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annotate +parametrization/dataSpline.m @ 1098:36d092a00040 feature/dataspline

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Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
author Martin Almquist <malmquist@stanford.edu>
date Tue, 09 Apr 2019 09:50:44 -0700
parents fdff002ebb32
children 60c875c18de3
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
1098
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
1 % dataSpline calculates a Curve through the points f_i using cubic spline interpolation.
1089
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>
parents:
diff changeset
2 % 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.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
3 % 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.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
4 %
1098
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
5 % f - m x D matrix of m points in D dimensions
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
6 function C = dataSpline(f)
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
7 m = size(f, 1);
1089
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>
parents:
diff changeset
8
1098
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
9 t = linspace(0,1,m);
1089
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>
parents:
diff changeset
10
1098
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
11 pp_g = spapi(4, t, f');
1092
47a72344db71 Bugfix in dataSpline(), reparameterize with parameter from 0 to 1 before using Curve.
Martin Almquist <malmquist@stanford.edu>
parents: 1091
diff changeset
12 pp_gp = fnder(pp_g);
1089
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>
parents:
diff changeset
13
1098
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
14 g = @(t) fnval(pp_g, t);
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
15 gp = @(t) fnval(pp_gp, t);
1089
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>
parents:
diff changeset
16
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>
parents:
diff changeset
17 C = parametrization.Curve(g, gp);
1098
36d092a00040 Bugfix Curve.arcLengthParametrization() by using linear interpolation instead of higher-order spline for parameter as a funciton of arclength. Generalize dataSpline() to curves in higher dimensions.
Martin Almquist <malmquist@stanford.edu>
parents: 1093
diff changeset
18 C = C.arcLengthParametrization();
1089
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>
parents:
diff changeset
19 end