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polygons2d
The polygons module of the MatGeom library 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 'Counter-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]);
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
resamplePolyline - Distribute N points equally spaced on 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
intersectLinePolyline - Intersection points between a line and a polyline
intersectPolylines - Find the common points between 2 polylines
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
polygonPoint - Extract a point from a polygon
polygonSubcurve - Extract a portion of a polygon
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
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
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
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 - 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
resamplePolygon - Distribute N points equally spaced on a polygon
densifyPolygon - Add several points on each edge of the polygon
expandPolygon - Expand a polygon by a given (signed) distance
triangulatePolygon - Compute a triangulation of the polygon
polygonSymmetryAxis - Try to identify symmetry axis of polygon
medialAxisConvex - Compute medial axis of a convex polygon
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
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
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
rectAsPolygon - Convert a (centered) rectangle into a series of points
readPolygonSet - Read a set of simple polygons stored in a file
writePolygonSet - Write a set of simple polygons into a file
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