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In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 29 Nov 2015 22:23:09 +0100
parents 3c39dd714fb6
children b30f3d8845f4
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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0
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1 classdef Curve
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2 properties
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3 g
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4 gp
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5 transformation
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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6 arc_length_fun
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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7
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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8 % arc_length_fun:
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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9 % function handle. arc_length(s)=distance
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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10 % between t=0 and t=s.
0
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11 end
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12 methods
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13 %TODO:
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14 % Errors or FD if there is no derivative function added.
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3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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15 % -semi-done
0
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16
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17 % Concatenation of curves
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18 % Subsections of curves
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3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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19 % Stretching of curve paramter - semi-done
0
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20 % Curve to cell array of linesegments
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21
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22 % Should supply either derivative or a difference operator D1
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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23 function obj = Curve(g,gp,transformation,D1,arc_length_fun)
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24 default_arg('gp',[]);
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25 default_arg('transformation',[]);
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3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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26 default_arg('D1',[]);
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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27 default_arg('arc_length_fun',[]);
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28 p_test = g(0);
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29 assert(all(size(p_test) == [2,1]), 'A curve parametrization must return a 2x1 vector.');
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3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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31 if(isempty(gp) && isempty(D1));
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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32 % Should be error instead of disp.
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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33 disp(['You really should supply either the exact derivative ',...
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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34 'or a suitable difference operator to compute an approximation.']);
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3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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35 elseif(isempty(gp))
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36 gp = grid.Curve.numerical_derivative(g,D1);
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37 end
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38
0
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39 if ~isempty(transformation)
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40 transformation.base_g = g;
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41 transformation.base_gp = gp;
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42 [g,gp] = grid.Curve.transform_g(g,gp,transformation);
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43 end
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44
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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45 if(isempty(arc_length_fun))
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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46 if(~isempty(D1)); N = length(D1); % Same accuracy as for deriv.
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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47 else N = 101; % Best way to let user choose?
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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48 end
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49 tvec = linspace(0,1,N);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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50 arc_vec = grid.Curve.arc_length(gp,0,tvec);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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51 arc_length_fun = grid.Curve.spline(tvec,arc_vec);
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52 end
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53
0
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54 obj.g = g;
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55 obj.gp = gp;
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56 obj.transformation = transformation;
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57 obj.arc_length_fun = arc_length_fun;
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60 end
0
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61
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62 % Made up length calculation!! Science this before actual use!!
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63 % Calculates the length of the curve. Makes sure the longet segment used is shorter than h_max.
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64 function [L,t] = curve_length(C,h_max)
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65 default_arg('h_max',0.001);
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66 g = C.g;
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67 h = 0.1;
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68 m = 1/h+1;
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69 t = linspace(0,1,m);
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70
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71 [p,d] = get_d(t,g);
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72
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73 while any(d>h_max)
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74 I = find(d>h_max);
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75
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76 % plot(p(1,:),p(2,:),'.')
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77 % waitforbuttonpress
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78
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79 new_t = [];
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80 for i = I
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81 new_t(end +1) = (t(i)+t(i+1))/2;
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82 end
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83 t = [t new_t];
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84 t = sort(t);
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85
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86 [p,d] = get_d(t,g);
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87 end
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88
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89 L = sum(d);
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90
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91 function [p,d] = get_d(t,g)
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92 n = length(t);
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93
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94 p = zeros(2,n);
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95 for i = 1:n
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96 p(:,i) = g(t(i));
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97 end
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98
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99 d = zeros(1,n-1);
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100 for i = 1:n-1
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101 d(i) = norm(p(:,i) - p(:,i+1));
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102 end
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103 end
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104 end
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105
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106 function n = normal(obj,t)
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107 deriv = obj.gp(t);
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108 normalization = sqrt(sum(deriv.^2,1));
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109 n = [-deriv(2,:)./normalization; deriv(1,:)./normalization];
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110 end
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111
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112
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113 % Plots a curve g(t) for 0<t<1, using n points. Returns a handle h to the plotted curve.
0
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114 % h = plot_curve(g,n)
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115 function h = plot(obj,n,marker)
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116 default_arg('n',100);
87
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117 default_arg('marker','line')
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118
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119 t = linspace(0,1,n);
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120
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121 p = obj.g(t);
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122
87
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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123 switch marker
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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124 case 'line'
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Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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125 h = line(p(1,:),p(2,:));
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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126 otherwise
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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127 h = plot(p(1,:),p(2,:),marker);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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128 end
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
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129 end
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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130
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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131 % Plots the derivative gp(t) for 0<t<1, using n points. Returns a handle h to the plotted curve.
