--- /dev/null
+# Created by Octave 3.6.2, Sun Jun 10 09:53:40 2012 UTC <root@brouzouf>
+# name: cache
+# type: cell
+# rows: 3
+# columns: 19
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 9
+curvature
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1038
+ -- Function File: KAPPA = curvature (T, PX, PY,METHOD,DEGREE)
+ -- Function File: KAPPA = curvature (T, POLY,METHOD,DEGREE)
+ -- Function File: KAPPA = curvature (PX, PY,METHOD,DEGREE)
+ -- Function File: KAPPA = curvature (POINTS,METHOD,DEGREE)
+ -- Function File: [KAPPA POLY T] = curvature (...)
+ Estimate curvature of a polyline defined by points.
+
+ First compute an approximation of the curve given by PX and PY,
+ with the parametrization T. Then compute the curvature of
+ approximated curve for each point. METHOD used for approximation
+ can be only: 'polynom', with specified degree. Further methods
+ will be provided in a future version. T, PX, and PY are N-by-1
+ array of the same length. The points can be specified as a single
+ N-by-2 array.
+
+ If the argument T is not given, the parametrization is estimated
+ using function `parametrize'.
+
+ If requested, POLY contains the approximating polygon evlauted at
+ the parametrization T.
+
+ See also: parametrize, polygons2d
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 51
+Estimate curvature of a polyline defined by points.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 20
+distancePointPolygon
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 229
+ -- Function File: DIST = distancePointPolygon (POINT,POLY)
+ Compute shortest distance between a point and a polygon
+
+ See also: polygons2d, points2d, distancePointPolyline,
+ distancePointEdge, projPointOnPolyline
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 56
+Compute shortest distance between a point and a polygon
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 21
+distancePointPolyline
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 453
+ -- Function File: DIST = distancePointPolyline (POINT,POLY)
+ Compute shortest distance between a point and a polyline Example:
+ pt1 = [30 20];
+ pt2 = [30 5];
+ poly = [10 10;50 10;50 50;10 50];
+ distancePointPolyline([pt1;pt2], poly)
+ ans =
+ 10
+ 5
+
+ See also: polygons2d, points2d, distancePointEdge,
+ projPointOnPolyline
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 80
+Compute shortest distance between a point and a polyline Example:
+ p
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 16
+distancePolygons
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 114
+ -- Function File: DIST = distancePolygons (POLY1,POLY2)
+ Compute the shortest distance between 2 polygons
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 49
+Compute the shortest distance between 2 polygons
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+drawPolygon
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 589
+ -- Function File: H = drawPolygon (COORD)
+ -- Function File: H = drawPolygon (PX, PY)
+ -- Function File: H = drawPolygon (POLYS)
+ Draw a polygon specified by a list of points.
+
+ drawPolygon(COORD); Packs coordinates in a single [N*2] array.
+
+ drawPolygon(PX, PY); Specifies coordinates in separate arrays.
+
+ drawPolygon(POLYS) Packs coordinate of several polygons in a
+ cell array. Each element of the array is a Ni*2 double array.
+
+ H = drawPolygon(...); Also return a handle to the list of line
+ objects.
+
+ See also: polygons2d, drawCurve
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 45
+Draw a polygon specified by a list of points.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 13
+expandPolygon
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 930
+ -- Function File: LOOPS = expandPolygon (POLY, DIST)
+ Expand a polygon by a given (signed) distance
+
+ Associates to each edge of the polygon POLY the parallel line
+ located at distance DIST from the current edge, and compute
+ intersections with neighbor parallel lines. The resulting
+ polygon is simplified to remove inner "loops", and can be
+ disconnected. The result is a cell array, each cell containing
+ a simple linear ring.
+
+ This is a kind of dilation, but behaviour on corners is different.
+ This function keeps angles of polygons, but there is no direct
+ relation between length of 2 polygons.
+
+ It is also possible to specify negative distance, and get all
+ points inside the polygon. If the polygon is convex, the result
+ equals morphological erosion of polygon by a ball with radius
+ equal to the given distance.
+
+ See also: polygons2d
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 46
+Expand a polygon by a given (signed) distance
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 16
+medialAxisConvex
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 878
+ -- Function File: [N E] = medialAxisConvex (POLYGON)
+ Compute medial axis of a convex polygon
+
+ POLYGON is given as a set of points [x1 y1;x2 y2 ...], returns
+ the medial axis of the polygon as a graph. N is a set of nodes.
