Mercurial > repos > public > sbplib
annotate +parametrization/old/curve_discretise.m @ 1198:2924b3a9b921 feature/d2_compatible
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Fri, 16 Aug 2019 14:30:28 -0700 |
| parents | 81e0ead29431 |
| children |
| rev | line source |
|---|---|
| 0 | 1 % Discretises the curve g with the smallest number of points such that all segments |
| 2 % are shorter than h. If do_plot is true the points of the discretisation and | |
| 3 % the normals of the curve in those points are plotted. | |
| 4 % | |
| 5 % [t,p,d] = curve_discretise(g,h,do_plot) | |
| 6 % | |
| 7 % t is a vector of input values to g. | |
| 8 % p is a cector of points. | |
| 9 % d are the length of the segments. | |
| 10 function [t,p,d] = curve_discretise(g,h,do_plot) | |
| 11 default_arg('do_plot',false) | |
| 12 | |
| 13 n = 10; | |
| 14 | |
| 15 [t,p,d] = curve_discretise_n(g,n); | |
| 16 | |
| 17 % ni = 0; | |
| 18 while any(d>h) | |
| 19 [t,p,d] = curve_discretise_n(g,n); | |
| 20 n = ceil(n*d(1)/h); | |
| 21 % ni = ni+1; | |
| 22 end | |
| 23 | |
| 24 % nj = 0; | |
| 25 while all(d<h) | |
| 26 [t,p,d] = curve_discretise_n(g,n); | |
| 27 n = n-1; | |
| 28 % nj = nj+1; | |
| 29 end | |
| 30 [t,p,d] = curve_discretise_n(g,n+1); | |
| 31 | |
| 32 % fprintf('ni = %d, nj = %d\n',ni,nj); | |
| 33 | |
| 34 if do_plot | |
| 35 fprintf('n:%d max: %f min: %f\n', n, max(d),min(d)); | |
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36 p = parametrization.map_curve(g,t); |
| 0 | 37 figure |
| 38 show(g,t,h); | |
| 39 end | |
| 40 | |
| 41 end | |
| 42 | |
| 43 function [t,p,d] = curve_discretise_n(g,n) | |
| 44 t = linspace(0,1,n); | |
| 45 t = equalize_d(g,t); | |
| 46 d = D(g,t); | |
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parents:
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47 p = parametrization.map_curve(g,t); |
| 0 | 48 end |
| 49 | |
| 50 function d = D(g,t) | |
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51 p = parametrization.map_curve(g,t); |
| 0 | 52 |
| 53 d = zeros(1,length(t)-1); | |
| 54 for i = 1:length(d) | |
| 55 d(i) = norm(p(:,i) - p(:,i+1)); | |
| 56 end | |
| 57 end | |
| 58 | |
| 59 function t = equalize_d(g,t) | |
| 60 d = D(g,t); | |
| 61 v = d-mean(d); | |
| 62 while any(abs(v)>0.01*mean(d)) | |
| 63 dt = t(2:end)-t(1:end-1); | |
| 64 t(2:end) = t(2:end) - cumsum(dt.*v./d); | |
| 65 | |
| 66 t = t/t(end); | |
| 67 d = D(g,t); | |
| 68 v = d-mean(d); | |
| 69 end | |
| 70 end | |
| 71 | |
| 72 | |
| 73 function show(g,t,hh) | |
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248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
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74 p = parametrization.map_curve(g,t); |
| 0 | 75 |
| 76 | |
| 77 | |
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Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
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78 h = parametrization.plot_curve(g); |
| 0 | 79 h.LineWidth = 2; |
| 80 axis equal | |
| 81 hold on | |
| 82 h = plot(p(1,:),p(2,:),'.'); | |
| 83 h.Color = [0.8500 0.3250 0.0980]; | |
| 84 h.MarkerSize = 24; | |
| 85 hold off | |
| 86 | |
|
248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
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87 n = parametrization.curve_normals(g,t); |
| 0 | 88 hold on |
| 89 for i = 1:length(t) | |
| 90 p0 = p(:,i); | |
| 91 p1 = p0 + hh*n(:,i); | |
| 92 l = [p0, p1]; | |
| 93 h = plot(l(1,:),l(2,:)); | |
| 94 h.Color = [0.8500 0.3250 0.0980]; | |
| 95 end | |
| 96 | |
| 97 end |