#include <2geom/d2.h> #include <2geom/sbasis.h> #include <2geom/sbasis-2d.h> #include <2geom/bezier-to-sbasis.h> #include <2geom/sbasis-geometric.h> #include #include #include <2geom/angle.h> using std::vector; using namespace Geom; using namespace std; // Author: Johan Engelen, 2009 // // Shows how to find the locations on a path where the derivative is parallel to a certain vector. //----------------------------------------------- std::string angle_formatter(double angle) { return default_formatter(decimal_round(deg_from_rad(angle),2)); } class FindDerivatives : public Toy { enum menu_item_t { SHOW_MENU = 0, TEST_CREATE, TEST_PROJECTION, TEST_ORTHO, TEST_DISTANCE, TEST_POSITION, TEST_SEG_BISEC, TEST_ANGLE_BISEC, TEST_COLLINEAR, TEST_INTERSECTIONS, TEST_COEFFICIENTS, TOTAL_ITEMS // this one must be the last item }; enum handle_label_t { }; enum toggle_label_t { }; enum slider_label_t { END_SHARED_SLIDERS = 0, ANGLE_SLIDER = END_SHARED_SLIDERS, A_COEFF_SLIDER = END_SHARED_SLIDERS, B_COEFF_SLIDER, C_COEFF_SLIDER }; static const char* menu_items[TOTAL_ITEMS]; static const char keys[TOTAL_ITEMS]; PointSetHandle curve_handle; PointHandle sample_point; void first_time(int /*argc*/, char** /*argv*/) override { draw_f = &FindDerivatives::draw_menu; } void init_common() { set_common_control_geometry = true; set_control_geometry = true; sliders.clear(); toggles.clear(); handles.clear(); } virtual void draw_common( cairo_t *cr, std::ostringstream *notify, int width, int height, bool /*save*/ ) { init_common_ctrl_geom(cr, width, height, notify); } void init_create() { init_common(); p1.pos = Point(400, 50); p2.pos = Point(450, 450); O.pos = Point(50, 400); sliders.emplace_back(0, 2*M_PI, 0, 0, "angle"); sliders[ANGLE_SLIDER].formatter(&angle_formatter); handles.push_back(&p1); handles.push_back(&p2); handles.push_back(&O); handles.push_back(&(sliders[ANGLE_SLIDER])); } void draw_create(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream */*timer_stream*/) { draw_common(cr, notify, width, height, save); init_create_ctrl_geom(cr, notify, width, height); Line l1(p1.pos, p2.pos); Line l2(O.pos, sliders[ANGLE_SLIDER].value()); cairo_set_source_rgba(cr, 0.0, 0.0, 0.0, 1.0); cairo_set_line_width(cr, 0.3); draw_line(cr, l1); draw_line(cr, l2); cairo_stroke(cr); draw_label(cr, p1, "P1"); draw_label(cr, p2, "P2"); draw_label(cr, O, "O"); draw_label(cr, l1, "L(P1,P2)"); draw_label(cr, l2, "L(O,angle)"); } void init_projection() { init_common(); p1.pos = Point(400, 50); p2.pos = Point(450, 450); p3.pos = Point(100, 250); p4.pos = Point(200, 450); O.pos = Point(50, 150); handles.push_back(&p1); handles.push_back(&p2); handles.push_back(&p3); handles.push_back(&p4); handles.push_back(&O); } void draw_projection(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream */*timer_stream*/) { draw_common(cr, notify, width, height, save); Line l1(p1.pos, p2.pos); LineSegment ls(p3.pos, p4.pos); Point np = projection(O.pos, l1); LineSegment lsp = projection(ls, l1); cairo_set_source_rgba(cr, 0.3, 0.3, 0.3, 1.0); cairo_set_line_width(cr, 0.2); draw_line(cr, l1); draw_segment(cr, ls); cairo_stroke(cr); cairo_set_line_width(cr, 0.3); cairo_set_source_rgba(cr, 0.0, 0.0, 1.0, 1.0); draw_segment(cr, lsp); draw_handle(cr, lsp[0]); draw_handle(cr, lsp[1]); cairo_stroke(cr); cairo_set_source_rgba(cr, 0.8, 0.0, 0.0, 1.0); draw_circ(cr, np); cairo_stroke(cr); cairo_set_source_rgba(cr, 0.5, 0.5, 0.5, 1.0); draw_label(cr, p1, "P1"); draw_label(cr, p2, "P2"); draw_label(cr, ls, "S"); draw_label(cr, lsp, "prj(S)"); draw_label(cr, O, "P"); draw_text(cr, np, "prj(P)"); cairo_stroke(cr); } void init_derivative() { init_common(); handles.push_back(&curve_handle); handles.push_back(&sample_point); for(unsigned i = 0; i < 4; i++) curve_handle.push_back(150+uniform()*300,150+uniform()*300); sample_point.pos = Geom::Point(250,300); } void draw_derivative(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) { D2 B = curve_handle.asBezier(); cairo_set_line_width (cr, 1); cairo_set_source_rgba (cr, 0., 0.5, 0., 1); cairo_d2_sb(cr, B); cairo_stroke(cr); Point vector = sample_point.pos - Geom::Point(400,400); cairo_move_to(cr, Geom::Point(400,400)); cairo_line_to(cr, sample_point.pos); cairo_set_source_rgba (cr, 0., 0., 0.5, 0.8); cairo_stroke(cr); // How to find location of points with certain derivative along a path: D2 deriv = derivative(B); SBasis dotp = dot(deriv, rot90(vector)); std::vector sol = roots(dotp); for (double i : sol) { draw_handle(cr, B.valueAt(i)); // the solutions are in vector 'sol' } cairo_set_source_rgba (cr, 0.5, 0.2, 0., 0.8); cairo_stroke(cr); Toy::draw(cr, notify, width, height, save,timer_stream); } void init_find_tangents() { init_common(); handles.push_back(&curve_handle); handles.push_back(&sample_point); toggles.emplace_back(" tangent / normal ", false); handles.push_back(&(toggles[0])); for(unsigned i = 0; i < 4; i++) curve_handle.push_back(150+uniform()*300,150+uniform()*300); sample_point.pos = Geom::Point(250,300); Point toggle_sp( 30, 30); toggles[0].bounds = Rect( toggle_sp, toggle_sp + Point(200,25) ); } void draw_find_tangents(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) { D2 B = curve_handle.asBezier(); cairo_set_line_width (cr, 1); cairo_set_source_rgba (cr, 0., 0.5, 0., 1); cairo_d2_sb(cr, B); cairo_stroke(cr); std::vector sol = toggles[0].on ? find_tangents(sample_point.pos, B) : find_normals(sample_point.pos, B); for (double i : sol) { draw_handle(cr, B.valueAt(i)); // the solutions are in vector 'sol' draw_segment(cr, B.valueAt(i), sample_point.pos); } cairo_set_source_rgba (cr, 0.5, 0.2, 0., 0.8); cairo_stroke(cr); Toy::draw(cr, notify, width, height, save,timer_stream); } void init_ortho() { init_common(); p1.pos = Point(400, 50); p2.pos = Point(450, 450); p3.pos = Point(100, 50); p4.pos = Point(150, 450); handles.push_back(&p1); handles.push_back(&p2); handles.push_back(&p3); handles.push_back(&p4); } void draw_ortho(cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream */*timer_stream*/) { draw_common(cr, notify, width, height, save); Line l1(p1.pos, p2.pos); Line l2 = make_orthogonal_line(p3.pos, l1); Line l3 = make_parallel_line(p4.pos, l1); cairo_set_source_rgba(cr, 0.0, 0.0, 0.0, 1.0); cairo_set_line_width(cr, 0.3); draw_line(cr, l1); draw_line(cr, l2); draw_line(cr, l3); cairo_stroke(cr); draw_label(cr, p1, "P1"); draw_label(cr, p2, "P2"); draw_label(cr, p3, "O1"); draw_label(cr, p4, "O2"); draw_label(cr, l1, "L"); draw_label(cr, l2, "L1 _|_ L"); draw_label(cr, l3, "L2 // L"); } void init_common_ctrl_geom(cairo_t* /*cr*/, int /*width*/, int /*height*/, std::ostringstream* /*notify*/) { if ( set_common_control_geometry ) { set_common_control_geometry = false; } } void init_create_ctrl_geom(cairo_t* /*cr*/, std::ostringstream* /*notify*/, int /*width*/, int height) { if ( set_control_geometry ) { set_control_geometry = false; sliders[ANGLE_SLIDER].geometry(Point(50, height - 50), 180); } } void init_coefficients_ctrl_geom(cairo_t* /*cr*/, std::ostringstream* /*notify*/, int /*width*/, int