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#include <iostream>
#include <2geom/path.h>
#include <2geom/svg-path-parser.h>
#include <2geom/path-intersection.h>
#include <2geom/basic-intersection.h>
#include <2geom/pathvector.h>
#include <2geom/exception.h>
#include <2geom/sbasis-geometric.h>
#include <2geom/path-intersection.h>
#include <2geom/nearest-time.h>
#include <2geom/line.h>
#include <2geom/bezier-to-sbasis.h>
#include <2geom/sbasis-to-bezier.h>
#include <cstdlib>
#include <map>
#include <vector>
#include <algorithm>
#include <optional>
#include <toys/path-cairo.h>
#include <toys/toy-framework-2.h>
#include <2geom/bezier-to-sbasis.h>
#include <2geom/ord.h>
#include <2geom/conicsec.h>
std::vector<Geom::RatQuad> xAx_to_RatQuads(Geom::xAx const &/*C*/, Geom::Rect const &/*bnd*/) {
// find points on boundary
// if there are exactly 0 points return
// if there are exactly 2 points fit ratquad and return
// if there are an odd number, split bnd on the point with the smallest dot(unit_vector(grad), rect_edge)
// sort into clockwise order ABCD
// compute corresponding tangents
// test boundary points against the line through A
// if all on one side
//
// if A,X and Y,Z
// ratquad from A,X and Y,Z
return std::vector<Geom::RatQuad>();
}
using namespace Geom;
using namespace std;
// File: convert.h
#include <sstream>
#include <stdexcept>
class BadConversion : public std::runtime_error {
public:
BadConversion(const std::string& s)
: std::runtime_error(s)
{ }
};
template <typename T>
inline std::string stringify(T x)
{
std::ostringstream o;
if (!(o << x))
throw BadConversion("stringify(T)");
return o.str();
}
namespace Geom{
xAx degen;
};
void draw_hull(cairo_t*cr, RatQuad rq) {
cairo_move_to(cr, rq.P[0]);
cairo_line_to(cr, rq.P[1]);
cairo_line_to(cr, rq.P[2]);
cairo_stroke(cr);
}
void draw(cairo_t* cr, xAx C, Rect bnd) {
if(bnd[1].extent() < 5) return;
vector<double> prev_rts;
double py = bnd[Y].min();
for(int i = 0; i < 100; i++) {
double t = i/100.;
double y = bnd[Y].valueAt(t);
vector<double> rts = C.roots(Point(1, 0), Point(0, y));
int top = 0;
for(unsigned j = 0; j < rts.size(); j++) {
if(bnd[0].contains(rts[j])) {
rts[top] = rts[j];
top++;
}
}
rts.erase(rts.begin()+top, rts.end());
if(rts.size() == prev_rts.size()) {
for(unsigned j = 0; j < rts.size(); j++) {
cairo_move_to(cr, prev_rts[j], py);
cairo_line_to(cr, rts[j], y);
cairo_stroke(cr);
}
/* } else if(prev_rts.size() == 1) {
for(unsigned j = 0; j < rts.size(); j++) {
cairo_move_to(cr, prev_rts[0], py);
cairo_line_to(cr, rts[j], y);
cairo_stroke(cr);
}
} else if(rts.size() == 1) {
for(unsigned j = 0; j < prev_rts.size(); j++) {
cairo_move_to(cr, prev_rts[j], py);
cairo_line_to(cr, rts[0], y);
cairo_stroke(cr);
}*/
} else {
draw(cr, C, Rect(bnd[0], Interval(py, y)));
/*for(unsigned j = 0; j < rts.size(); j++) {
cairo_move_to(cr, rts[j], y);
cairo_rel_line_to(cr, 1,1);
}*/
}
prev_rts = rts;
py = y;
}
}
template <typename T>
static T det(T a, T b, T c, T d) {
return a*d - b*c;
}
template <typename T>
static T det(T M[2][2]) {
return M[0][0]*M[1][1] - M[1][0]*M[0][1];
}
template <typename T>
static T det3(T M[3][3]) {
return ( M[0][0] * det(M[1][1], M[1][2],
M[2][1], M[2][2])
-M[1][0] * det(M[0][1], M[0][2],
M[2][1], M[2][2])
+M[2][0] * det(M[0][1], M[0][2],
M[1][1], M[1][2]));
}
class Conic6: public Toy {
PointSetHandle C1H, C2H;
std::vector<Slider> sliders;
Point mouse_sampler;
void mouse_moved(GdkEventMotion* e) override {
mouse_sampler = Point(e->x, e->y);
Toy::mouse_moved(e);
}
void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {
cairo_set_source_rgba (cr, 0., 0., 0, 1);
cairo_set_line_width (cr, 1);
Rect screen_rect(Interval(10, width-10), Interval(10, height-10));
Geom::xAx C1 = xAx::fromPoints(C1H.pts);
::draw(cr, C1, screen_rect);
*notify << C1;
Geom::xAx C2 = xAx::fromPoints(C2H.pts);
::draw(cr, C2, screen_rect);
*notify << C2;
SBasis T(Linear(-1,1));
SBasis S(Linear(1,1));
SBasis C[3][3] = {{T*C1.c[0]+S*C2.c[0], (T*C1.c[1]+S*C2.c[1])/2, (T*C1.c[3]+S*C2.c[3])/2},
{(T*C1.c[1]+S*C2.c[1])/2, T*C1.c[2]+S*C2.c[2], (T*C1.c[4]+S*C2.c[4])/2},
{(T*C1.c[3]+S*C2.c[3])/2, (T*C1.c[4]+S*C2.c[4])/2, T*C1.c[5]+S*C2.c[5]}};
SBasis D = det3(C);
std::vector<double> rts = Geom::roots(D);
if(rts.empty()) {
T = Linear(1,1);
S = Linear(-1,1);
SBasis C[3][3] = {{T*C1.c[0]+S*C2.c[0], (T*C1.c[1]+S*C2.c[1])/2, (T*C1.c[3]+S*C2.c[3])/2},
{(T*C1.c[1]+S*C2.c[1])/2, T*C1.c[2]+S*C2.c[2], (T*C1.c[4]+S*C2.c[4])/2},
{(T*C1.c[3]+S*C2.c[3])/2, (T*C1.c[4]+S*C2.c[4])/2, T*C1.c[5]+S*C2.c[5]}};
D = det3(C);
rts = Geom::roots(D);
}
// at this point we have a T and S and perhaps some roots that represent our degenerate conic
// Let's just pick one randomly (can we do better?)
