1math::geometry(n) Tcl Math Library math::geometry(n)
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8 math::geometry - Geometrical computations
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11 package require Tcl ?8.3?
12 package require math::geometry ?1.0.3?
14 ::math::geometry::angle line
16 ::math::geometry::calculateDistanceToLine P line
18 ::math::geometry::calculateDistanceToLineSegment P linesegment
20 ::math::geometry::calculateDistanceToPolyline P polyline
22 ::math::geometry::findClosestPointOnLine P line
24 ::math::geometry::findClosestPointOnLineSegment P linesegment
26 ::math::geometry::findClosestPointOnPolyline P polyline
28 ::math::geometry::lengthOfPolyline polyline
30 ::math::geometry::movePointInDirection P direction dist
32 ::math::geometry::lineSegmentsIntersect linesegment1 linesegment2
34 ::math::geometry::findLineSegmentIntersection linesegment1 linesegment2
36 ::math::geometry::findLineIntersection line1 line2
38 ::math::geometry::polylinesIntersect polyline1 polyline2
40 ::math::geometry::polylinesBoundingIntersect polyline1 polyline2 granu‐
42 larity
43 ::math::geometry::intervalsOverlap y1 y2 y3 y4 strict
45 ::math::geometry::rectanglesOverlap P1 P2 Q1 Q2 strict
47 ::math::geometry::bbox polyline
49 ::math::geometry::pointInsidePolygon P polyline
51 ::math::geometry::rectangleInsidePolygon P1 P2 polyline
53 ::math::geometry::areaPolygon polygon
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57
59 The math::geometry package is a collection of functions for computa‐
60 tions and manipulations on two-dimensional geometrical objects, such as
61 points, lines and polygons.
62 The geometrical objects are implemented as plain lists of coordinates.
64 For instance a line is defined by a list of four numbers, the x- and y-
65 coordinate of a first point and the x- and y-coordinates of a second
66 point on the line.
67 The various types of object are recognised by the number of coordinate
69 pairs and the context in which they are used: a list of four elements
70 can be regarded as an infinite line, a finite line segment but also as
71 a polyline of one segment and a point set of two points.
72 Currently the following types of objects are distinguished:
74 · point - a list of two coordinates representing the x- and y-
76 coordinates respectively.
77 · line - a list of four coordinates, interpreted as the x- and y-
79 coordinates of two distinct points on the line.
80 · line segment - a list of four coordinates, interpreted as the x-
82 and y-coordinates of the first and the last points on the line
83 segment.
84 · polyline - a list of an even number of coordinates, interpreted
86 as the x- and y-coordinates of an ordered set of points.
87 · polygon - like a polyline, but the implicit assumption is that
89 the polyline is closed (if the first and last points do not
90 coincide, the missing segment is automatically added).
91 · point set - again a list of an even number of coordinates, but
93 the points are regarded without any ordering.
94
96 The package defines the following public procedures:
97 ::math::geometry::angle line
99 Calculate the angle from the positive x-axis to a given line (in
100 two dimensions only).
101 list line
103 Coordinates of the line
104 ::math::geometry::calculateDistanceToLine P line
107 Calculate the distance of point P to the (infinite) line and
108 return the result
109 list P List of two numbers, the coordinates of the point
111 list line
113 List of four numbers, the coordinates of two points on
114 the line
115 ::math::geometry::calculateDistanceToLineSegment P linesegment
118 Calculate the distance of point P to the (finite) line segment
119 and return the result.
120 list P List of two numbers, the coordinates of the point
122 list linesegment
124 List of four numbers, the coordinates of the first and
125 last points of the line segment
126 ::math::geometry::calculateDistanceToPolyline P polyline
130 Calculate the distance of point P to the polyline and return the
131 result.
132 list P List of two numbers, the coordinates of the point
134 list polyline
136 List of numbers, the coordinates of the vertices of the
137 polyline
138 ::math::geometry::findClosestPointOnLine P line
141 Return the point on a line which is closest to a given point.
142 list P List of two numbers, the coordinates of the point
144 list line
146 List of four numbers, the coordinates of two points on
147 the line
148 ::math::geometry::findClosestPointOnLineSegment P linesegment
151 Return the point on a line segment which is closest to a given
152 point.
153 list P List of two numbers, the coordinates of the point
155 list linesegment
157 List of four numbers, the first and last points on the
158 line segment
159 ::math::geometry::findClosestPointOnPolyline P polyline
162 Return the point on a polyline which is closest to a given
163 point.
164 list P List of two numbers, the coordinates of the point
166 list polyline
168 List of numbers, the vertices of the polyline
169 ::math::geometry::lengthOfPolyline polyline
172 Return the length of the polyline (note: it not regarded as a
173 polygon)
174 list polyline
176 List of numbers, the vertices of the polyline
177 ::math::geometry::movePointInDirection P direction dist
180 Move a point over a given distance in a given direction and
181 return the new coordinates (in two dimensions only).
182 list P Coordinates of the point to be moved
184 double direction
186 Direction (in degrees; 0 is to the right, 90 upwards)
187 list dist
189 Distance over which to move the point
190 ::math::geometry::lineSegmentsIntersect linesegment1 linesegment2
193 Check if two line segments intersect or coincide. Returns 1 if
194 that is the case, 0 otherwise (in two dimensions only).
195 list linesegment1
197 First line segment
198 list linesegment2
200 Second line segment
201 ::math::geometry::findLineSegmentIntersection linesegment1 linesegment2
204 Find the intersection point of two line segments. Return the
205 coordinates or the keywords "coincident" or "none" if the line
206 segments coincide or have no points in common (in two dimensions
207 only).
208 list linesegment1
210 First line segment
211 list linesegment2
213 Second line segment
214 ::math::geometry::findLineIntersection line1 line2
217 Find the intersection point of two (infinite) lines. Return the
218 coordinates or the keywords "coincident" or "none" if the lines
219 coincide or have no points in common (in two dimensions only).
220 list line1
222 First line
223 list line2
225 Second line
226 ::math::geometry::polylinesIntersect polyline1 polyline2
229 Check if two polylines intersect or not (in two dimensions
230 only).
231 list polyline1
233 First polyline
234 list polyline2
236 Second polyline
237 ::math::geometry::polylinesBoundingIntersect polyline1 polyline2 granu‐
240 larity
241 Check whether two polylines intersect, but reduce the correct‐
242 ness of the result to the given granularity. Use this for
243 faster, but weaker, intersection checking.
244 How it works:
246 Each polyline is split into a number of smaller polylines, con‐
248 sisting of granularity points each. If a pair of those smaller
249 lines' bounding boxes intersect, then this procedure returns 1,
250 otherwise it returns 0.
251 list polyline1
253 First polyline
254 list polyline2
256 Second polyline
257 int granularity
259 Number of points in each part (<=1 means check every
260 edge)
261 ::math::geometry::intervalsOverlap y1 y2 y3 y4 strict
264 Check if two intervals overlap.
265 double y1,y2
267 Begin and end of first interval
268 double y3,y4
270 Begin and end of second interval
271 logical strict
273 Check for strict or non-strict overlap
274 ::math::geometry::rectanglesOverlap P1 P2 Q1 Q2 strict
277 Check if two rectangles overlap.
278 list P1
280 upper-left corner of the first rectangle
281 list P2
283 lower-right corner of the first rectangle
284 list Q1
286 upper-left corner of the second rectangle
287 list Q2
289 lower-right corner of the second rectangle
290 list strict
292 choosing strict or non-strict interpretation
293 ::math::geometry::bbox polyline
296 Calculate the bounding box of a polyline. Returns a list of four
297 coordinates: the upper-left and the lower-right corner of the
298 box.
299 list polyline
301 The polyline to be examined
302 ::math::geometry::pointInsidePolygon P polyline
305 Determine if a point is completely inside a polygon. If the
306 point touches the polygon, then the point is not completely
307 inside the polygon.
308 list P Coordinates of the point
310 list polyline
312 The polyline to be examined
313 ::math::geometry::rectangleInsidePolygon P1 P2 polyline
316 Determine if a rectangle is completely inside a polygon. If
317 polygon touches the rectangle, then the rectangle is not com‐
318 plete inside the polygon.
319 list P1
321 Upper-left corner of the rectangle
322 list P2
324 Lower-right corner of the rectangle
325 list polygon
328 The polygon in question
329 ::math::geometry::areaPolygon polygon
332 Calculate the area of a polygon.
333 list polygon
335 The polygon in question
336
338 This document, and the package it describes, will undoubtedly contain
339 bugs and other problems. Please report such in the category math ::
340 geometry of the Tcllib SF Trackers [http://source‐
341 forge.net/tracker/?group_id=12883]. Please also report any ideas for
342 enhancements you may have for either package and/or documentation.
343
345 angle, distance, line, math, plane geometry, point
346
348 Copyright (c) 2004 by Ideogramic ApS and other parties
349math 1.0.3 math::geometry(n)