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## Copyright (C) 2024 David Legland
## 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
## 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 AUTHOR 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 the copyright holders.
%CONTENTS POLYGONS Manipulation of planar polygons and polylines.
% Version 1.24 07-Jun-2018 .
%
% 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]);
%
%
% Polylines
% polylinePoint - Extract a point from a polyline.
% polylineLength - Return length of a polyline given as a list of points.
% polylineCentroid - Computes the centroid of a curve defined by a series of points.
% polylineSubcurve - Extract a portion of a polyline.
% resamplePolyline - Distribute N points equally spaced on a polyline.
% resamplePolylineByLength - Resample a polyline with a fixed sampling step.
% 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.
% intersectLinePolyline - Intersection points between a line and a polyline.
% intersectPolylines - Find the common points between 2 polylines.
% clipPolyline - Clip an open polyline with a rectangular box.
% polylineSelfIntersections - Find self-intersection points of a polyline.
% simplifyPolyline - Douglas-Peucker simplification of a polyline.
% smoothPolyline - Smooth a polyline using local averaging.
% polylineCurvature - Estimate curvature on polyline vertices using polynomial fit.
% removeMultipleVertices - Remove multiple vertices of a polygon or polyline.
% padPolyline - Add vertices at each extremity of the polyline.
%
% Polygon basic manipulation
% reversePolygon - Reverse a polygon, by iterating vertices from the end.
% smoothPolygon - Smooth a polygon using local averaging.
% simplifyPolygon - Douglas-Peucker simplification of a polygon.
% projPointOnPolygon - Compute position of a point projected on a polygon.
% splitPolygons - Convert a NaN separated polygon list to a cell array of polygons.
% polygonLoops - Divide a possibly self-intersecting polygon into a set of simple loops.
% polygonPoint - Extract a point from a polygon.
% polygonSubcurve - Extract a portion of a polygon.
% polygonEdges - Return the edges of a simple or multiple polygon.
% polygonVertices - Extract all vertices of a (multi-)polygon.
%
% Polygon clipping and intersections
% intersectLinePolygon - Intersection points between a line and a polygon.
% intersectRayPolygon - Intersection points between a ray and a polygon.
% intersectEdgePolygon - Intersection point of an edge with a polygon.
% polygonSelfIntersections - Find self-intersection points of a polygon.
% clipPolygon - Clip a polygon with a rectangular box.
% clipPolygonByLine - Clip a polygon with a directed line.
%
% Point Sets
% 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.
% convexHull - Convex hull of a set of points.
% randomPointInPolygon - Generate random point(s) in a 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 - Computes the centroid (center of mass) of a polygon.
% polygonArea - Compute the signed area of a polygon.
% polygonEquivalentEllipse - Compute equivalent ellipse with same second order moments as polygon.
% polygonSecondAreaMoments - Compute second-order area moments of a polygon.
% polygonLength - Perimeter of a polygon.
% polygonNormalAngle - Normal angle at each vertex of a polygon.
% polygonBounds - Computes the bounding box of a polygon.
% polygonOuterNormal - Outer normal vector for a given vertex(ices).
% distancePointPolygon - Shortest distance between a point and a polygon.
% distancePolygons - Compute the shortest distance between 2 polygons.
% distancePolygonsNoCross - Compute the shortest distance between 2 polygons.
% polygonSignature - Polar signature of a polygon (polar distance to origin).
% signatureToPolygon - Reconstruct a polygon from its polar signature.
% polygonCurvature - Estimate curvature on polygon vertices using polynomial fit.
%
% More complex operations on polygons
% resamplePolygon - Distribute N points equally spaced on a polygon.
% resamplePolygonByLength - Resample a polygon with a fixed sampling step.
% densifyPolygon - Add several points on each edge of the polygon.
% expandPolygon - Expand a polygon by a given (signed) distance.
% triangulatePolygon - Computes a triangulation of the input polygon.
% polygonSymmetryAxis - Try to identify symmetry axis of polygon.
% polygonSkeleton - Skeletonization of a polygon with a dense distribution of vertices.
% medialAxisConvex - Compute medial axis of a convex polygon.
%
% Curves (polylines with lot of vertices)
% parametrize - Parametrization of a polyline, based on edges lengths.
% 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.
%
% 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
% contourMatrixToPolylines - Converts a contour matrix array into a polyline set.
% parsePolygon - Conversion between different polygon formats.
% polygonToPolyshape - Convert a matGeom polygon to a MATLAB polyshape object.
% polygonToRow - Convert polygon coordinates to a row vector.
% rowToPolygon - Create a polygon from a row vector.
% readPolygonSet - Read a set of simple polygons stored in a file.
% writePolygonSet - Write a set of simple polygons into a file.
%
% 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.
% drawVertices - Draw the vertices of a polygon or polyline.
%
%
% Credits:
% * function intersectPolylines uses the 'interX' contribution from "NS"
% (file exchange 22441, called 'curve-intersections')
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-11-07
% Copyright 2005-2023 INRAE
help(mfilename);
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