1 #define __LINE_GEOMETRY_C__
3 /*
4 * Routines for dealing with lines (intersections, etc.)
5 *
6 * Authors:
7 * Maximilian Albert <Anhalter42@gmx.de>
8 *
9 * Copyright (C) 2007 authors
10 *
11 * Released under GNU GPL, read the file 'COPYING' for more information
12 */
14 #include "line-geometry.h"
15 #include "inkscape.h"
16 #include "desktop-style.h"
17 #include "desktop-handles.h"
18 #include "display/sp-canvas.h"
19 #include "display/sodipodi-ctrl.h"
20 //#include "display/curve.cpp"
22 namespace Box3D {
24 /**
25 * Draw a line beginning at 'start'. If is_endpoint is true, use 'vec' as the endpoint
26 * of the segment. Otherwise interpret it as the direction of the line.
27 * FIXME: Think of a better way to distinguish between the two constructors of lines.
28 */
29 Line::Line(NR::Point const &start, NR::Point const &vec, bool is_endpoint) {
30 pt = start;
31 if (is_endpoint)
32 v_dir = vec - start;
33 else
34 v_dir = vec;
35 normal = v_dir.ccw();
36 d0 = NR::dot(normal, pt);
37 }
39 Line::Line(Line const &line) {
40 pt = line.pt;
41 v_dir = line.v_dir;
42 normal = line.normal;
43 d0 = line.d0;
44 }
46 Line &Line::operator=(Line const &line) {
47 pt = line.pt;
48 v_dir = line.v_dir;
49 normal = line.normal;
50 d0 = line.d0;
52 return *this;
53 }
55 NR::Maybe<NR::Point> Line::intersect(Line const &line) {
56 NR::Coord denom = NR::dot(v_dir, line.normal);
57 NR::Maybe<NR::Point> no_point = NR::Nothing();
58 if (fabs(denom) < 1e-6)
59 return no_point;
61 NR::Coord lambda = (line.d0 - NR::dot(pt, line.normal)) / denom;
62 return pt + lambda * v_dir;
63 }
65 void Line::set_direction(NR::Point const &dir)
66 {
67 v_dir = dir;
68 normal = v_dir.ccw();
69 d0 = NR::dot(normal, pt);
70 }
72 NR::Point Line::closest_to(NR::Point const &pt)
73 {
74 /* return the intersection of this line with a perpendicular line passing through pt */
75 NR::Maybe<NR::Point> result = this->intersect(Line(pt, (this->v_dir).ccw(), false));
76 g_return_val_if_fail (result, NR::Point (0.0, 0.0));
77 return *result;
78 }
80 double Line::lambda (NR::Point const pt)
81 {
82 double sign = (NR::dot (pt - this->pt, this->v_dir) > 0) ? 1.0 : -1.0;
83 double lambda = sign * NR::L2 (pt - this->pt);
84 // FIXME: It may speed things up (but how much?) if we assume that
85 // pt lies on the line and thus skip the following test
86 NR::Point test = point_from_lambda (lambda);
87 if (!pts_coincide (pt, test)) {
88 g_warning ("Point does not lie on line.\n");
89 return 0;
90 }
91 return lambda;
92 }
94 /* The coordinates of w with respect to the basis {v1, v2} */
95 std::pair<double, double> coordinates (NR::Point const &v1, NR::Point const &v2, NR::Point const &w)
96 {
97 double det = determinant (v1, v2);;
98 if (fabs (det) < epsilon) {
99 // vectors are not linearly independent; we indicate this in the return value(s)
100 return std::make_pair (HUGE_VAL, HUGE_VAL);
101 }
103 double lambda1 = determinant (w, v2) / det;
104 double lambda2 = determinant (v1, w) / det;
105 return std::make_pair (lambda1, lambda2);
106 }
108 /* whether w lies inside the sector spanned by v1 and v2 */
109 bool lies_in_sector (NR::Point const &v1, NR::Point const &v2, NR::Point const &w)
110 {
111 std::pair<double, double> coords = coordinates (v1, v2, w);
112 if (coords.first == HUGE_VAL) {
113 // catch the case that the vectors are not linearly independent
114 // FIXME: Can we assume that it's safe to return true if the vectors point in different directions?
115 return (NR::dot (v1, v2) < 0);
116 }
117 return (coords.first >= 0 and coords.second >= 0);
118 }
120 bool lies_in_quadrangle (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D, NR::Point const &pt)
121 {
122 return (lies_in_sector (D - A, B - A, pt - A) && lies_in_sector (D - C, B - C, pt - C));
123 }
125 static double pos_angle (NR::Point v, NR::Point w)
126 {
127 return fabs (NR::atan2 (v) - NR::atan2 (w));
128 }
130 /*
131 * Returns the two corners of the quadrangle A, B, C, D spanning the edge that is hit by a semiline
132 * starting at pt and going into direction dir.
133 * If none of the sides is hit, it returns a pair containing two identical points.
134 */
135 std::pair<NR::Point, NR::Point>
136 side_of_intersection (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D,
137 NR::Point const &pt, NR::Point const &dir)
138 {
139 NR::Point dir_A (A - pt);
140 NR::Point dir_B (B - pt);
141 NR::Point dir_C (C - pt);
142 NR::Point dir_D (D - pt);
144 std::pair<NR::Point, NR::Point> result;
145 double angle = -1;
146 double tmp_angle;
148 if (lies_in_sector (dir_A, dir_B, dir)) {
149 result = std::make_pair (A, B);
150 angle = pos_angle (dir_A, dir_B);
151 }
152 if (lies_in_sector (dir_B, dir_C, dir)) {
153 tmp_angle = pos_angle (dir_B, dir_C);
154 if (tmp_angle > angle) {
155 angle = tmp_angle;
156 result = std::make_pair (B, C);
157 }
158 }
159 if (lies_in_sector (dir_C, dir_D, dir)) {
160 tmp_angle = pos_angle (dir_C, dir_D);
161 if (tmp_angle > angle) {
162 angle = tmp_angle;
163 result = std::make_pair (C, D);
164 }
165 }
166 if (lies_in_sector (dir_D, dir_A, dir)) {
167 tmp_angle = pos_angle (dir_D, dir_A);
168 if (tmp_angle > angle) {
169 angle = tmp_angle;
170 result = std::make_pair (D, A);
171 }
172 }
173 if (angle == -1) {
174 // no intersection found; return a pair containing two identical points
175 return std::make_pair (A, A);
176 } else {
177 return result;
178 }
179 }
181 double cross_ratio (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D)
182 {
183 Line line (A, D);
184 double lambda_A = line.lambda (A);
185 double lambda_B = line.lambda (B);
186 double lambda_C = line.lambda (C);
187 double lambda_D = line.lambda (D);
189 if (fabs (lambda_D - lambda_A) < epsilon || fabs (lambda_C - lambda_B) < epsilon) {
190 // We return NR_HUGE so that we can catch this case in the calling functions
191 return NR_HUGE;
192 }
193 return (((lambda_C - lambda_A) / (lambda_D - lambda_A)) * ((lambda_D - lambda_B) / (lambda_C - lambda_B)));
194 }
196 double cross_ratio (VanishingPoint const &V, NR::Point const &B, NR::Point const &C, NR::Point const &D)
197 {
198 if (V.is_finite()) {
199 return cross_ratio (V.get_pos(), B, C, D);
200 } else {
201 if (B == D) {
202 // catch this case so that the line BD below is non-degenerate
203 return 0;
204 }
205 Line line (B, D);
206 double lambda_B = line.lambda (B);
207 double lambda_C = line.lambda (C);
208 double lambda_D = line.lambda (D);
210 if (fabs (lambda_C - lambda_B) < epsilon) {
211 // We return NR_HUGE so that we can catch this case in the calling functions
212 return NR_HUGE;
213 }
214 return (lambda_D - lambda_B) / (lambda_C - lambda_B);
215 }
216 }
218 NR::Point fourth_pt_with_given_cross_ratio (NR::Point const &A, NR::Point const &C, NR::Point const &D, double gamma)
219 {
220 Line line (A, D);
221 double lambda_A = line.lambda (A);
222 double lambda_C = line.lambda (C);
223 double lambda_D = line.lambda (D);
225 double beta = (lambda_C - lambda_A) / (lambda_D - lambda_A);
226 if (fabs (beta - gamma) < epsilon) {
227 // FIXME: How to handle the case when the point can't be computed?
228 // g_warning ("Cannot compute point with given cross ratio.\n");
229 return NR::Point (0.0, 0.0);
230 }
231 return line.point_from_lambda ((beta * lambda_D - gamma * lambda_C) / (beta - gamma));
232 }
234 void create_canvas_point(NR::Point const &pos, double size, guint32 rgba)
235 {
236 SPDesktop *desktop = inkscape_active_desktop();
237 SPCanvasItem * canvas_pt = sp_canvas_item_new(sp_desktop_controls(desktop), SP_TYPE_CTRL,
238 "size", size,
239 "filled", 1,
240 "fill_color", rgba,
241 "stroked", 1,
242 "stroke_color", 0x000000ff,
243 NULL);
244 SP_CTRL(canvas_pt)->moveto(pos);
245 }
247 void create_canvas_line(NR::Point const &p1, NR::Point const &p2, guint32 rgba)
248 {
249 SPDesktop *desktop = inkscape_active_desktop();
250 SPCanvasItem *line = sp_canvas_item_new(sp_desktop_controls(desktop),
251 SP_TYPE_CTRLLINE, NULL);
252 sp_ctrlline_set_coords(SP_CTRLLINE(line), p1, p2);
253 sp_ctrlline_set_rgba32 (SP_CTRLLINE(line), rgba);
254 sp_canvas_item_show (line);
255 }
257 } // namespace Box3D
259 /*
260 Local Variables:
261 mode:c++
262 c-file-style:"stroustrup"
263 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
264 indent-tabs-mode:nil
265 fill-column:99
266 End:
267 */
268 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :