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sb-of-sb.cpp
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1#include <time.h>
2#include <vector>
3#include <toys/path-cairo.h>
4#include <toys/toy-framework-2.h>
5
6#include <2geom/sbasis.h>
7#include <2geom/sbasis-geometric.h>
8#include <2geom/bezier-to-sbasis.h>
9
10#include <2geom/orphan-code/sbasis-of.h>
11
12using namespace Geom;
13using namespace std;
14
15SBasis toSBasis(SBasisOf<double> const &f){
16 SBasis result(f.size(), Linear());
17 for (unsigned i=0; i<f.size(); i++){
18 result[i] = Linear(f[i][0],f[i][1]);
19 }
20 return result;
21}
22SBasisOf<double> toSBasisOfDouble(SBasis const &f){
23 SBasisOf<double> result;
24 for (auto i : f){
25 result.push_back(LinearOf<double>(i[0],i[1]));
26 }
27 return result;
28}
29
30
31#if 0
32template<unsigned dim>
33class LinearDim;
34template<unsigned dim>
35class SBasisDim;
36
37template<unsigned dim>
38class LinearDim : public LinearOf<SBasisDim<dim-1> >{
39public:
40 LinearDim() : LinearOf<SBasisDim<dim-1> >() {};
41 LinearDim(SBasisDim <dim-1> const &a, SBasisDim<dim-1> const &b ) : LinearOf<SBasisDim<dim-1> >(a,b) {};
42 LinearDim(LinearDim <dim-1> const &a, LinearDim<dim-1> const &b ) :
43 LinearOf<SBasisDim<dim-1> >(SBasisDim<dim-1>(a),SBasisDim<dim-1>(b)) {};
44};
45
46template<>
47class LinearDim<1> : public LinearOf<double>{
48public:
49 LinearDim() : LinearOf<double>() {};
50 LinearDim(double const &a, double const &b ) : LinearOf<double>(a,b) {};
51};
52
53
54template<unsigned dim>
55class SBasisDim : public SBasisOf<SBasisDim<dim-1> >{
56public:
57 SBasisDim() : SBasisOf<SBasisDim<dim-1> >() {};
58 SBasisDim(LinearDim<dim> const &lin) :
59 SBasisOf<SBasisDim<dim-1> >(LinearOf<SBasisDim<dim-1> >(lin[0],lin[1])) {};
60};
61
62template<>
63class SBasisDim<1> : public SBasisOf<double>{
64/*
65public:
66 SBasisDim<1>() : SBasisOf<double>() {};
67 SBasisDim(SBasisOf<double> other) : SBasisOf<double>(other) {};
68 SBasisDim(LinearOf<double> other) : SBasisOf<double>(other) {};
69*/
70};
71
72SBasis toSBasis(SBasisDim<1> f){
73 SBasis result(f.size(), Linear());
74 for (unsigned i=0; i<f.size(); i++){
75 result[i] = Linear(f[i][0],f[i][1]);
76 }
77 return result;
78}
79
80template<unsigned dim_f,unsigned dim_g>
81SBasisDim<dim_g> compose(SBasisDim<dim_f> const &f, std::vector<SBasisDim<dim_g> > const &g ){
82
83 assert( dim_f <= g.size() );
84
85 SBasisDim<dim_g> u0 = g[dim_f-1];
86 SBasisDim<dim_g> u1 = -u0 + 1;
87 SBasisDim<dim_g> s = multiply(u0,u1);
88 SBasisDim<dim_g> r;
89
90 for(int i = f.size()-1; i >= 0; i--) {
91 if ( dim_f>1 ){
92 r = s*r + compose(f[i][0],g)*u0 + compose(f[i][1],g)*u1;
93 }else{
94 r = s*r + f[i][0]*u0 + f[i][1]*u1;
95 }
96 }
97 return r;
98}
99
100#endif
101
102template <typename T>
103SBasisOf<T> multi_compose(SBasisOf<double> const &f, SBasisOf<T> const &g ){
104
105 //assert( f.input_dim() <= g.size() );
106
107 SBasisOf<T> u0 = g;
108 SBasisOf<T> u1 = -u0 + LinearOf<SBasisOf<double> >(SBasisOf<double>(LinearOf<double>(1,1)));
109 SBasisOf<T> s = multiply(u0,u1);
110 SBasisOf<T> r;
111
112 for(int i = f.size()-1; i >= 0; i--) {
113 r = s*r + f[i][0]*u0 + f[i][1]*u1;
114 }
115 return r;
116}
117SBasisOf<double> compose(SBasisOf<SBasisOf<double> > const &f,
118 SBasisOf<double> const &x,
119 SBasisOf<double> const &y){
120 SBasisOf<double> y0 = -y + LinearOf<double>(1,1);
121 SBasisOf<double> s = multiply(y0,y);
122 SBasisOf<double> r;
123
124 for(int i = f.size()-1; i >= 0; i--) {
125 r = s*r + compose(f[i][0],x)*y0 + compose(f[i][1],x)*y;
126 }
127 return r;
128}
129
130SBasisOf<double> compose(SBasisOf<SBasisOf<double> > const &f,
131 D2<SBasisOf<double> > const &X){
132 return compose(f, X[0], X[1]);
133}
134
139
140/*
141static
142SBasis eval_v(SBasisOf<SBasis> const &f, double v){
143 SBasis result(f.size(), Linear());
144 for (unsigned i=0; i<f.size(); i++){
145 result[i] = Linear(f[i][0].valueAt(v),f[i][1].valueAt(v));
146 }
147 return result;
148}
149static
150SBasis eval_v(SBasisOf<SBasisOf<double> > const &f, double v){
151 SBasis result(f.size(), Linear());
152 for (unsigned i=0; i<f.size(); i++){
153 result[i] = Linear(f[i][0].valueAt(v),f[i][1].valueAt(v));
154 }
155 return result;
156}*/
157static
158SBasisOf<double> eval_dim(SBasisOf<SBasisOf<double> > const &f, double t, unsigned dim){
159 if (dim == 1) return f.valueAt(t);
160 SBasisOf<double> result;
161 for (unsigned i=0; i<f.size(); i++){
162 result.push_back(LinearOf<double>(f[i][0].valueAt(t),f[i][1].valueAt(t)));
163 }
164 return result;
165}
166
167/*
168static
169SBasis eval_v(SBasisDim<2> const &f, double v){
170 SBasis result;
171 for (unsigned i=0; i<f.size(); i++){
172 result.push_back(Linear(f[i][0].valueAt(v),f[i][1].valueAt(v)));
173 }
174 return result;
175}
176*/
177
178struct Frame
179{
180 Geom::Point O;
181 Geom::Point x;
182 Geom::Point y;
183 Geom::Point z;
184 // find the point on the x,y plane that projects to P
185 Point unproject(Point P) {
186 return P * from_basis(x, y, O).inverse();
187 }
188};
189
190void
191plot3d(cairo_t *cr, SBasis const &x, SBasis const &y, SBasis const &z, Frame frame){
192 D2<SBasis> curve;
193 for (unsigned dim=0; dim<2; dim++){
194 curve[dim] = x*frame.x[dim] + y*frame.y[dim] + z*frame.z[dim];
195 curve[dim] += frame.O[dim];
196 }
197 cairo_d2_sb(cr, curve);
198}
199void
200plot3d(cairo_t *cr, SBasis const &x, SBasis const &y, SBasisOf<double> const &z, Frame frame){
201 D2<SBasis> curve;
202 for (unsigned dim=0; dim<2; dim++){
203 curve[dim] = x*frame.x[dim] + y*frame.y[dim] + toSBasis(z)*frame.z[dim];
204 curve[dim] += frame.O[dim];
205 }
206 cairo_d2_sb(cr, curve);
207}
208
209void
210plot3d(cairo_t *cr,
211 Piecewise<SBasis> const &x,
212 Piecewise<SBasis> const &y,
213 Piecewise<SBasis> const &z, Frame frame){
214
215 Piecewise<SBasis> xx = partition(x,y.cuts);
216 Piecewise<SBasis> xxx = partition(xx,z.cuts);
217 Piecewise<SBasis> yyy = partition(y,xxx.cuts);
218 Piecewise<SBasis> zzz = partition(z,xxx.cuts);
219
220 for (unsigned i=0; i<xxx.size(); i++){
221 plot3d(cr, xxx[i], yyy[i], zzz[i], frame);
222 }
223}
224
225void
226plot3d(cairo_t *cr, SBasisOf<SBasisOf<double> > const &f, Frame frame){
227 int iMax = 5;
228 for (int i=0; i<iMax; i++){
229 plot3d(cr, Linear(0,1), Linear(i/(iMax-1.)), eval_dim(f, i/(iMax-1.), 0), frame);
230 plot3d(cr, Linear(i/(iMax-1.)), Linear(0,1), eval_dim(f, i/(iMax-1.), 1), frame);
231 }
232}
233
234SBasisOf<SBasisOf<double> > integral(SBasisOf<SBasisOf<double> > const &f, unsigned var){
235 //variable of f = 1, variable of f's coefficients = 0.
