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 g_return_val_if_fail(fabs(denom) > 1e-6, no_point );
60 NR::Coord lambda = (line.d0 - NR::dot(pt, line.normal)) / denom;
61 return pt + lambda * v_dir;
62 }
64 void Line::set_direction(NR::Point const &dir)
65 {
66 v_dir = dir;
67 normal = v_dir.ccw();
68 d0 = NR::dot(normal, pt);
69 }
71 NR::Point Line::closest_to(NR::Point const &pt)
72 {
73 /* return the intersection of this line with a perpendicular line passing through pt */
74 NR::Maybe<NR::Point> result = this->intersect(Line(pt, (this->v_dir).ccw(), false));
75 g_return_val_if_fail (result, NR::Point (0.0, 0.0));
76 return *result;
77 }
79 double Line::lambda (NR::Point const pt)
80 {
81 double sign = (NR::dot (pt - this->pt, this->v_dir) > 0) ? 1.0 : -1.0;
82 double lambda = sign * NR::L2 (pt - this->pt);
83 // FIXME: It may speed things up (but how much?) if we assume that
84 // pt lies on the line and thus skip the following test
85 NR::Point test = point_from_lambda (lambda);
86 if (!pts_coincide (pt, test)) {
87 g_warning ("Point does not lie on line.\n");
88 return 0;
89 }
90 return lambda;
91 }
93 inline static double determinant (NR::Point const &a, NR::Point const &b)
94 {
95 return (a[NR::X] * b[NR::Y] - a[NR::Y] * b[NR::X]);
96 }
98 /* The coordinates of w with respect to the basis {v1, v2} */
99 std::pair<double, double> coordinates (NR::Point const &v1, NR::Point const &v2, NR::Point const &w)
100 {
101 double det = determinant (v1, v2);;
102 if (fabs (det) < epsilon) {
103 // vectors are not linearly independent; we indicate this in the return value(s)
104 return std::make_pair (HUGE_VAL, HUGE_VAL);
105 }
107 double lambda1 = determinant (w, v2) / det;
108 double lambda2 = determinant (v1, w) / det;
109 return std::make_pair (lambda1, lambda2);
110 }
112 /* whether w lies inside the sector spanned by v1 and v2 */
113 bool lies_in_sector (NR::Point const &v1, NR::Point const &v2, NR::Point const &w)
114 {
115 std::pair<double, double> coords = coordinates (v1, v2, w);
116 if (coords.first == HUGE_VAL) {
117 // catch the case that the vectors are not linearly independent
118 // FIXME: Can we assume that it's safe to return true if the vectors point in different directions?
119 return (NR::dot (v1, v2) < 0);
120 }
121 return (coords.first >= 0 and coords.second >= 0);
122 }
124 static double pos_angle (NR::Point A, NR::Point B)
125 {
126 return fabs (NR::atan2 (A) - NR::atan2 (B));
127 }
129 /*
130 * Returns the two corners of the quadrangle A, B, C, D spanning the edge that is hit by a semiline
131 * starting at pt and going into direction dir.
132 * If none of the sides is hit, it returns a pair containing two identical points.
