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# name: cache
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# rows: 3
# columns: 24
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
curvature
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1035
-- 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: 228
-- 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: 55
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: 449
-- 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:
pt1
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
distancePolygons
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 112
-- Function File: DIST = distancePolygons (POLY1,POLY2)
Compute the shortest distance between 2 polygons
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Compute the shortest distance between 2 polygons
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
drawPolygon
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# type: sq_string
# elements: 1
# length: 577
-- 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: 12
drawPolyline
# name: <cell-element>
# type: sq_string
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# length: 1073
-- Function File: = drawPolyline (, )
DRAWPOLYLINE Draw a polyline specified by a list of points
drawPolyline(COORD); packs coordinates in a single [N*2] array.
drawPolyline(PX, PY); specifies coordinates in separate arrays. PX
and PY must be column vectors with the same length.
drawPolyline(..., TYPE); where TYPE is either 'closed' or 'open',
specifies if last point must be connected to the first one
('closed') or not ('open'). Default is 'open'.
drawPolyline(..., PARAM, VALUE); specify plot options as described
for plot command.
H = drawPolyline(...) also return a handle to the list of line
objects.
Example:
# Draw a curve representing an ellipse
t = linspace(0, 2*pi, 100)';
px = 10*cos(t); py = 5*sin(t);
drawPolyline([px py], 'closed');
axis equal;
# The same, with different drawing options
drawPolyline([px py], 'closed', 'lineWidth', 2, 'lineStyle', '--');
See also: polygons2d, drawPolygon.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
DRAWPOLYLINE Draw a polyline specified by a list of points
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 13
expandPolygon
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# type: sq_string
# elements: 1
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-- 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
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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: 857
-- 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: 39
Compute medial axis of a convex polygon
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
parametrize
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# type: sq_string
# elements: 1
# length: 1235
-- 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.
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# type: sq_string
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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: 11
polygonArea
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 882
-- Function File: AREA = polygonArea (POINTS)
-- Function File: AREA = polygonArea (PX,PY)
Compute the signed area of a polygon.
Compute area of a polygon defined by POINTS. POINTS is a N-by-2
matrix containing coordinates of vertices.
Vertices of the polygon are supposed to be oriented
Counter-Clockwise (CCW). In this case, the signed area is positive.
If vertices are oriented Clockwise (CW), the signed area is
negative.
If polygon is self-crossing, the result is undefined.
If POINTS is a cell, each element is considered a polygon and the
area of each one is returned in the matrix AREA. The matrix has
the same shape as the cell.
References: Algorithm adapted from P. Bourke web page
http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
See also: polygons2d, polygonCentroid, drawPolygon.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
Compute the signed area of a polygon.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
polygonCentroid
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 584
-- Function File: [ PT, AREA ] = polygonCentroid (POINTS)
-- Function File: [ ... ]= polygonCentroid (PTX,PTY)
Compute the centroid (center of mass) of a polygon.
Computes the center of mass of a polygon defined by POINTS. POINTS
is a N-by-2 matrix. The two columns can be given separately using
PTX and PTY for the x and y component respectively.
The area of the polygon is returned in the second output argument.
Adapted from
<http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/>
See also: polygons2d, polygonArea, drawPolygon.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the centroid (center of mass) of a polygon.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
polygonLoops
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 642
-- 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: 70
Divide a possibly self-intersecting polygon into a set of simple loops
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 12
polygonPoint
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 132
-- Function File: POINT = polygonPoint (POLY, POS)
Extract a point from a polygon
See also: polygons2d, polylinePoint.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
Extract a point from a polygon
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
polygonSelfIntersections
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 669
-- 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: 42
Find-self intersection points of a polygon
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
polygonSubcurve
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 512
-- Function File: POLY2 = polygonSubcurve (POLYGON, POS0,POS1)
Extract a portion of a polygon
Create a new polyline, by keeping vertices located between
positions POS0 and POS1, and adding points corresponding to
positions POS0 and POS1 if they are not already vertices.
Example:
Nv = 100;
poly = circleAsPolygon ([10 20 30], Nv);
poly2 = polygonSubcurve (poly, 15, 65);
drawPolyline (poly2);
See also: polygons2d, polylineSubcurve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
Extract a portion of a polygon
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
polygons2d
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6874
-- 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>
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Description of functions operating on 2D polygons
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polylineSelfIntersections
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-- 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
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Find self-intersections points of a polyline
# name: <cell-element>
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# length: 14
reversePolygon
# name: <cell-element>
# type: sq_string
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-- 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
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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
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-- 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: 54
Reverse a polyline, by iterating vertices from the end
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
simplifypolygon
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-- 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
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Simplify a polygon using the Ramer-Douglas-Peucker algorithm.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
simplifypolyline
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-- 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
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Simplify or subsample a polyline using the Ramer-Douglas-Peucker
algorithm, a.k.
# name: <cell-element>
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splitPolygons
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-- 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
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Convert a NaN separated polygon list to a cell array of polygons.
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supportFunction
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-- 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.
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Compute support function of a polygon
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