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annotate +parametrization/dataSpline.m @ 1089:d7f6c10eab13 feature/dataspline

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Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
author Martin Almquist <malmquist@stanford.edu>
date Thu, 04 Apr 2019 17:57:24 -0700
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children b4054942e277
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
Martin Almquist <malmquist@stanford.edu>
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1 % Accepts data points (t_i, f_i) and returns a Curve object,
d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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2 % using spline interpolation.
d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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3 % The spline curve is parametrized with the arc length parametrization
d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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4 % to facilitate better grids.
d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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5 %
d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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6 % t_data - vector
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7 % f_data - vector
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8 % C - curve object
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9 function C = dataSpline(t_data, f_data)
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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11 assert(length(t_data)==length(f_data),'Vectors must be same length');
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12 m_data = length(t_data);
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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14 % Create spline interpolant
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15 f = parametrization.Curve.spline(t_data, f_data);
d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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17 % Reparametrize with a parameter s in [0, 1]
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18 tmin = min(t_data);
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19 tmax = max(t_data);
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20 t = @(s) tmin + s*(tmax-tmin);
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22 % Create parameterized curve
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23 g = @(s) [t(s); f(t(s))];
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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25 % Compute numerical derivative of curve using twice as many points as in data set
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26 m = 2*m_data;
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27 ops = sbp.D2Standard(m, {0, 1}, 6);
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28 gp = parametrization.Curve.numericalDerivative(g, ops.D1);
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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30 % Create curve object
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31 C = parametrization.Curve(g, gp);
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33 % Reparametrize with arclength parametrization
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34 C = C.arcLengthParametrization(m_data);
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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36 % To avoid nested function calls, evaluate curve and compute final spline.
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37 tv = linspace(0, 1, m_data);
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38 gv = C.g(tv);
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39 g = parametrization.Curve.spline(tv, gv);
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40 C = parametrization.Curve(g);
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d7f6c10eab13 Add function parametrization/dataSpline which accepts data points and returns a Curve object consisting of a spline interpolant with the arclength parametrization.
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42 end