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comparison +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
comparison
equal deleted inserted replaced
1097:eec03e78c6f2 1098:36d092a00040
1 % Accepts data points (t_i, f_i) and returns a Curve object, 1 % dataSpline calculates a Curve through the points f_i using cubic spline interpolation.
2 % using spline interpolation.
3 % The spline curve is parametrized with the arc length parametrization 2 % The spline curve is parametrized with the arc length parametrization
4 % to facilitate better grids. 3 % to facilitate better grids.
5 % 4 %
6 % t_data - vector 5 % f - m x D matrix of m points in D dimensions
7 % f_data - vector 6 function C = dataSpline(f)
8 % C - curve object 7 m = size(f, 1);
9 function C = dataSpline(t_data, f_data)
10 8
11 assert(length(t_data)==length(f_data),'Vectors must be same length'); 9 t = linspace(0,1,m);
12 m_data = length(t_data);
13 10
14 pp_g = spapi(4, t_data, f_data); 11 pp_g = spapi(4, t, f');
15 pp_gp = fnder(pp_g); 12 pp_gp = fnder(pp_g);
16 13
17 % Reparametrize with parameter s from 0 to 1 to use Curve class 14 g = @(t) fnval(pp_g, t);
18 tmin = min(t_data); 15 gp = @(t) fnval(pp_gp, t);
19 tmax = max(t_data);
20 t = @(s) tmin + s*(tmax-tmin);
21 dt_ds = @(s) 0*s + (tmax-tmin);
22 g = @(s) [t(s); fnval(pp_g, t(s))];
23 gp = @(s) [dt_ds(s); fnval(pp_gp, t(s)).*dt_ds(s)];
24 16
25 % Create Curve object and reparametrize with arclength parametrization
26 C = parametrization.Curve(g, gp); 17 C = parametrization.Curve(g, gp);
27 C = C.arcLengthParametrization(m_data); 18 C = C.arcLengthParametrization();
28 end 19 end