133 */
134 std::pair<NR::Point, NR::Point>
135 side_of_intersection (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D,
136 NR::Point const &pt, NR::Point const &dir)
137 {
138 NR::Point dir_A (A - pt);
139 NR::Point dir_B (B - pt);
140 NR::Point dir_C (C - pt);
141 NR::Point dir_D (D - pt);
143 std::pair<NR::Point, NR::Point> result;
144 double angle = -1;
145 double tmp_angle;
147 if (lies_in_sector (dir_A, dir_B, dir)) {
148 result = std::make_pair (A, B);
149 angle = pos_angle (dir_A, dir_B);
150 }
151 if (lies_in_sector (dir_B, dir_C, dir)) {
152 tmp_angle = pos_angle (dir_B, dir_C);
153 if (tmp_angle > angle) {
154 angle = tmp_angle;
155 result = std::make_pair (B, C);
156 }
157 }
158 if (lies_in_sector (dir_C, dir_D, dir)) {
159 tmp_angle = pos_angle (dir_C, dir_D);
160 if (tmp_angle > angle) {
161 angle = tmp_angle;
162 result = std::make_pair (C, D);
163 }
164 }
165 if (lies_in_sector (dir_D, dir_A, dir)) {
166 tmp_angle = pos_angle (dir_D, dir_A);
167 if (tmp_angle > angle) {
168 angle = tmp_angle;
169 result = std::make_pair (D, A);
170 }
171 }
172 if (angle == -1) {
173 // no intersection found; return a pair containing two identical points
174 return std::make_pair (A, A);
175 } else {
176 return result;
177 }
178 }
180 double cross_ratio (NR::Point const &A, NR::Point const &B, NR::Point const &C, NR::Point const &D)
181 {
182 Line line (A, D);
183 double lambda_A = line.lambda (A);
184 double lambda_B = line.lambda (B);
185 double lambda_C = line.lambda (C);
186 double lambda_D = line.lambda (D);
188 if (fabs (lambda_D - lambda_A) < epsilon || fabs (lambda_C - lambda_B) < epsilon) {
189 // FIXME: What should we return if the cross ratio can't be computed?
190 return 0;
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 Line line (B, D);
202 double lambda_B = line.lambda (B);
203 double lambda_C = line.lambda (C);
204 double lambda_D = line.lambda (D);
206 if (fabs (lambda_C - lambda_B) < epsilon) {
207 // FIXME: What should we return if the cross ratio can't be computed?
208 return 0;
209 //return NR_HUGE;
210 }
211 return (lambda_D - lambda_B) / (lambda_C - lambda_B);
212 }
213 }
215 NR::Point fourth_pt_with_given_cross_ratio (NR::Point const &A, NR::Point const &C, NR::Point const &D, double gamma)
216 {
217 Line line (A, D);
218 double lambda_A = line.lambda (A);
219 double lambda_C = line.lambda (C);
220 double lambda_D = line.lambda (D);
222 double beta = (lambda_C - lambda_A) / (lambda_D - lambda_A);
223 if (fabs (beta - gamma) < epsilon) {
224 // FIXME: How to handle the case when the point can't be computed?
225 // g_warning ("Cannot compute point with given cross ratio.\n");
226 return NR::Point (0.0, 0.0);
227 }
228 return line.point_from_lambda ((beta * lambda_D - gamma * lambda_C) / (beta - gamma));
229 }
231 void create_canvas_point(NR::Point const &pos, double size, guint32 rgba)
232 {
233 SPDesktop *desktop = inkscape_active_desktop();
234 SPCanvasItem * canvas_pt = sp_canvas_item_new(sp_desktop_controls(desktop), SP_TYPE_CTRL,
235 "size", size,
236 "filled", 1,
237 "fill_color", rgba,
238 "stroked", 1,
239 "stroke_color", 0x000000ff,
240 NULL);
241 SP_CTRL(canvas_pt)->moveto(pos);
242 }
244 void create_canvas_line(NR::Point const &p1, NR::Point const &p2, guint32 rgba)
245 {
246 SPDesktop *desktop = inkscape_active_desktop();
247 SPCanvasItem *line = sp_canvas_item_new(sp_desktop_controls(desktop),
248 SP_TYPE_CTRLLINE, NULL);
249 sp_ctrlline_set_coords(SP_CTRLLINE(line), p1, p2);
250 sp_ctrlline_set_rgba32 (SP_CTRLLINE(line), rgba);
251 sp_canvas_item_show (line);
252 }
254 } // namespace Box3D
256 /*
257 Local Variables:
258 mode:c++
259 c-file-style:"stroustrup"
260 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
261 indent-tabs-mode:nil
262 fill-column:99
263 End:
264 */
265 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :