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-rw-r--r--src/toys/conic-6.cpp304
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diff --git a/src/toys/conic-6.cpp b/src/toys/conic-6.cpp
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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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