//for(unsigned i = 0; i < rts.size(); i++) {
if(!rts.empty()) {
cairo_save(cr);
unsigned i = 0;
double t = T.valueAt(rts[i]);
double s = S.valueAt(rts[i]);
*notify << t << "; " << s << std::endl;
/*double C0[3][3] = {{t*C1.c[0]+s*C2.c[0], (t*C1.c[1]+s*C2.c[1])/2, (t*C1.c[3]+s*C2.c[3])/2},
{(t*C1.c[1]+s*C2.c[1])/2, t*C1.c[2]+s*C2.c[2], (t*C1.c[4]+s*C2.c[4])/2},
{(t*C1.c[3]+s*C2.c[3])/2, (t*C1.c[4]+s*C2.c[4])/2, t*C1.c[5]+s*C2.c[5]}};*/
xAx xC0 = C1*t + C2*s;
//::draw(cr, xC0, screen_rect); // degen
std::optional<Point> oB0 = xC0.bottom();
Point B0 = *oB0;
//*notify << B0 << " = " << C1.gradient(B0);
draw_circ(cr, B0);
Point n0, n1;
// Are these just the eigenvectors of A11?
if(fabs(xC0.c[0]) > fabs(xC0.c[2])) {
double b = 0.5*xC0.c[1]/xC0.c[0];
double c = xC0.c[2]/xC0.c[0];
double d = std::sqrt(b*b-c);
n0 = Point(1, b+d);
n1 = Point(1, b-d);
} else {
double b = 0.5*xC0.c[1]/xC0.c[2];
double c = xC0.c[0]/xC0.c[2];
double d = std::sqrt(b*b-c);
n0 = Point(b+d, 1);
n1 = Point(b-d, 1);
}
cairo_set_source_rgb(cr, 0.7, 0.7, 0.7);
Line L0 = Line::from_origin_and_vector(B0, rot90(n0));
draw_line(cr, L0, screen_rect);
Line L1 = Line::from_origin_and_vector(B0, rot90(n1));
draw_line(cr, L1, screen_rect);
cairo_set_source_rgb(cr, 1, 0., 0.);
rts = C1.roots(L0);
for(double rt : rts) {
Point P = L0.pointAt(rt);
draw_cross(cr, P);
*notify << C1.valueAt(P) << "; " << C2.valueAt(P) << "\n";
}
rts = C1.roots(L1);
for(double rt : rts) {
Point P = L1.pointAt(rt);
draw_cross(cr, P);
*notify << C1.valueAt(P) << "; "<< C2.valueAt(P) << "\n";
}
cairo_stroke(cr);
cairo_restore(cr);
}
::draw(cr, C1*sliders[0].value() + C2*sliders[1].value(), screen_rect);
std::vector<Point> res = intersect(C1, C2);
for(auto & re : res) {
draw_circ(cr, re);
}
cairo_stroke(cr);
//*notify << "w = " << w << "; lambda = " << rq.lambda() << "\n";
Toy::draw(cr, notify, width, height, save, timer_stream);
}
public:
Conic6() {
for(int j = 0; j < 5; j++){
C1H.push_back(uniform()*400, 100+ uniform()*300);
C2H.push_back(uniform()*400, 100+ uniform()*300);
}
handles.push_back(&C1H);
handles.push_back(&C2H);
sliders.emplace_back(-1.0, 1.0, 0, 0.0, "a");
sliders.emplace_back(-1.0, 1.0, 0, 0.0, "b");
sliders.emplace_back(0.0, 5.0, 0, 0.0, "c");
handles.push_back(&(sliders[0]));
handles.push_back(&(sliders[1]));
handles.push_back(&(sliders[2]));
sliders[0].geometry(Point(50, 20), 250);
sliders[1].geometry(Point(50, 50), 250);
sliders[2].geometry(Point(50, 80), 250);
}
void first_time(int /*argc*/, char**/* argv*/) override {
}
};
int main(int argc, char **argv) {
init(argc, argv, new Conic6());
return 0;
}
/*
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=4:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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