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.
removeMultipleVertices - Remove multiple vertices of a polygon or 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.
clipPolygonHP - Clip a polygon with a Half-plane defined by 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
polygonToRow - Convert polygon coordinates to a row vector.
rowToPolygon - Create a polygon from a row vector.
contourMatrixToPolylines - Converts a contour matrix array into a polyline set.
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')
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Author: David Legland
e-mail: david.legland@inrae.fr
created the 07/11/2005.
Project homepage: http://github.com/mattools/matGeom
Copyright INRAE