Mercurial > repos > public > sbplib
annotate +parametrization/old/curve_discretise.m @ 1037:2d7ba44340d0 feature/burgers1d
Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Fri, 18 Jan 2019 09:02:02 +0100 |
| 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)); | |
|
248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
|
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); | |
|
248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
|
47 p = parametrization.map_curve(g,t); |
| 0 | 48 end |
| 49 | |
| 50 function d = D(g,t) | |
|
248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
|
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) | |
|
248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
|
74 p = parametrization.map_curve(g,t); |
| 0 | 75 |
| 76 | |
| 77 | |
|
248
81e0ead29431
Fixed package names in +parametrization
Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
|
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
|
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 |