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%% 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>
%%
%% All rights reserved.
%% (simplified BSD License)
%%
%% Redistribution and use in source and binary forms, with or without
%% modification, are permitted provided that the following conditions are met:
%%
%% 1. Redistributions of source code must retain the above copyright notice, this
%% list of conditions and the following disclaimer.
%%
%% 2. Redistributions in binary form must reproduce the above copyright notice,
%% this list of conditions and the following disclaimer in the documentation
%% and/or other materials provided with the distribution.
%%
%% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
%% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
%% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
%% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
%% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
%% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
%% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
%% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
%% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
%% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
%% POSSIBILITY OF SUCH DAMAGE.
%%
%% The views and conclusions contained in the software and documentation are
%% those of the authors and should not be interpreted as representing official
%% policies, either expressed or implied, of copyright holder.
%% -*- 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
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