%% Copyright (c) 2011, INRA
%% 2005-2011, David Legland <david.legland@grignon.inra.fr>
%% 2011 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
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%% -*- texinfo -*-
%% @deftypefn {Function File} {} polygons2d ()
%% Description of functions operating on 2D polygons
%%
%%   The 'polygons' module contains functions operating on shapes composed
%%   of a vertex list, like polygons or polylines.
%%
%%   We call 'polyline' the curve defined by a series of vertices.
%%   A polyline can be either closed or open, depending on whether the last
%%   vertex is connected to the first one or not. This can be given as an
%%   option is some functions in the module.
%%   A 'polygon' is the planar domain delimited by a closed polyline. We
%%   sometimes want to consider 'complex polygons', whose boundary is
%%   composed of several disjoint domains. The domain defined by a single
%%   closed polyline is called 'simple polygon'.
%%   We call 'curve' a polyline with many vertices, such that the polyline
%%   can be considered as a discrete approximation of a "real" curve.
%%
%%   A simple polygon or polyline is represented by a N-by-2 array, each row
%%   of the array representing the coordinates of a vertex. 
%%   Simple polygons are assumed to be closed, so there is no need to repeat
%%   the first vertex at the end. 
%%   As both polygons and polylines can be represented by a list of vertex
%%   coordinates, some functions also consider the vertex list itself. Such
%%   functions are prefixed by 'pointSet'. Also, many functions prefixed by
%%   'polygon' or 'polyline' works also on the other type of shape.
%%
%%   For multiple-connected polygons, the different connected boundaries are
%%   separated by a row [NaN NaN].
%%
%%   For some functions, the orientation of the polygon can be relevant: CCW
%%   stands for 'Conter-Clockwise' (positive orientation), CW stands for
%%   'Clockwise'.
%%
%%   Polylines are parametrized in the following way:
%%   * the i-th vertex is located at position i-1
%%   * points of the i-th edge have positions ranging linearly from i-1 to i
%%   The parametrization domain for an open polyline is from 0 to Nv-1, and
%%   from 0 to Nv for a closed polyline (positions 0 and Nv correspond to
%%   the same point).
%%
%%   Example:
%%   % Simple polygon:
%%   P1 = [1 1;2 1;2 2;1 2];
%%   drawPolygon(P1);
%%   axis([0 5 0 5]);
%%   % Multiple polygon:
%%   P2 = [10 10;40 10;40 40;10 40;NaN NaN;20 20;20 30;30 30;30 20];
%%   figure;drawPolygon(P2); axis([0 50 0 50]);
%%
%%
%% Point Sets
%%   pointSetBounds            - Bounding box of a set of points
%%   pointSetsAverage          - Compute the average of several point sets
%%   minimumCaliperDiameter    - Minimum caliper diameter of a set of points
%%   findPoint                 - Find index of a point in an set from its coordinates
%%
%% Polylines
%%   polylinePoint             - Extract a point from a polyline
%%   polylineLength            - Return length of a polyline given as a list of points
%%   polylineCentroid          - Compute centroid of a curve defined by a series of points
%%   polylineSubcurve          - Extract a portion of a polyline
%%   reversePolyline           - Reverse a polyline, by iterating vertices from the end
%%   isPointOnPolyline         - Test if a point belongs to a polyline
%%   projPointOnPolyline       - Compute position of a point projected on a polyline
%%   distancePointPolyline     - Compute shortest distance between a point and a polyline
%%   distancePolylines         - Compute the shortest distance between 2 polylines
%%   intersectPolylines        - Find the common points between 2 polylines
%%   polylineSelfIntersections - Find self-intersections points of a polyline
%%
%% Curves (polylines with lot of vertices)
%%   parametrize               - Parametrization of a curve, based on edges length
%%   curvature                 - Estimate curvature of a polyline defined by points
%%   cart2geod                 - Convert cartesian coordinates to geodesic coord.
%%   geod2cart                 - Convert geodesic coordinates to cartesian coord.
%%   curveMoment               - Compute inertia moment of a 2D curve
%%   curveCMoment              - Compute centered inertia moment of a 2D curve
%%   curveCSMoment             - Compute centered scaled moment of a 2D curve
%%
%% Polygons
%%   polygonPoint              - Extract a point from a polygon
%%   polygonSubcurve           - Extract a portion of a polygon
%%   reversePolygon            - Reverse a polygon, by iterating vertices from the end
%%   projPointOnPolygon        - Compute position of a point projected on a polygon
%%   splitPolygons             - Convert a NaN separated polygon list to a cell array of polygons
%%   clipPolygon               - Clip a polygon with a rectangular box
%%   clipPolygonHP             - Clip a polygon with a Half-plane defined by a directed line
%%   intersectLinePolygon      - Intersection points between a line and a polygon
%%   intersectRayPolygon       - Intersection points between a ray and a polygon
%%   polygonSelfIntersections  - Find-self intersection points of a polygon
%%   convexHull                - Convex hull of a set of points
%%   polygonLoops              - Divide a possibly self-intersecting polygon into a set of simple loops
%%   expandPolygon             - Expand a polygon by a given (signed) distance
%%   medialAxisConvex          - Compute medial axis of a convex polygon
%%
%% Measures on Polygons
%%   isPointInPolygon          - Test if a point is located inside a polygon
%%   polygonContains           - Test if a point is contained in a multiply connected polygon
%%   polygonCentroid           - Compute the centroid (center of mass) of a polygon
%%   polygonArea               - Compute the signed area of a polygon
%%   polygonLength             - Perimeter of a polygon
%%   polygonNormalAngle        - Compute the normal angle at a vertex of the polygon
%%   polygonBounds             - Compute the bounding box of a polygon
%%   distancePointPolygon      - Compute shortest distance between a point and a polygon
%%   distancePolygons          - Compute the shortest distance between 2 polygons
%%
%% Triangles
%%   isPointInTriangle         - Test if a point is located inside a triangle
%%   triangleArea              - Area of a triangle
%%
%% Functions from stochastic geometry
%%   steinerPoint              - Compute steiner point (weighted centroid) of a polygon
%%   steinerPolygon            - Create a Steiner polygon from a set of vectors
%%   supportFunction           - Compute support function of a polygon
%%   convexification           - Compute the convexification of a polygon
%%
%% Input, Output and conversions
%%   readPolygon               - Read a polygon stored in a file
%%   polygonToRow              - Convert polygon coordinates to a row vector
%%   rowToPolygon              - Create a polygon from a row vector
%%   rectAsPolygon             - Convert a (centered) rectangle into a series of points
%%
%% Drawing functions
%%   drawPolyline              - Draw a polyline specified by a list of points
%%   drawPolygon               - Draw a polygon specified by a list of points
%%   fillPolygon               - Fill a polygon specified by a list of points
%%
%%
%%   Credits:
%%   * function intersectPolylines uses the 'interX' contribution from "NS"
%%       (file exchange 22441, called 'curve-intersections')
%%
%% -----
%% Author: David Legland
%% e-mail: david.legland@@grignon.inra.fr
%% created the  07/11/2005.
%% Homepage: @url{http://matgeom.sourceforge.net/}
%% @url{http://www.pfl-cepia.inra.fr/index.php?page=geom2d}
%% Copyright INRA - Cepia Software Platform.
%%
%% @end deftypefn 

function polygons2d ()

help('polygons2d');

endfunction