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132 % h = plot_curve(gp,n)
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133 function h = plot_derivative(obj,n,marker)
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134 default_arg('n',100);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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135 default_arg('marker','line')
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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136
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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137 t = linspace(0,1,n);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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138
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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139 p = obj.gp(t);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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140
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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141 switch marker
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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142 case 'line'
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143 h = line(p(1,:),p(2,:));
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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144 otherwise
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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145 h = plot(p(1,:),p(2,:),marker);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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146 end
0
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147 end
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148
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149 function h= plot_normals(obj,l,n,m)
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150 default_arg('l',0.1);
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151 default_arg('n',10);
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152 default_arg('m',100);
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153 t_n = linspace(0,1,n);
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154
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155 normals = obj.normal(t_n)*l;
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156
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157 n0 = obj.g(t_n);
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158 n1 = n0 + normals;
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159
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160 h = line([n0(1,:); n1(1,:)],[n0(2,:); n1(2,:)]);
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161 set(h,'Color',Color.red);
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162 obj.plot(m);
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163 end
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164
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165 function h= show(obj,name)
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166 p = obj.g(1/2);
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167 n = obj.normal(1/2);
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168 p = p + n*0.1;
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169
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170 % Add arrow
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171
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172 h = text(p(1),p(2),name);
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173 h.HorizontalAlignment = 'center';
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174 h.VerticalAlignment = 'middle';
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175
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176 obj.plot();
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177 end
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178 % Shows curve with name and arrow for direction.
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179
86
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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180
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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181 function curve = stretch_parameter(obj,type)
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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parents: 0
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182 default_arg('type','arc_length');
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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183 switch type
87
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184 % Arc length parameterization.
86
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Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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185 case 'arc_length'
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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186 arcLength = obj.arc_length_fun;
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
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187 arcPar = @(t) util.fzero_vec(@(s)arcLength(s) - t*arcLength(1),[0-10*eps,1+10*eps]);
86
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Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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188 g_new = @(t)obj.g(arcPar(t));
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parents: 0
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189 gp_old = obj.gp;
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parents: 0
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190 gp_new = @(t) normalize(gp_old(arcPar(t)));
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Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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191
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0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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192 arc_len_new = @(t) t;
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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193 curve = grid.Curve(g_new,gp_new,[],[],arc_len_new);
86
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parents: 0
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194
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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195 otherwise
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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196 error('That stretching is not implemented.');
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Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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197 end
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parents: 0
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198
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
199 end
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Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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200
0
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201 % how to make it work for methods without returns
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202 function p = subsref(obj,S)
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203 %Should i add error checking here?
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204 %Maybe if you want performance you fetch obj.g and then use that
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205 switch S(1).type
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206 case '()'
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207 p = obj.g(S.subs{1});
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208 % case '.'
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209
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210 % p = obj.(S.subs);
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211 otherwise
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212 p = builtin('subsref',obj,S);
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213 % error()
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214 end
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215 end
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216
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217
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218
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219
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220 %% TRANSFORMATION OF A CURVE
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221 function D = reverse(C)
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222 % g = C.g;
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223 % gp = C.gp;
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224 % D = grid.Curve(@(t)g(1-t),@(t)-gp(1-t));
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225 D = C.transform([],[],-1);
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226 end
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227
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228 function D = transform(C,A,b,flip)
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229 default_arg('A',[1 0; 0 1]);
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230 default_arg('b',[0; 0]);
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231 default_arg('flip',1);
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232 if isempty(C.transformation)
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233 g = C.g;
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234 gp = C.gp;
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235 transformation.A = A;
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236 transformation.b = b;
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237 transformation.flip = flip;
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238 else
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239 g = C.transformation.base_g;
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240 gp = C.transformation.base_gp;
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241 A_old = C.transformation.A;
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242 b_old = C.transformation.b;
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243 flip_old = C.transformation.flip;
