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#define __LINE_GEOMETRY_C__
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* Routines for dealing with lines (intersections, etc.)
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* Maximilian Albert <Anhalter42@gmx.de>
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* Copyright (C) 2007 authors
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* Released under GNU GPL, read the file 'COPYING' for more information
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#include "line-geometry.h"
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#include "desktop-style.h"
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#include "desktop-handles.h"
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#include "display/sp-canvas.h"
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#include "display/sodipodi-ctrl.h"
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* Draw a line beginning at 'start'. If is_endpoint is true, use 'vec' as the endpoint
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* of the segment. Otherwise interpret it as the direction of the line.
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* FIXME: Think of a better way to distinguish between the two constructors of lines.
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Line::Line(NR::Point const &start, NR::Point const &vec, bool is_endpoint) {
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d0 = NR::dot(normal, pt);
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Line::Line(Line const &line) {
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Line &Line::operator=(Line const &line) {
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NR::Maybe<NR::Point> Line::intersect(Line const &line) {
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NR::Coord denom = NR::dot(v_dir, line.normal);
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NR::Maybe<NR::Point> no_point = NR::Nothing();
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if (fabs(denom) < 1e-6)
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NR::Coord lambda = (line.d0 - NR::dot(pt, line.normal)) / denom;
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return pt + lambda * v_dir;
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void Line::set_direction(NR::Point const &dir)
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d0 = NR::dot(normal, pt);
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NR::Point Line::closest_to(NR::Point const &pt)
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/* return the intersection of this line with a perpendicular line passing through pt */
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NR::Maybe<NR::Point> result = this->intersect(Line(pt, (this->v_dir).ccw(), false));
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g_return_val_if_fail (result, NR::Point (0.0, 0.0));
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double Line::lambda (NR::Point const pt)
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double sign = (NR::dot (pt - this->pt, this->v_dir) > 0) ? 1.0 : -1.0;
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double lambda = sign * NR::L2 (pt - this->pt);
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// FIXME: It may speed things up (but how much?) if we assume that
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// pt lies on the line and thus skip the following test
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NR::Point test = point_from_lambda (lambda);
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if (!pts_coincide (pt, test)) {
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g_warning ("Point does not lie on line.\n");
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/* The coordinates of w with respect to the basis {v1, v2} */
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std::pair<double, double> coordinates (NR::Point const &v1, NR::Point const &v2, NR::Point const &w)
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double det = determinant (v1, v2);;
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if (fabs (det) < epsilon) {
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// vectors are not linearly independent; we indicate this in the return value(s)
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return std::make_pair (HUGE_VAL, HUGE_VAL);
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double lambda1 = determinant (w, v2) / det;
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double lambda2 = determinant (v1, w) / det;
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return std::make_pair (lambda1, lambda2);
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/* whether w lies inside the sector spanned by v1 and v2 */
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bool lies_in_sector (NR::Point const &v1, NR::Point const &v2, NR::Point const &w)
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std::pair<double, double> coords = coordinates (v1, v2, w);
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if (coords.first == HUGE_VAL) {
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// catch the case that the vectors are not linearly independent
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// FIXME: Can we assume that it's safe to return true if the vectors point in different directions?
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return (NR::dot (v1, v2) < 0);
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return (coords.first >= 0 and coords.second >= 0);
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bool lies_in_quadrangle (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D, NR::Point const &pt)
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return (lies_in_sector (D - A, B - A, pt - A) && lies_in_sector (D - C, B - C, pt - C));
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static double pos_angle (NR::Point v, NR::Point w)
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return fabs (NR::atan2 (v) - NR::atan2 (w));
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* Returns the two corners of the quadrangle A, B, C, D spanning the edge that is hit by a semiline
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* starting at pt and going into direction dir.
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* If none of the sides is hit, it returns a pair containing two identical points.
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std::pair<NR::Point, NR::Point>
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side_of_intersection (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D,
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NR::Point const &pt, NR::Point const &dir)
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NR::Point dir_A (A - pt);
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NR::Point dir_B (B - pt);
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NR::Point dir_C (C - pt);
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NR::Point dir_D (D - pt);
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std::pair<NR::Point, NR::Point> result;
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if (lies_in_sector (dir_A, dir_B, dir)) {
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result = std::make_pair (A, B);
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angle = pos_angle (dir_A, dir_B);
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if (lies_in_sector (dir_B, dir_C, dir)) {
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tmp_angle = pos_angle (dir_B, dir_C);
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if (tmp_angle > angle) {
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result = std::make_pair (B, C);
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if (lies_in_sector (dir_C, dir_D, dir)) {
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tmp_angle = pos_angle (dir_C, dir_D);
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if (tmp_angle > angle) {
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result = std::make_pair (C, D);
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if (lies_in_sector (dir_D, dir_A, dir)) {
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tmp_angle = pos_angle (dir_D, dir_A);
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if (tmp_angle > angle) {
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result = std::make_pair (D, A);
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// no intersection found; return a pair containing two identical points
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return std::make_pair (A, A);
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NR::Maybe<NR::Point> Line::intersection_with_viewbox (SPDesktop *desktop)
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NR::Rect vb = desktop->get_display_area();
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/* remaining viewbox corners */
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NR::Point ul (vb.min()[NR::X], vb.max()[NR::Y]);
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NR::Point lr (vb.max()[NR::X], vb.min()[NR::Y]);
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std::pair <NR::Point, NR::Point> e = side_of_intersection (vb.min(), lr, vb.max(), ul, this->pt, this->v_dir);
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if (e.first == e.second) {
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// perspective line lies outside the canvas
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return NR::Nothing();
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Line line (e.first, e.second);
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return this->intersect (line);
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void create_canvas_point(NR::Point const &pos, double size, guint32 rgba)
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SPDesktop *desktop = inkscape_active_desktop();
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SPCanvasItem * canvas_pt = sp_canvas_item_new(sp_desktop_controls(desktop), SP_TYPE_CTRL,
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"stroke_color", 0x000000ff,
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SP_CTRL(canvas_pt)->moveto(pos);
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void create_canvas_line(NR::Point const &p1, NR::Point const &p2, guint32 rgba)
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SPDesktop *desktop = inkscape_active_desktop();
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SPCanvasItem *line = sp_canvas_item_new(sp_desktop_controls(desktop),
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SP_TYPE_CTRLLINE, NULL);
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sp_ctrlline_set_coords(SP_CTRLLINE(line), p1, p2);
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sp_ctrlline_set_rgba32 (SP_CTRLLINE(line), rgba);
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sp_canvas_item_show (line);
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c-file-style:"stroustrup"
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c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
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// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :