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curve2polyline


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 -- Function File: POLYLINE = curve2polyline (CURVE)
 -- Function File: POLYLINE = curve2polyline (...,PROPERTY,VALUE,...)
     Adaptive sampling of a parametric curve.

     The CURVE is described as a 2-by-N matrix.  Rows correspond to the
     polynomial (compatible with 'polyval') describing the respective
     component of the curve.  The curve must be parametrized in the
     interval [0,1].  The vertices of the polyline are accumulated in
     regions of the curve where the curvature is higher.

     *Parameters*
     ''Nmax''
          Maximum number of vertices.  Not used.
     ''Tol''
          Tolerance for the error criteria.  Default value '1e-4'.
     ''MaxIter''
          Maximum number of iterations.  Default value '10'.
     ''Method''
          Not implemented.

     This function is based on the algorithm described in L. H. de
     Figueiredo (1993).  "Adaptive Sampling of Parametric Curves".
     Graphic Gems III.

     See also: shape2polygon, curveval.


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Adaptive sampling of a parametric curve.



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curveval


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 -- Function File: P = curveval (CURVE, T)
     Evaluates parametric CURVE at T.


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Evaluates parametric CURVE at T.



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plotShape


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 -- H = plotShape (SHAPE)
 -- H = plotShape (..., PROP, VALUE)
     Pots a 2D shape defined by piecewise smooth polynomials in the
     current axis.

     SHAPE is a cell where each elements is a 2-by-(poly_degree+1)
     matrix containing a pair of polynomials.

     Additional property value pairs are passed to 'drawPolygon'.

     See also: drawPolygon, shape2polygon.


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Pots a 2D shape defined by piecewise smooth polynomials in the current
axis.



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shape2polygon


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 -- Function File: POLYGON = shape2polygon (SHAPE)
 -- Function File: POLYGON = shape2polygon (...,PROPERTY,VALUE,...)
     Transforms a 2D shape described by piecewise smooth polynomials
     into a polygon.

     SHAPE is a n-by-1 cell where each element is a pair of polynomials
     compatible with polyval.  POLYGON is a k-by-2 matrix, where each
     row represents a vertex.  The property-value pairs are passed to
     'curve2polyline'.

     See also: polygon2shape, curve2poyline.


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Transforms a 2D shape described by piecewise smooth polynomials into a
polygon.



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shapeArea


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 -- Function File: [A, CCW]= shapeArea (PP)
     Calculate the area of a 2D shape defined with piecewise smooth
     polynomials.

     Shape is defined with piecewise smooth polynomials.  PP is a cell
     where each elements is a 2-by-(poly_degree+1) array containing a
     pair of polynomials.

     'px(i,:) = pp{i}(1,:)' and 'py(i,:) = pp{i}(2,:)'.

     The returned area is always positive even if the shape is
     parametrized in a clockwise direction.  If the case of a clockwise
     parametrized shape 'CCW == -1' otherwise 'CCW == 1'.

     See also: shapeCentroid, shape2polygon, plotShape.


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Calculate the area of a 2D shape defined with piecewise smooth
polynomials.



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shapeCentroid


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 -- Function File: CM = shapeCentroid (PP)
     Centroid of a simple plane shape defined with piecewise smooth
     polynomials.

     The shape is defined with piecewise smooth polynomials.  PP is a
     cell where each elements is a 2-by-(poly_degree+1) matrix
     containing a pair of polynomials.  'px(i,:) = pp{i}(1,:)' and
     'py(i,:) = pp{i}(2,:)'.

     The edges of the shape should not self-intersect.  This function
     does not check for the sanity of the shape.

     See also: shapearea, shape2polygon.


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Centroid of a simple plane shape defined with piecewise smooth
polynomials.



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transformShape


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 -- Function File: NSHAPE = transformShape (SHAPE, T)
     Applies transformation to a shape defined by piecewise smooth
     polynomials.

     SHAPE is a cell where each elements is a 2-by-(poly_degree+1)
     matrix containing a pair of polynomials.

     Format of T can be one of :
           [c] , [a b] , [a b c] or [a b c]
           [f]   [d e]   [d e f]    [d e f]
                                    [0 0 1]

     See also: shape2polygon, plotShape.


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Applies transformation to a shape defined by piecewise smooth
polynomials.