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244
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245 transformation.A = A*A_old;
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246 transformation.b = A*b_old + b;
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247 transformation.flip = flip*flip_old;
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248 end
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249
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250 D = grid.Curve(g,gp,transformation);
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251
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252 end
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253
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254 function D = translate(C,a)
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255 g = C.g;
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256 gp = C.gp;
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257
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258 % function v = g_fun(t)
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259 % x = g(t);
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260 % v(1,:) = x(1,:)+a(1);
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261 % v(2,:) = x(2,:)+a(2);
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262 % end
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263
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264 % D = grid.Curve(@g_fun,gp);
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265
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266 D = C.transform([],a);
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267 end
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268
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269 function D = mirror(C, a, b)
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270 assert_size(a,[2,1]);
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271 assert_size(b,[2,1]);
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272
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273 g = C.g;
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274 gp = C.gp;
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275
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276 l = b-a;
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277 lx = l(1);
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278 ly = l(2);
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279
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280
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281 % fprintf('Singular?\n')
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282
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283 A = [lx^2-ly^2 2*lx*ly; 2*lx*ly ly^2-lx^2]/(l'*l);
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284
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285 % function v = g_fun(t)
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286 % % v = a + A*(g(t)-a)
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287 % x = g(t);
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288
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289 % ax1 = x(1,:)-a(1);
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290 % ax2 = x(2,:)-a(2);
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291 % v(1,:) = a(1)+A(1,:)*[ax1;ax2];
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292 % v(2,:) = a(2)+A(2,:)*[ax1;ax2];
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293 % end
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294
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295 % function v = gp_fun(t)
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296 % v = A*gp(t);
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297 % end
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298
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299 % D = grid.Curve(@g_fun,@gp_fun);
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300
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301 % g = A(g-a)+a = Ag - Aa + a;
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302 b = - A*a + a;
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303 D = C.transform(A,b);
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304
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305 end
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306
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307 function D = rotate(C,a,rad)
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308 assert_size(a, [2,1]);
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309 assert_size(rad, [1,1]);
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310 g = C.g;
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311 gp = C.gp;
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312
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313
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314 A = [cos(rad) -sin(rad); sin(rad) cos(rad)];
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315
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316 % function v = g_fun(t)
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317 % % v = a + A*(g(t)-a)
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318 % x = g(t);
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319
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320 % ax1 = x(1,:)-a(1);
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321 % ax2 = x(2,:)-a(2);
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322 % v(1,:) = a(1)+A(1,:)*[ax1;ax2];
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323 % v(2,:) = a(2)+A(2,:)*[ax1;ax2];
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324 % end
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325
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326 % function v = gp_fun(t)
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327 % v = A*gp(t);
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328 % end
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329
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330 % D = grid.Curve(@g_fun,@gp_fun);
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331
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332
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333 % g = A(g-a)+a = Ag - Aa + a;
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334 b = - A*a + a;
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335 D = C.transform(A,b);
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336 end
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337 end
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338
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339 methods (Static)
86
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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340
87
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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341 % Length of arc from parameter t0 to t1 (which may be vectors).
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342 % Computed using derivative.
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parents: 86
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343 function L = arc_length(deriv,t0,t1)
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parents: 86
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344 speed = @(t) sp(deriv(t));
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parents: 86
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345
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
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346 function s = sp(deriv)
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parents: 86
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347 s = sqrt(sum(deriv.^2,1));
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parents: 86
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348 end
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349 L = util.integral_vec(speed,t0,t1);
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parents: 86
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350 end
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parents: 86
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351
86
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parents: 0
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352 function gp_out = numerical_derivative(g,D1)
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parents: 0
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353 m = length(D1); L = 1; % Assume curve parameter from 0 to 1.
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parents: 0
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354 t = linspace(0,L,m);
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parents: 0
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355 g = g(t)';
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parents: 0
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356 gp = (D1*g)';
87
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
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parents: 86
diff changeset
357
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parents: 86
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358 gp1_fun = grid.Curve.spline(t,gp(1,:));
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359 gp2_fun = grid.Curve.spline(t,gp(2,:));
86
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
360 gp_out = @(t) [gp1_fun(t);gp2_fun(t)];
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
361
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
362 end
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
363
87
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
364 % Returns a function handle to the spline.
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
365 function f = spline(tval,fval,spline_order)
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
366 default_arg('spline_order',4);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
367 [m,~] = size(tval);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
368 assert(m==1,'Need row vectors.');
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
369
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
370 % make vectors longer to be safe slightly beyond edges.