236 if (var == 1) return Geom::integral(f);
237 SBasisOf<SBasisOf<double> > result;
238 for(unsigned i = 0; i< f.size(); i++) {
239 result.push_back(LinearOf<SBasisOf<double> >(Geom::integral(f[i][0]), Geom::integral(f[i][1])));
240 }
241 return result;
242}
243
244Piecewise<SBasis> convole(SBasisOf<double> const &f, Interval dom_f,
245 SBasisOf<double> const &g, Interval dom_g){
246
247 if ( dom_f.extent() < dom_g.extent() ) return convole(g, dom_g, f, dom_f);
248
249 SBasisOf<SBasisOf<double> > u,v;
250 u.push_back(LinearOf<SBasisOf<double> >(LinearOf<double>(0,1),
251 LinearOf<double>(0,1)));
252 v.push_back(LinearOf<SBasisOf<double> >(LinearOf<double>(0,0),
253 LinearOf<double>(1,1)));
254 SBasisOf<SBasisOf<double> > v_u = v - u*(dom_f.extent()/dom_g.extent());
255 v_u += SBasisOf<SBasisOf<double> >(SBasisOf<double>(dom_f.min()/dom_g.extent()));
256 SBasisOf<SBasisOf<double> > gg = multi_compose(g,(v - u*(dom_f.extent()/dom_g.extent())));
257 SBasisOf<SBasisOf<double> > ff = SBasisOf<SBasisOf<double> >(f);
258 SBasisOf<SBasisOf<double> > hh = ::integral(ff*gg,0);
259
260 Piecewise<SBasis> result;
261 result.cuts.push_back(dom_f.min()+dom_g.min());
262 //Note: we know dom_f.extent() >= dom_g.extent()!!
263 double rho = dom_f.extent()/dom_g.extent();
264 SBasisOf<double> a,b,t;
265 SBasis seg;
266 a = SBasisOf<double>(LinearOf<double>(0.,0.));
267 b = SBasisOf<double>(LinearOf<double>(0.,1/rho));
268 t = SBasisOf<double>(LinearOf<double>(dom_f.min()/dom_g.extent(),dom_f.min()/dom_g.extent()+1));
269 seg = toSBasis(compose(hh,b,t)-compose(hh,a,t));
270 result.push(seg,dom_f.min() + dom_g.max());
271 if (dom_f.extent() > dom_g.extent()){
272 a = SBasisOf<double>(LinearOf<double>(0.,1-1/rho));
273 b = SBasisOf<double>(LinearOf<double>(1/rho,1.));
274 t = SBasisOf<double>(LinearOf<double>(dom_f.min()/dom_g.extent()+1, dom_f.max()/dom_g.extent() ));
275 seg = toSBasis(compose(hh,b,t)-compose(hh,a,t));
276 result.push(seg,dom_f.max() + dom_g.min());
277 }
278 a = SBasisOf<double>(LinearOf<double>(1.-1/rho,1.));
279 b = SBasisOf<double>(LinearOf<double>(1.,1.));
280 t = SBasisOf<double>(LinearOf<double>(dom_f.max()/dom_g.extent(), dom_f.max()/dom_g.extent()+1 ));
281 seg = toSBasis(compose(hh,b,t)-compose(hh,a,t));
282 result.push(seg,dom_f.max() + dom_g.max());
283 return result;
284}
285
286template <typename T>
287SBasisOf<T> subderivative(SBasisOf<T> const& f) {
288 SBasisOf<T> res;
289 for(unsigned i = 0; i < f.size(); i++) {
290 res.push_back(LinearOf<T>(derivative(f[i][0]), derivative(f[i][1])));
291 }
292 return res;
293}
294
298
303//TODO: handle the case when B is "behind" A for the natural orientation of the level set.
304//TODO: more generally, there might be up to 4 solutions. Choose the best one!
305D2<SBasis>
306sbofsb_cubic_solve(SBasisOf<SBasisOf<double> > const &f, Geom::Point const &A, Geom::Point const &B){
307 D2<SBasis>result;//(Linear(A[X],B[X]),Linear(A[Y],B[Y]));
308 //g_warning("check 0 = %f = %f!", f.apply(A[X],A[Y]), f.apply(B[X],B[Y]));
309
310 SBasisOf<SBasisOf<double> > f_u = derivative(f);
311 SBasisOf<SBasisOf<double> > f_v = subderivative(f);
312 SBasisOf<SBasisOf<double> > f_uu = derivative(f_u);
313 SBasisOf<SBasisOf<double> > f_uv = derivative(f_v);
314 SBasisOf<SBasisOf<double> > f_vv = subderivative(f_v);
315
316 Geom::Point dfA(f_u.valueAt(A[X]).valueAt(A[Y]),f_v.valueAt(A[X]).valueAt(A[Y]));
317 Geom::Point dfB(f_u.valueAt(B[X]).valueAt(B[Y]),f_v.valueAt(B[X]).valueAt(B[Y]));
318
319 Geom::Point V0 = rot90(dfA);
320 Geom::Point V1 = rot90(dfB);
321
322 double D2fVV0 = f_uu.valueAt(A[X]).valueAt(A[Y])*V0[X]*V0[X]+
323 2*f_uv.valueAt(A[X]).valueAt(A[Y])*V0[X]*V0[Y]+
324 f_vv.valueAt(A[X]).valueAt(A[Y])*V0[Y]*V0[Y];
325 double D2fVV1 = f_uu.valueAt(B[X]).valueAt(B[Y])*V1[X]*V1[X]+
326 2*f_uv.valueAt(B[X]).valueAt(B[Y])*V1[X]*V1[Y]+
327 f_vv.valueAt(B[X]).valueAt(B[Y])*V1[Y]*V1[Y];
328
329 std::vector<D2<SBasis> > candidates = cubics_fitting_curvature(A,B,V0,V1,D2fVV0,D2fVV1);
330 if (candidates.size()==0) {
331 return D2<SBasis>(SBasis(A[X],B[X]),SBasis(A[Y],B[Y]));
332 }
333 //TODO: I'm sure std algorithm could do that for me...
334 double error = -1;
335 unsigned best = 0;
336 for (unsigned i=0; i<candidates.size(); i++){
337 Interval bounds = *bounds_fast(compose(f,candidates[i]));
338 double new_error = (fabs(bounds.max())>fabs(bounds.min()) ? fabs(bounds.max()) : fabs(bounds.min()) );
339 if ( new_error < error || error < 0 ){
340 error = new_error;
341 best = i;
342 }
343 }
344 return candidates[best];
345}
346
347class SBasis0fSBasisToy: public Toy {
348 PointSetHandle hand;
349 PointSetHandle cut_hand;
350 void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {
351
352 double slider_top = width/4.;
353 double slider_bot = width*3./4.;
354 double slider_margin = width/8.;
355 if(hand.pts.empty()) {
356 hand.pts.emplace_back(width*3./16., 3*width/4.);
357 hand.pts.push_back(hand.pts[0] + Geom::Point(width/2., 0));
358 hand.pts.push_back(hand.pts[0] + Geom::Point(width/8., -width/12.));
359 hand.pts.push_back(hand.pts[0] + Geom::Point(0,-width/4.));
360 hand.pts.emplace_back(slider_margin,slider_bot);
361 hand.pts.emplace_back(width-slider_margin,slider_top);
362 }
363
364 hand.pts[4][X] = slider_margin;
365 if (hand.pts[4][Y]<slider_top) hand.pts[4][Y] = slider_top;
366 if (hand.pts[4][Y]>slider_bot) hand.pts[4][Y] = slider_bot;
367 hand.pts[5][X] = width-slider_margin;
368 if (hand.pts[5][Y]<slider_top) hand.pts[5][Y] = slider_top;
369 if (hand.pts[5][Y]>slider_bot) hand.pts[5][Y] = slider_bot;
370
371 //double tA = (slider_bot-hand.pts[4][Y])/(slider_bot-slider_top);
372 //double tB = (slider_bot-hand.pts[5][Y])/(slider_bot-slider_top);
373
