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1 % Discretises the curve g with the smallest number of points such that all segments
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2 % are shorter than h. If do_plot is true the points of the discretisation and
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3 % the normals of the curve in those points are plotted.
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4 %
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5 % [t,p,d] = curve_discretise(g,h,do_plot)
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6 %
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7 % t is a vector of input values to g.
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8 % p is a cector of points.
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9 % d are the length of the segments.
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10 function [t,p,d] = curve_discretise(g,h,do_plot)
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11 default_arg('do_plot',false)
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12
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13 n = 10;
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14
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15 [t,p,d] = curve_discretise_n(g,n);
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16
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17 % ni = 0;
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18 while any(d>h)
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19 [t,p,d] = curve_discretise_n(g,n);
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20 n = ceil(n*d(1)/h);
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21 % ni = ni+1;
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22 end
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23
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24 % nj = 0;
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25 while all(d<h)
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26 [t,p,d] = curve_discretise_n(g,n);
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27 n = n-1;
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28 % nj = nj+1;
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29 end
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30 [t,p,d] = curve_discretise_n(g,n+1);
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31
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32 % fprintf('ni = %d, nj = %d\n',ni,nj);
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33
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34 if do_plot
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35 fprintf('n:%d max: %f min: %f\n', n, max(d),min(d));
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36 p = grid.map_curve(g,t);
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37 figure
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38 show(g,t,h);
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39 end
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40
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41 end
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42
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43 function [t,p,d] = curve_discretise_n(g,n)
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44 t = linspace(0,1,n);
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45 t = equalize_d(g,t);
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46 d = D(g,t);
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47 p = grid.map_curve(g,t);
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48 end
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49
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50 function d = D(g,t)
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51 p = grid.map_curve(g,t);
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52
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53 d = zeros(1,length(t)-1);
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54 for i = 1:length(d)
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55 d(i) = norm(p(:,i) - p(:,i+1));
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56 end
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57 end
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58
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59 function t = equalize_d(g,t)
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60 d = D(g,t);
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61 v = d-mean(d);
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62 while any(abs(v)>0.01*mean(d))
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63 dt = t(2:end)-t(1:end-1);
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64 t(2:end) = t(2:end) - cumsum(dt.*v./d);
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65
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66 t = t/t(end);
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67 d = D(g,t);
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68 v = d-mean(d);
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69 end
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70 end
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71
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72
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73 function show(g,t,hh)
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74 p = grid.map_curve(g,t);
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75
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76
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77
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78 h = grid.plot_curve(g);
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79 h.LineWidth = 2;
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80 axis equal
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81 hold on
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82 h = plot(p(1,:),p(2,:),'.');
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83 h.Color = [0.8500 0.3250 0.0980];
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84 h.MarkerSize = 24;
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85 hold off
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86
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87 n = grid.curve_normals(g,t);
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88 hold on
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89 for i = 1:length(t)
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90 p0 = p(:,i);
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91 p1 = p0 + hh*n(:,i);
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92 l = [p0, p1];
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93 h = plot(l(1,:),l(2,:));
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94 h.Color = [0.8500 0.3250 0.0980];
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95 end
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96
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97 end |