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
371 dt0 = tval(2)-tval(1); dt1 = tval(end)-tval(end-1);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
372 df0 = fval(2)-fval(1); df1 = fval(end)-fval(end-1);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
373 tval = [tval(1)-dt0, tval, tval(end)+dt1];
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
374 fval = [fval(1)-df0, fval, fval(end)+df1];
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
375
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
376 f_spline = spapi( optknt(tval,spline_order), tval, fval );
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
377 f = @(t) fnval(f_spline,t);
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
378 end
0a29a60e0b21 In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
Martin Almquist <martin.almquist@it.uu.se>
parents: 86
diff changeset
379
0
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diff changeset
380 function obj = line(p1, p2)
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381
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382 function v = g_fun(t)
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parents:
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383 v(1,:) = p1(1) + t.*(p2(1)-p1(1));
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parents:
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384 v(2,:) = p1(2) + t.*(p2(2)-p1(2));
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parents:
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385 end
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386 g = @g_fun;
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parents:
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387
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parents:
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388 obj = grid.Curve(g);
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parents:
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389 end
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parents:
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390
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parents:
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391 function obj = circle(c,r,phi)
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parents:
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392 default_arg('phi',[0; 2*pi])
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parents:
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393 default_arg('c',[0; 0])
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394 default_arg('r',1)
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parents:
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395
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parents:
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396 function v = g_fun(t)
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parents:
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397 w = phi(1)+t*(phi(2)-phi(1));
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parents:
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398 v(1,:) = c(1) + r*cos(w);
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parents:
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399 v(2,:) = c(2) + r*sin(w);
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parents:
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400 end
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parents:
diff changeset
401
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parents:
diff changeset
402 function v = g_fun_deriv(t)
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parents:
diff changeset
403 w = phi(1)+t*(phi(2)-phi(1));
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parents:
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404 v(1,:) = -(phi(2)-phi(1))*r*sin(w);
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parents:
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405 v(2,:) = (phi(2)-phi(1))*r*cos(w);
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parents:
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406 end
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parents:
diff changeset
407
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parents:
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408 obj = grid.Curve(@g_fun,@g_fun_deriv);
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parents:
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409 end
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parents:
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410
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Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
411 function obj = bezier(p0, p1, p2, p3)
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parents:
diff changeset
412 function v = g_fun(t)
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parents:
diff changeset
413 v(1,:) = (1-t).^3*p0(1) + 3*(1-t).^2.*t*p1(1) + 3*(1-t).*t.^2*p2(1) + t.^3*p3(1);
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parents:
diff changeset
414 v(2,:) = (1-t).^3*p0(2) + 3*(1-t).^2.*t*p1(2) + 3*(1-t).*t.^2*p2(2) + t.^3*p3(2);
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parents:
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415 end
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parents:
diff changeset
416
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parents:
diff changeset
417 function v = g_fun_deriv(t)
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parents:
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418 v(1,:) = 3*(1-t).^2*(p1(1)-p0(1)) + 6*(1-t).*t*(p2(1)-p1(1)) + 3*t.^2*(p3(1)-p2(1));
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parents:
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419 v(2,:) = 3*(1-t).^2*(p1(2)-p0(2)) + 6*(1-t).*t*(p2(2)-p1(2)) + 3*t.^2*(p3(2)-p2(2));
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parents:
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420 end
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parents:
diff changeset
421
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parents:
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422 obj = grid.Curve(@g_fun,@g_fun_deriv);
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parents:
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423 end
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parents:
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424
48b6fb693025 Initial commit.
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parents:
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425
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parents:
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426 function [g_out,gp_out] = transform_g(g,gp,tr)
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parents:
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427 A = tr.A;
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parents:
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428 b = tr.b;
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parents:
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429 flip = tr.flip;
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parents:
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430
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parents:
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431 function v = g_fun_noflip(t)
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parents:
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432 % v = A*g + b
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parents:
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433 x = g(t);
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parents:
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434
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parents:
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435 v(1,:) = A(1,:)*x+b(1);
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parents:
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436 v(2,:) = A(2,:)*x+b(2);
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parents:
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437 end
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parents:
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438
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Jonatan Werpers <jonatan@werpers.com>
parents:
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439 function v = g_fun_flip(t)
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parents:
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440 % v = A*g + b
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parents:
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441 x = g(1-t);
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442
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parents:
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443 v(1,:) = A(1,:)*x+b(1);
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parents:
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444 v(2,:) = A(2,:)*x+b(2);
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445 end
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parents:
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446
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parents:
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447
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parents:
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448 switch flip
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parents:
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449 case 1
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450 g_out = @g_fun_noflip;
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451 gp_out = @(t)A*gp(t);
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452 case -1
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453 g_out = @g_fun_flip;
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454 gp_out = @(t)-A*gp(1-t);
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455 end
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parents:
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456 end
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parents:
diff changeset
457
86
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
458 end
0
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parents:
diff changeset
459 end
86
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
460
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
461 function g_norm = normalize(g0)
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
462 g1 = g0(1,:); g2 = g0(2,:);
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
463 normalization = sqrt(sum(g0.^2,1));
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
464 g_norm = [g1./normalization; g2./normalization];
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
465 end
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
466
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
467
3c39dd714fb6 In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents: 0
diff changeset
468