374 cairo_move_to(cr,Geom::Point(slider_margin,slider_bot));
375 cairo_line_to(cr,Geom::Point(slider_margin,slider_top));
376 cairo_move_to(cr,Geom::Point(width-slider_margin,slider_bot));
377 cairo_line_to(cr,Geom::Point(width-slider_margin,slider_top));
378 cairo_set_line_width(cr,.5);
379 cairo_set_source_rgba (cr, 0., 0.3, 0., 1.);
380 cairo_stroke(cr);
381
382 Frame frame;
383 frame.O = hand.pts[0];//
384 frame.x = hand.pts[1]-hand.pts[0];//
385 frame.y = hand.pts[2]-hand.pts[0];//
386 frame.z = hand.pts[3]-hand.pts[0];//
387
388 plot3d(cr,Linear(0,1),Linear(0,0),Linear(0,0),frame);
389 plot3d(cr,Linear(0,1),Linear(1,1),Linear(0,0),frame);
390 plot3d(cr,Linear(0,0),Linear(0,1),Linear(0,0),frame);
391 plot3d(cr,Linear(1,1),Linear(0,1),Linear(0,0),frame);
392 cairo_set_line_width(cr,.2);
393 cairo_set_source_rgba (cr, 0., 0., 0., 1.);
394 cairo_stroke(cr);
395
396
397
398 SBasisOf<SBasisOf<double> > f,u,v;
399 u.push_back(LinearOf<SBasisOf<double> >(LinearOf<double>(-1,-1),LinearOf<double>(1,1)));
400 v.push_back(LinearOf<SBasisOf<double> >(LinearOf<double>(-1,1),LinearOf<double>(-1,1)));
401#if 1
402 f = u*u + v*v - LinearOf<SBasisOf<double> >(LinearOf<double>(1,1),LinearOf<double>(1,1));
403 //*notify << "input dim = " << f.input_dim() <<"\n";
404 plot3d(cr,f,frame);
405 cairo_set_line_width(cr,1);
406 cairo_set_source_rgba (cr, .5, 0.5, 0.5, 1.);
407 cairo_stroke(cr);
408
409 LineSegment ls(frame.unproject(cut_hand.pts[0]),
410 frame.unproject(cut_hand.pts[1]));
411 SBasis cutting = toSBasis(compose(f, ls.toSBasis()));
412 //cairo_sb(cr, cutting);
413 //cairo_stroke(cr);
414 plot3d(cr, ls.toSBasis()[0], ls.toSBasis()[1], SBasis(0.0), frame);
415 vector<double> rts = roots(cutting);
416 if(rts.size() >= 2) {
417 Geom::Point A = ls.pointAt(rts[0]);
418 Geom::Point B = ls.pointAt(rts[1]);
419
420 //Geom::Point A(1,0.5);
421 //Geom::Point B(0.5,1);
422 D2<SBasis> zeroset = sbofsb_cubic_solve(f,A,B);
423 plot3d(cr, zeroset[X], zeroset[Y], SBasis(Linear(0.)),frame);
424 cairo_set_line_width(cr,1);
425 cairo_set_source_rgba (cr, 0.9, 0., 0., 1.);
426 cairo_stroke(cr);
427 }
428#else
429
430 SBasisOf<SBasisOf<double> > g = u - v ;
431 g += LinearOf<SBasisOf<double> >(SBasisOf<double>(LinearOf<double>(.5,.5)));
432 SBasisOf<double> h;
433 h.push_back(LinearOf<double>(0,0));
434 h.push_back(LinearOf<double>(0,0));
435 h.push_back(LinearOf<double>(1,1));
436
437 f = multi_compose(h,g);
438 plot3d(cr,f,frame);
439 cairo_set_line_width(cr,1);
440 cairo_set_source_rgba (cr, .75, 0.25, 0.25, 1.);
441 cairo_stroke(cr);
442/*
443 SBasisDim<1> g = SBasisOf<double>(LinearOf<double>(0,1));
444 g.push_back(LinearOf<double>(-1,-1));
445 std::vector<SBasisDim<2> > vars;
446 vars.push_back(ff);
447 plot3d(cr,compose(g,vars),frame);
448 cairo_set_source_rgba (cr, .5, 0.9, 0.5, 1.);
449 cairo_stroke(cr);
450*/
451#endif
452 Toy::draw(cr, notify, width, height, save,timer_stream);
453 }
454
455public:
456 SBasis0fSBasisToy(){
457 handles.push_back(&hand);
458 handles.push_back(&cut_hand);