height) { if ( set_control_geometry ) { set_control_geometry = false; sliders[A_COEFF_SLIDER].geometry(Point(50, height - 160), 400); sliders[B_COEFF_SLIDER].geometry(Point(50, height - 110), 400); sliders[C_COEFF_SLIDER].geometry(Point(50, height - 60), 400); } } void draw_segment(cairo_t* cr, Point const& p1, Point const& p2) { cairo_move_to(cr, p1); cairo_line_to(cr, p2); } void draw_segment(cairo_t* cr, Point const& p1, double angle, double length) { Point p2; p2[X] = length * std::cos(angle); p2[Y] = length * std::sin(angle); p2 += p1; draw_segment(cr, p1, p2); } void draw_segment(cairo_t* cr, LineSegment const& ls) { draw_segment(cr, ls[0], ls[1]); } void draw_ray(cairo_t* cr, Ray const& r) { double angle = r.angle(); draw_segment(cr, r.origin(), angle, m_length); } void draw_line(cairo_t* cr, Line const& l) { double angle = l.angle(); draw_segment(cr, l.origin(), angle, m_length); draw_segment(cr, l.origin(), angle, -m_length); } void draw_label(cairo_t* cr, PointHandle const& ph, const char* label) { draw_text(cr, ph.pos+op, label); } void draw_label(cairo_t* cr, Line const& l, const char* label) { draw_text(cr, projection(Point(m_width/2-30, m_height/2-30), l)+op, label); } void draw_label(cairo_t* cr, LineSegment const& ls, const char* label) { draw_text(cr, middle_point(ls[0], ls[1])+op, label); } void draw_label(cairo_t* cr, Ray const& r, const char* label) { Point prj = r.pointAt(r.nearestTime(Point(m_width/2-30, m_height/2-30))); if (L2(r.origin() - prj) < 100) { prj = r.origin() + 100*r.vector(); } draw_text(cr, prj+op, label); } void init_menu() { handles.clear(); sliders.clear(); toggles.clear(); } void draw_menu( cairo_t * /*cr*/, std::ostringstream *notify, int /*width*/, int /*height*/, bool /*save*/, std::ostringstream */*timer_stream*/ ) { *notify << std::endl; for (int i = SHOW_MENU; i < TOTAL_ITEMS; ++i) { *notify << " " << keys[i] << " - " << menu_items[i] << std::endl; } } void key_hit(GdkEventKey *e) override { char choice = std::toupper(e->keyval); switch ( choice ) { case 'A': init_menu(); draw_f = &FindDerivatives::draw_menu; break; case 'B': init_derivative(); draw_f = &FindDerivatives::draw_derivative; break; case 'C': init_find_tangents(); draw_f = &FindDerivatives::draw_find_tangents; break; case 'D': init_ortho(); draw_f = &FindDerivatives::draw_ortho; break; } redraw(); } void draw( cairo_t *cr, std::ostringstream *notify, int width, int height, bool save, std::ostringstream *timer_stream) override { m_width = width; m_height = height; m_length = (m_width > m_height) ? m_width : m_height; m_length *= 2; (this->*draw_f)(cr, notify, width, height, save, timer_stream); Toy::draw(cr, notify, width, height, save, timer_stream); } public: FindDerivatives() { op = Point(5,5); } private: typedef void (FindDerivatives::* draw_func_t) (cairo_t*, std::ostringstream*, int, int, bool, std::ostringstream*); draw_func_t draw_f; bool set_common_control_geometry; bool set_control_geometry; PointHandle p1, p2, p3, p4, p5, p6, O; std::vector toggles; std::vector sliders; Point op; double m_width, m_height, m_length; }; // end class FindDerivatives const char* FindDerivatives::menu_items[] = { "show this menu", "derivative matching on curve", "find normals", "find tangents" }; const char FindDerivatives::keys[] = { 'A', 'B', 'C', 'D' }; int main(int argc, char **argv) { init( argc, argv, new FindDerivatives()); 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:expandtab:shiftwidth = 4:tabstop = 8:softtabstop = 4:encoding = utf-8:textwidth = 99 :