math::geometry -
Geometrical computations
package require Tcl ? 8.3 ?
package require math::geometry ? 1.0.3 ?
::math::geometry::angle line
::math::geometry::calculateDistanceToLine P line
::math::geometry::calculateDistanceToLineSegment P linesegment
::math::geometry::calculateDistanceToPolyline P polyline
::math::geometry::findClosestPointOnLine P line
::math::geometry::findClosestPointOnLineSegment P linesegment
::math::geometry::findClosestPointOnPolyline P polyline
::math::geometry::lengthOfPolyline polyline
::math::geometry::movePointInDirection P direction dist
::math::geometry::lineSegmentsIntersect linesegment1 linesegment2
::math::geometry::findLineSegmentIntersection linesegment1 linesegment2
::math::geometry::findLineIntersection line1 line2
::math::geometry::polylinesIntersect polyline1 polyline2
::math::geometry::polylinesBoundingIntersect polyline1 polyline2 granularity
::math::geometry::intervalsOverlap y1 y2 y3 y4 strict
::math::geometry::rectanglesOverlap P1 P2 Q1 Q2 strict
::math::geometry::bbox polyline
::math::geometry::pointInsidePolygon P polyline
::math::geometry::rectangleInsidePolygon P1 P2 polyline
::math::geometry::areaPolygon polygon
The math::geometry package is a collection of functions for
computations and manipulations on two-dimensional geometrical objects,
such as points, lines and polygons.
The geometrical objects are implemented as plain lists of coordinates.
For instance a line is defined by a list of four numbers, the x- and
y-coordinate of a first point and the x- and y-coordinates of a second
point on the line.
The various types of object are recognised by the number of coordinate
pairs and the context in which they are used: a list of four elements
can be regarded as an infinite line, a finite line segment but also
as a polyline of one segment and a point set of two points.
Currently the following types of objects are distinguished:
-
point - a list of two coordinates representing the x- and
y-coordinates respectively.
-
line - a list of four coordinates, interpreted as the x- and
y-coordinates of two distinct points on the line.
-
line segment - a list of four coordinates, interpreted as the
x- and y-coordinates of the first and the last points on the line
segment.
-
polyline - a list of an even number of coordinates,
interpreted as the x- and y-coordinates of an ordered set of points.
-
polygon - like a polyline, but the implicit assumption is that
the polyline is closed (if the first and last points do not coincide,
the missing segment is automatically added).
-
point set - again a list of an even number of coordinates, but
the points are regarded without any ordering.
The package defines the following public procedures:
-
::math::geometry::angle line
-
Calculate the angle from the positive x-axis to a given line
(in two dimensions only).
| Type | Name | Mode |
| list | line | |
| | Coordinates of the line
|
-
::math::geometry::calculateDistanceToLine P line
-
Calculate the distance of point P to the (infinite) line and return the
result
| Type | Name | Mode |
| list | P | |
| | List of two numbers, the coordinates of the point
|
| list | line | |
| | List of four numbers, the coordinates of two points
on the line
|
-
::math::geometry::calculateDistanceToLineSegment P linesegment
-
Calculate the distance of point P to the (finite) line segment and
return the result.
| Type | Name | Mode |
| list | P | |
| | List of two numbers, the coordinates of the point
|
| list | linesegment | |
| | List of four numbers, the coordinates of the
first and last points of the line segment
|
-
::math::geometry::calculateDistanceToPolyline P polyline
-
Calculate the distance of point P to the polyline and
return the result.
| Type | Name | Mode |
| list | P | |
| | List of two numbers, the coordinates of the point
|
| list | polyline | |
| | List of numbers, the coordinates of the
vertices of the polyline
|
-
::math::geometry::findClosestPointOnLine P line
-
Return the point on a line which is closest to a given point.
| Type | Name | Mode |
| list | P | |
| | List of two numbers, the coordinates of the point
|
| list | line | |
| | List of four numbers, the coordinates of two points
on the line
|
-
::math::geometry::findClosestPointOnLineSegment P linesegment
-
Return the point on a line segment which is closest to a given
point.
| Type | Name | Mode |
| list | P | |
| | List of two numbers, the coordinates of the point
|
| list | linesegment | |
| | List of four numbers, the first and last
points on the line segment
|
-
::math::geometry::findClosestPointOnPolyline P polyline
-
Return the point on a polyline which is closest to a given
point.
| Type | Name | Mode |
| list | P | |
| | List of two numbers, the coordinates of the point
|
| list | polyline | |
| | List of numbers, the vertices of the polyline
|
-
::math::geometry::lengthOfPolyline polyline
-
Return the length of the polyline (note: it not regarded as a
polygon)
| Type | Name | Mode |
| list | polyline | |
| | List of numbers, the vertices of the polyline
|
-
::math::geometry::movePointInDirection P direction dist
-
Move a point over a given distance in a given direction and return the
new coordinates (in two dimensions only).
| Type | Name | Mode |
| list | P | |
| | Coordinates of the point to be moved
|
| double | direction | |
| | Direction (in degrees; 0 is to the right, 90
upwards)
|
| list | dist | |
| | Distance over which to move the point
|
-
::math::geometry::lineSegmentsIntersect linesegment1 linesegment2
-
Check if two line segments intersect or coincide. Returns 1 if that is
the case, 0 otherwise (in two dimensions only).
-
::math::geometry::findLineSegmentIntersection linesegment1 linesegment2
-
Find the intersection point of two line segments. Return the coordinates
or the keywords "coincident" or "none" if the line segments coincide or
have no points in common (in two dimensions only).
-
::math::geometry::findLineIntersection line1 line2
-
Find the intersection point of two (infinite) lines. Return the coordinates
or the keywords "coincident" or "none" if the lines coincide or
have no points in common (in two dimensions only).
| Type | Name | Mode |
| list | line1 | |
| | First line
|
| list | line2 | |
| | Second line
|
-
::math::geometry::polylinesIntersect polyline1 polyline2
-
Check if two polylines intersect or not (in two dimensions only).
-
::math::geometry::polylinesBoundingIntersect polyline1 polyline2 granularity
-
Check whether two polylines intersect, but reduce
the correctness of the result to the given granularity.
Use this for faster, but weaker, intersection checking.
How it works:
Each polyline is split into a number of smaller polylines,
consisting of granularity points each. If a pair of those smaller
lines' bounding boxes intersect, then this procedure returns 1,
otherwise it returns 0.
| Type | Name | Mode |
| list | polyline1 | |
| | First polyline
|
| list | polyline2 | |
| | Second polyline
|
| int | granularity | |
| | Number of points in each part (<=1 means check
every edge)
|
-
::math::geometry::intervalsOverlap y1 y2 y3 y4 strict
-
Check if two intervals overlap.
| Type | Name | Mode |
| double | y1,y2 | |
| | Begin and end of first interval
|
| double | y3,y4 | |
| | Begin and end of second interval
|
| logical | strict | |
| | Check for strict or non-strict overlap
|
-
::math::geometry::rectanglesOverlap P1 P2 Q1 Q2 strict
-
Check if two rectangles overlap.
| Type | Name | Mode |
| list | P1 | |
| | upper-left corner of the first rectangle
|
| list | P2 | |
| | lower-right corner of the first rectangle
|
| list | Q1 | |
| | upper-left corner of the second rectangle
|
| list | Q2 | |
| | lower-right corner of the second rectangle
|
| list | strict | |
| | choosing strict or non-strict interpretation
|
-
::math::geometry::bbox polyline
-
Calculate the bounding box of a polyline. Returns a list of four
coordinates: the upper-left and the lower-right corner of the box.
| Type | Name | Mode |
| list | polyline | |
| | The polyline to be examined
|
-
::math::geometry::pointInsidePolygon P polyline
-
Determine if a point is completely inside a polygon. If the point
touches the polygon, then the point is not completely inside the
polygon.
| Type | Name | Mode |
| list | P | |
| | Coordinates of the point
|
| list | polyline | |
| | The polyline to be examined
|
-
::math::geometry::rectangleInsidePolygon P1 P2 polyline
-
Determine if a rectangle is completely inside a polygon. If polygon
touches the rectangle, then the rectangle is not complete inside the
polygon.
| Type | Name | Mode |
| list | P1 | |
| | Upper-left corner of the rectangle
|
| list | P2 | |
| | Lower-right corner of the rectangle
|
| list | polygon | |
| | The polygon in question
|
-
::math::geometry::areaPolygon polygon
-
Calculate the area of a polygon.
| Type | Name | Mode |
| list | polygon | |
| | The polygon in question
|
This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category
math :: geometry of the
http://sourceforge.net/tracker/?group_id=12883.
Please also report any ideas for enhancements you may have for either
package and/or documentation.
math, plane geometry, point, line, distance, angle