+ The first elements of N are the vertices of the original polygon.
+ E is a set of edges, containing indices of source and target
+ nodes. Edges are sorted according to order of creation. Index
+ of first vertex is lower than index of last vertex, i.e. edges
+ always point to newly created nodes.
+
+ Notes: - Is not fully implemented, need more development
+ (usually crashes for polygons with more than 6-7 points...)
+ - Works only for convex polygons. - Complexity is not optimal:
+ this algorithm is O(n*log n), but linear algorithms exist.
+
+ See also: polygons2d, bisector
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 40
+Compute medial axis of a convex polygon
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 11
+parametrize
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 1240
+ -- Function File: PAR = parametrize (POLY)
+ -- Function File: PAR = parametrize (PX,PY)
+ -- Function File: PAR = parametrize (...,NORMALIZE)
+ Parametrization of a curve, based on edges length
+
+ Returns a parametrization of the curve defined by the serie of
+ points, based on euclidean distance between two consecutive points.
+ POLY is a N-by-2 array, representing coordinates of vertices. The
+ result PAR is N-by-1, and contains the cumulative length of edges
+ until corresponding vertex. The function also accepts the polygon
+ as two inputs PX and PY representinx coordinates x and y
+ respectively. When optional argument NORMALIZE is non-empty PAR
+ is rescaled such that the last element equals 1, i.e.
+ `PAR(end)==1'.
+
+ Example
+ % Parametrize a circle approximation
+ poly = circleToPolygon([0 0 1], 200);
+ p = parametrize(poly);
+ p(end)
+ ans =
+ 6.2829
+ p = parametrize(poly,'norm');
+ p(end)
+ ans =
+ 1
+ p = parametrize(poly,true);
+ p(end)
+ ans =
+ 1
+
+ See also: polygons2d, polylineLength
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 50
+Parametrization of a curve, based on edges length
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 13
+polygon2shape
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 544
+ -- Function File: SHAPE = polygon2shape (POLYGON)
+ Converts a polygon to a shape with edges defined by smooth
+ polynomials.
+
+ POLYGON is a N-by-2 matrix, each row representing a vertex. SHAPE
+ is a N-by-1 cell, where each element is a pair of polynomials
+ compatible with polyval.
+
+ In its current state, the shape is formed by polynomials of degree
+ 1. Therefore the shape representation costs more memory except for
+ colinear points in the polygon.
+
+ See also: shape2polygon, simplifypolygon, polyval
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+Converts a polygon to a shape with edges defined by smooth polynomials.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 12
+polygonLoops
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 647
+ -- Function File: LOOPS = polygonLoops (POLY)
+ Divide a possibly self-intersecting polygon into a set of simple
+ loops
+
+ POLY is a polygone defined by a series of vertices, LOOPS is a
+ cell array of polygons, containing the same vertices of the
+ original polygon, but no loop self-intersect, and no couple of
+ loops intersect each other.
+
+ Example:
+ poly = [0 0;0 10;20 10;20 20;10 20;10 0];
+ loops = polygonLoops(poly);
+ figure(1); hold on;
+ drawPolygon(loops);
+ polygonArea(loops)
+
+ See also: polygons2d, polygonSelfIntersections
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 71
+Divide a possibly self-intersecting polygon into a set of simple loops
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 24
+polygonSelfIntersections
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 675
+ -- Function File: PTS = polygonSelfIntersections (POLY)
+ -- Function File: [PTS POS1 POS2] = polygonSelfIntersections (POLY)
+ Find-self intersection points of a polygon
+
+ Return the position of self intersection points
+
+ Also return the 2 positions of each intersection point (the
+ position when meeting point for first time, then position when
+ meeting point for the second time).
+
+ Example
+ # use a '8'-shaped polygon
+ poly = [10 0;0 0;0 10;20 10;20 20;10 20];
+ polygonSelfIntersections(poly)
+ ans =
+ 10 10
+
+ See also: polygons2d, polylineSelfIntersections
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 43
+Find-self intersection points of a polygon
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 10
+polygons2d
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 7637
+ -- 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:
+ `http://matgeom.sourceforge.net/'
+ `http://www.pfl-cepia.inra.fr/index.php?page=geom2d' Copyright
+ INRA - Cepia Software Platform.
