octave-geometry 1.7.0-1build1 / usr / share / octave / packages / geometry-1.7.0 / polynomialCurves2d / doc-cache

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drawPolynomialCurve


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 -- Function File: H = drawPolynomialCurve (BND, XCOEF, YCOEF)
 -- Function File: H = drawPolynomialCurve (BND, COEFS)
 -- Function File: H = drawPolynomialCurve (..., NPTS)
     Draw a polynomial curve approximation




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Draw a polynomial curve approximation



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polynomialCurveCentroid


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 -- Function File: C = polynomialCurveCentroid (T, XCOEF, YCOEF)
 -- Function File: C = polynomialCurveCentroid (T, COEFS)
 -- Function File: C = polynomialCurveCentroid (..., TOL)
     Compute the centroid of a polynomial curve

     XCOEF and YCOEF are row vectors of coefficients, in the form: [a0
     a1 a2 ...  an] T is a 1x2 row vector, containing the bounds of the
     parametrization variable: T = [T0 T1], with T taking all values
     between T0 and T1.  C contains coordinate of the polynomial curve
     centroid.

     COEFS is either a 2xN matrix (one row for the coefficients of each
     coordinate), or a cell array.

     TOL is the tolerance fo computation (absolute).

     See also: polynomialCurves2d, polynomialCurveLength.




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Compute the centroid of a polynomial curve



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polynomialCurveDerivative


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 -- Function File: V = polynomialCurveDerivative (T, XCOEF,YCOEF)
 -- Function File: V = polynomialCurveDerivative (T, COEFS)
     Compute derivative vector of a polynomial curve

     XCOEF and YCOEF are row vectors of coefficients, in the form: [a0
     a1 a2 ...  an] V is a 1x2 array containing direction of derivative
     of polynomial curve, computed for position T.  If T is a vector, V
     has as many rows as the length of T.

     COEFS is either a 2xN matrix (one row for the coefficients of each
     coordinate), or a cell array.

     See also: polynomialCurves2d, polynomialCurveNormal,
     polynomialCurvePoint, polynomialCurveCurvature.




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Compute derivative vector of a polynomial curve



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polynomialCurveFit


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 -- Function File: [XC, YC] = polynomialCurveFit (T, XT, YT, ORDER)
 -- Function File: [XC, YC] = polynomialCurveFit (T, POINTS, ORDER)
 -- Function File: [XC, YC] = polynomialCurveFit (..., TI, CONDI)
     Fit a polynomial curve to a series of points

     T is a Nx1 vector.

     XT and YT are coordinate for each parameter value (column vectors).
     ORDER is the degree of the polynomial used for interpolation.  XC
     and YC are polynomial coefficients, given in ORDER+1 row vectors,
     starting from degree 0 and up to degree ORDER.  POINTS specifies
     coordinate of points in a Nx2 array.

     Impose some specific conditions using TI and CONDI.

     TI is a value of the parametrization variable.  CONDI is a cell
     array, with 2 columns, and as many rows as the derivatives
     specified for the given TI.  Format for CONDI is:

     CONDI = {X_I, Y_I; X_I', Y_I'; X_I", Y_I"; ...};

     with X_I and Y_I being the imposed coordinate at position TI, X_I'
     and Y_I' being the imposed first derivatives, X_I" and Y_I" the
     imposed second derivatives, and so on...  To specify a derivative
     without specifying derivative with lower degree, value of lower
     derivative can be let empty, using '[]'.

     Requires the optimization Toolbox.

     Run 'demo polynomialCurveFit' to see exaples of use.

     See also: polynomialCurves2d.




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Fit a polynomial curve to a series of points



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polynomialCurvePoint


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 -- Function File: POINT = polynomialCurvePoint (T, XCOEF,YCOEF)
 -- Function File: POINT = polynomialCurvePoint (T, COEFS)
     Compute point corresponding to a position

     XCOEF and YCOEF are row vectors of coefficients, in the form: [a0
     a1 a2 ...  an] T is a either a scalar, or a column vector,
     containing values of the parametrization variable.  POINT is a 1x2
     array containing coordinate of point corresponding to position
     given by T.  If T is a vector, POINT has as many rows as T.

     COEFS is either a 2xN matrix (one row for the coefficients of each
     coordinate), or a cell array.

     See also: polynomialCurves2d, polynomialCurveLength.




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Compute point corresponding to a position



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polynomialCurveSetFit


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 -- Function File: COEFS= polynomialCurveSetFit (IMG)
 -- Function File: ... = polynomalCurveSetFit (IMG, DEG)
 -- Function File: [... LBL] = polynomalCurveSetFit (...)
     Fit a set of polynomial curves to a segmented image

     Result is a cell array of matrices.  Each matrix is DEG+1-by-2, and
     contains coefficients of polynomial curve for each coordinate.
     BNDS contains the boundary of the parametrizations.  IMG is first
     binarised, then skeletonized.

     Also returns an image of labels LBL for the segmented curves.  The
     max label is the number of curves, and the length of COEFS.

     Requires the toolboxes: - Optimization - Image Processing

     See also: polynomialCurves2d, polynomialCurveFit.




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Fit a set of polynomial curves to a segmented image