459 cut_hand.push_back(100,100);
460 cut_hand.push_back(500,500);
461 }
462};
463
464int main(int argc, char **argv) {
465 init(argc, argv, new SBasis0fSBasisToy);
466 return 0;
467}
468
469/*
470 Local Variables:
471 mode:c++
472 c-file-style:"stroustrup"
473 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
474 indent-tabs-mode:nil
475 fill-column:99
476 End:
477*/
478// vim: filetype = cpp:expandtab:shiftwidth = 4:tabstop = 8:softtabstop = 4:encoding = utf-8:textwidth = 99 :
main
int main()
Definition bendpath-test.cpp:108
bezier-to-sbasis.h
Conversion between Bezier control points and SBasis curves.
bounds
Geom::IntRect bounds
Definition canvas.cpp:182
Geom::Affine::inverse
Affine inverse() const
Compute the inverse matrix.
Definition affine.cpp:388
Geom::D2
Adaptor that creates 2D functions from 1D ones.
Definition d2.h:55
Geom::GenericInterval::extent
constexpr C extent() const
Definition generic-interval.h:99
Geom::GenericInterval::min
constexpr C min() const
Definition generic-interval.h:97
Geom::GenericInterval::max
constexpr C max() const
Definition generic-interval.h:98
Geom::GenericRect::min
CPoint min() const
Get the corner of the rectangle with smallest coordinate values.
Definition generic-rect.h:128
Geom::GenericRect::max
CPoint max() const
Get the corner of the rectangle with largest coordinate values.
Definition generic-rect.h:131
Geom::Interval
Range of real numbers that is never empty.
Definition interval.h:59
Geom::Linear
Function that interpolates linearly between two values.
Definition linear.h:55
Geom::OptInterval
Range of real numbers that can be empty.
Definition interval.h:199
Geom::Piecewise
Function defined as discrete pieces.
Definition piecewise.h:71
Geom::Piecewise::size
unsigned size() const
Definition piecewise.h:131
Geom::Piecewise::cuts
std::vector< double > cuts
Definition piecewise.h:75
Geom::Point
Two-dimensional point that doubles as a vector.
Definition point.h:66
Geom::SBasisOf::valueAt
T valueAt(double t) const
Definition sbasis-of.h:103
Geom::SBasis
Polynomial in symmetric power basis.
Definition sbasis.h:70
PointSetHandle::push_back
void push_back(double x, double y)
Definition toy-framework-2.h:188
PointSetHandle::pts
std::vector< Geom::Point > pts
Definition toy-framework-2.h:183
Toy::handles
vector< Handle * > handles
Definition toy-framework-2.h:317
Toy::save
virtual void save(FILE *f)
Definition toy-framework-2.cpp:270
Toy::draw
virtual void draw(cairo_t *cr, std::ostringstream *notify, int w, int h, bool save, std::ostringstream *timing_stream)
Definition toy-framework-2.cpp:166
multi_compose
SBasisOf< T > multi_compose(SBasisOf< double > const &f, SBasisOf< T > const &g)
Definition convole.cpp:82
plot3d
void plot3d(cairo_t *cr, SBasis const &x, SBasis const &y, SBasis const &z, Frame frame)
Definition convole.cpp:203
result
Css & result
Definition ctrl-handle-styling.cpp:32
Geom::Y
@ Y
Definition coord.h:48
Geom::X
@ X
Definition coord.h:48
Geom::SL::v
size_t v
Definition multi-index.h:105
Geom
Various utility functions.
Definition affine.h:22
Geom::from_basis
Affine from_basis(const Point &x_basis, const Point &y_basis, const Point &offset=Point(0, 0))
Creates a Affine given an axis and origin point.
Definition affine.cpp:26
Geom::multiply
Bezier multiply(Bezier const &f, Bezier const &g)
Definition bezier.h:337
Geom::compose
D2< T > compose(D2< T > const &a, T const &b)
Definition d2.h:405
Geom::roots
std::vector< double > roots(SBasis const &s)
Geom::integral
Bezier integral(Bezier const &a)
Definition bezier.cpp:294
Geom::derivative
Bezier derivative(Bezier const &a)
Definition bezier.cpp:282
Geom::toSBasis
SBasis toSBasis(SBasisN< 1 > f)
Definition sbasisN.h:640
Geom::cubics_fitting_curvature
std::vector< D2< SBasis > > cubics_fitting_curvature(Point const &M0, Point const &M1, Point const &dM0, Point const &dM1, double d2M0xdM0, double d2M1xdM1, int insist_on_speed_signs=1, double epsilon=1e-5)
Geom::bounds_fast
OptInterval bounds_fast(Bezier const &b)
Definition bezier.cpp:305
Geom::rot90
D2< T > rot90(D2< T > const &a)
Definition d2.h:397
std
STL namespace.
cairo_line_to
void cairo_line_to(cairo_t *cr, Geom::Point p1)
Definition cairo-helpers.cpp:19
cairo_t
struct _cairo cairo_t
Definition path-cairo.h:16
cairo_move_to
void cairo_move_to(cairo_t *cr, Geom::Point p1)
Definition cairo-helpers.cpp:14
cairo_d2_sb
void cairo_d2_sb(cairo_t *cr, Geom::D2< Geom::SBasis > const &p)
Definition cairo-helpers.cpp:123
sbofsb_cubic_solve
D2< SBasis > sbofsb_cubic_solve(SBasisOf< SBasisOf< double > > const &f, Geom::Point const &A, Geom::Point const &B)
Finds a path which traces the 0 contour of f, traversing from A to B as a single cubic d2<sbasis>.
Definition sb-of-sb.cpp:306
convole
Piecewise< SBasis > convole(SBasisOf< double > const &f, Interval dom_f, SBasisOf< double > const &g, Interval dom_g)
Definition sb-of-sb.cpp:244
multi_compose
SBasisOf< T > multi_compose(SBasisOf< double > const &f, SBasisOf< T > const &g)
Definition sb-of-sb.cpp:103
toSBasisOfDouble
SBasisOf< double > toSBasisOfDouble(SBasis const &f)
Definition sb-of-sb.cpp:22
eval_dim
static SBasisOf< double > eval_dim(SBasisOf< SBasisOf< double > > const &f, double t, unsigned dim)
Definition sb-of-sb.cpp:158
plot3d
void plot3d(cairo_t *cr, SBasis const &x, SBasis const &y, SBasis const &z, Frame frame)
Definition sb-of-sb.cpp:191
subderivative
SBasisOf< T > subderivative(SBasisOf< T > const &f)
Definition sb-of-sb.cpp:287
sbasis-geometric.h
two-dimensional geometric operators.
sbasis-of.h
Defines S-power basis function class with coefficient in arbitrary ring.
sbasis.h
Polynomial in symmetric power basis (S-basis)
curve
Definition curve.h:24
height
double height
Definition convex_hull.cpp:107
width
double width
Definition convex_hull.cpp:106
cairo_set_source_rgba
void cairo_set_source_rgba(cairo_t *cr, colour c)
Definition toy-framework-2.cpp:119
init
void init(int argc, char **argv, Toy *t, int width=600, int height=600)
Definition toy-framework-2.cpp:600