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 50
+Description of functions operating on 2D polygons
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 25
+polylineSelfIntersections
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 830
+ -- Function File: PTS = polylineSelfIntersections (POLY)
+ Find self-intersections points of a polyline
+
+ Return the position of self intersection points
+
+ Also return the 2 positions of each intersection point (the
+ position when meeting point for first time, then position when
+ meeting point for the second time).
+
+ Example
+ # use a gamma-shaped polyline
+ poly = [0 0;0 10;20 10;20 20;10 20;10 0];
+ polylineSelfIntersections(poly)
+ ans =
+ 10 10
+
+ # use a 'S'-shaped polyline
+ poly = [10 0;0 0;0 10;20 10;20 20;10 20];
+ polylineSelfIntersections(poly)
+ ans =
+ 10 10
+
+ See also: polygons2d, intersectPolylines, polygonSelfIntersections
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 45
+Find self-intersections points of a polyline
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 14
+reversePolygon
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 300
+ -- Function File: POLY2 = reversePolygon (POLY)
+ Reverse a polygon, by iterating vertices from the end
+
+ POLY2 = reversePolygon(POLY) POLY2 has same vertices as POLY,
+ but in different order. The first vertex of the polygon is still
+ the same.
+
+ See also: reversePolyline
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 54
+Reverse a polygon, by iterating vertices from the end
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 15
+reversePolyline
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 269
+ -- Function File: POLY2 = reversePolyline (POLY)
+ Reverse a polyline, by iterating vertices from the end
+
+ POLY2 = reversePolyline(POLY) POLY2 has same vertices as POLY,
+ but POLY2(i,:) is the same as POLY(END-i+1,:).
+
+ See also: reversePolygon
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 55
+Reverse a polyline, by iterating vertices from the end
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 15
+simplifypolygon
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 231
+ -- Function File: SPOLY = simplifypolygon (POLY)
+ Simplify a polygon using the Ramer-Douglas-Peucker algorithm.
+
+ POLY is a N-by-2 matrix, each row representing a vertex.
+
+ See also: simplifypolyline, shape2polygon
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 61
+Simplify a polygon using the Ramer-Douglas-Peucker algorithm.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 16
+simplifypolyline
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 909
+ -- Function File: [PLINE2 IDX] = simplifypolyline (PLINE)
+ -- Function File: ... = simplifypolyline (...,PROPERTY,VALUE,...)
+ Simplify or subsample a polyline using the Ramer-Douglas-Peucker
+ algorithm, a.k.a. the iterative end-point fit algorithm or the
+ split-and-merge algorithm.
+
+ The PLINE as a N-by-2 matrix. Rows correspond to the verices
+ (compatible with `polygons2d'). The vector IDX constains the
+ indexes on vetices in PLINE that generates PLINE2, i.e. `pline2 =
+ pline(idx,:)'.
+
+ *Parameters*
+ `'Nmax''
+ Maximum number of vertices. Default value `1e3'.
+
+ `'Tol''
+ Tolerance for the error criteria. Default value `1e-4'.
+
+ `'MaxIter''
+ Maximum number of iterations. Default value `10'.
+
+ `'Method''
+ Not implemented.
+
+ Run `demo simplifypolyline' to see an example.
+
+ See also: curve2polyline, curveval
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 78
+Simplify or subsample a polyline using the Ramer-Douglas-Peucker
+algorithm, a.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 13
+splitPolygons
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 348
+ -- Function File: POLYGONS = splitPolygons (POLYGON)
+ Convert a NaN separated polygon list to a cell array of polygons.
+
+ POLYGON is a N-by-2 array of points, with possibly couples of NaN
+ values. The functions separates each component separated by NaN
+ values, and returns a cell array of polygons.
+
+ See also: polygons2d
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 65
+Convert a NaN separated polygon list to a cell array of polygons.
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 15
+supportFunction
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 522
+ -- Function File: H = suppportFunction (POLYGON)
+ -- Function File: H = suppportFunction (POLYGON, N)
+ -- Function File: H = suppportFunction (POLYGON, V)
+ Compute support function of a polygon
+
+ H = supportFunction(POLYGON, N) uses N points for suport
+ function approximation
+
+ H = supportFunction(POLYGON) assume 24 points for approximation
+
+ H = supportFunction(POLYGON, V) where V is a vector, uses vector
+ V of angles to compute support function.
+
+ See also: convexification
+
+
+
+
+
+# name: <cell-element>
+# type: sq_string
+# elements: 1
+# length: 38
+Compute support function of a polygon
+
+
+
+
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff