1 files changed, 93 insertions, 0 deletions
diff --git a/src/toys/evolute.cpp b/src/toys/evolute.cpp
new file mode 100644
index 0000000..a5deb08
--- /dev/null
+++ b/src/toys/evolute.cpp
@@ -0,0 +1,93 @@
+#include <2geom/basic-intersection.h>
+#include <2geom/d2.h>
+#include <2geom/sbasis.h>
+#include <2geom/sbasis-2d.h>
+#include <2geom/bezier-to-sbasis.h>
+
+#include <toys/path-cairo.h>
+#include <toys/toy-framework-2.h>
+
+using std::vector;
+using namespace Geom;
+
+/*
+jfb: I think the evolute goes to infinity at inflection points, in which case you cannot "join" the pieces by hand.
+jfb: for the evolute toy, you could not only cut at inflection points, but event remove the domains where  cross(dda,da)<c*|da|^3, where c is a small constant, as these points will be off screen anyway.
+*/
+
+class Evolution: public Toy {
+    PointSetHandle psh;
+void draw(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override {
+    cairo_set_line_width (cr, 0.5);
+    cairo_set_source_rgba (cr, 0., 0., 0, 1);
+
+    D2<SBasis> A(psh.asBezier());
+
+    D2<SBasis> dA = derivative(A);
+    D2<SBasis> ddA = derivative(dA);
+    SBasis crs = cross(ddA, dA);
+    cairo_d2_sb(cr, D2<SBasis>(Linear(0,1000), crs*(500./bounds_exact(crs)->extent())));
+    vector<double> rts = roots(crs);
+    for(double rt : rts) {
+        draw_handle(cr, A(rt));
+    }
+    cairo_d2_sb(cr, A);
+    cairo_stroke(cr);
+    Interval r(0, 1);
+    if(!rts.empty())
+        r.setMax(rts[0]);
+    //if(rts[0] == 0)
+    //rts.erase(rts.begin(), rts.begin()+1);
+    A = portion(A, r.min(), r.max());
+    dA = portion(dA, r.min(), r.max());
+    ddA = portion(ddA, r.min(), r.max());
+    crs = portion(crs, r.min(), r.max());
+    cairo_stroke(cr);
+    Piecewise<SBasis> s = divide(dA[0]*dot(dA,dA), crs, 100, 1);
+    D2<Piecewise<SBasis> > ev4(Piecewise<SBasis>(A[0]) + divide(-dA[1]*dot(dA,dA), crs, 100, 1),
+                               Piecewise<SBasis>(A[1]) + divide(dA[0]*dot(dA,dA), crs, 100, 1));
+    cairo_d2_pw_sb(cr, ev4);
+    cairo_stroke(cr);
+    if(1) {
+        std::cout << "bnd" << *bounds_exact(dot(ev4, ev4)) << std::endl;
+        cairo_d2_pw_sb(cr, D2<Piecewise<SBasis> >(Piecewise<SBasis>(SBasis(Linear(0,1000))), dot(ev4, ev4)*1000));
+        cairo_stroke(cr);
+        vector<double> rts = roots(dot(ev4, ev4)-1);
+        for(double rt : rts) {
+            std::cout << rt << std::endl;
+            draw_handle(cr, ev4(rt));
+        }
+    }
+    cairo_set_source_rgba (cr, 1., 0., 1, 1);
+
+    Toy::draw(cr, notify, width, height, save,timer_stream);
+}
+public:
+Evolution (unsigned bez_ord) {
+    handles.push_back(&psh);
+    for(unsigned i = 0; i < bez_ord; i++)
+        psh.push_back(uniform()*400, uniform()*400);
+}
+};
+
+int main(int argc, char **argv) {
+    unsigned bez_ord=5;
+    if(argc > 1)
+        sscanf(argv[1], "%d", &bez_ord);
+    init(argc, argv, new Evolution(bez_ord));
+
+    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=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :