


math::geometry(n)        Tcl Math Library       math::geometry(n)


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NAME
       math::geometry - Geometrical computations

SYNOPSIS
       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 granu-
       larity

       ::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

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math                          1.0.3                             1





math::geometry(n)        Tcl Math Library       math::geometry(n)


DESCRIPTION
       The  math::geometry  package  is a collection of functions for computa-
       tions 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:

       o      point  -  a  list  of two coordinates representing the x- and y-
              coordinates respectively.

       o      line - a list of four coordinates, interpreted as the x- and  y-
              coordinates of two distinct points on the line.

       o      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.

       o      polyline  - a list of an even number of coordinates, interpreted
              as the x- and y-coordinates of an ordered set of points.

       o      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).

       o      point set - again a list of an even number of  coordinates,  but
              the points are regarded without any ordering.


PROCEDURES
       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).

              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

              list P List of two numbers, the coordinates of the point



math                          1.0.3                             2





math::geometry(n)        Tcl Math Library       math::geometry(n)


              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.

              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.

              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.

              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.

              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.

              list P List of two numbers, the coordinates of the point



math                          1.0.3                             3





math::geometry(n)        Tcl Math Library       math::geometry(n)


              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)

              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).

              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).

              list linesegment1
                     First line segment

              list linesegment2
                     Second line segment


       ::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).

              list linesegment1
                     First line segment

              list linesegment2
                     Second line segment


       ::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).




math                          1.0.3                             4





math::geometry(n)        Tcl Math Library       math::geometry(n)


              list line1
                     First line

              list line2
                     Second line


       ::math::geometry::polylinesIntersect polyline1 polyline2
              Check  if  two  polylines  intersect  or  not (in two dimensions
              only).

              list polyline1
                     First polyline

              list polyline2
                     Second polyline


       ::math::geometry::polylinesBoundingIntersect polyline1 polyline2 granu-
       larity
              Check  whether  two polylines intersect, but reduce the correct-
              ness 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, con-
              sisting of granularity points each. If a pair of  those  smaller
              lines'  bounding boxes intersect, then this procedure returns 1,
              otherwise it returns 0.

              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.

              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                          1.0.3                             5





math::geometry(n)        Tcl Math Library       math::geometry(n)


       ::math::geometry::rectanglesOverlap P1 P2 Q1 Q2 strict
              Check if two rectangles overlap.

              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.

              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.

              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  com-
              plete inside the polygon.

              list P1
                     Upper-left corner of the rectangle

              list P2
                     Lower-right corner of the rectangle


              list polygon
                     The polygon in question




math                          1.0.3                             6





math::geometry(n)        Tcl Math Library       math::geometry(n)


       ::math::geometry::areaPolygon polygon
              Calculate the area of a polygon.

              list polygon
                     The polygon in question


BUGS, IDEAS, FEEDBACK
       This  document,  and the package it describes, will undoubtedly contain
       bugs and other problems.  Please report such in the  category  math  ::
       geometry     of     the     Tcllib    SF    Trackers    [http://source-
       forge.net/tracker/?group_id=12883].  Please also report any  ideas  for
       enhancements you may have for either package and/or documentation.

KEYWORDS
       angle, distance, line, math, plane geometry, point

CATEGORY
       Mathematics

COPYRIGHT
       Copyright (c) 2004 by Ideogramic ApS and other parties



































math                          1.0.3                             7


