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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## 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
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##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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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
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