
f.segs.front()[dim] = SBasis(Linear(a[dim],0));
}else{
f.segs.front()[dim][0][0] = a[dim];
}
}
}
static void set_last_point(Piecewise<D2<SBasis> > &f, Point a){
if ( f.empty() ){
f.concat(Piecewise<D2<SBasis> >(D2<SBasis>(Linear(a[X]),Linear(a[Y]))));
return;
}
for (unsigned dim=0; dim<2; dim++){
if (f.segs.back()[dim].size() == 0){
f.segs.back()[dim] = SBasis(Linear(0,a[dim]));
}else{
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 :
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