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PL/SQL Determine if the coordinates of a point is within four points
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math::geometry(n) Tcl Math Library math::geometry(n) __________________________________________________________________________________________________________________________________________________ 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 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 _________________________________________________________________ DESCRIPTION
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 ele- ments 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 seg- ment. 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 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 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). 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 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. 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::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 complete 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::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://sourceforge.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 COPYRIGHT
Copyright (c) 2004 by Ideogramic ApS and other parties math 1.0.3 math::geometry(n)
