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annotate +grid/Curve.m @ 105:1df4f3704b76 feature/arclen-param

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Added error checking for all methods that use the derivative gp. Removed that from the to do list. Updated some comments.
author Martin Almquist <martin.almquist@it.uu.se>
date Mon, 07 Dec 2015 18:51:41 +0100
parents ffd9e68f63cc
children 06c3034966b7
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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
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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6
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7 end
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8 methods
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9 %TODO:
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10 % Concatenation of curves
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11 % Subsections of curves
105
1df4f3704b76 Added error checking for all methods that use the derivative gp. Removed that from the to do list. Updated some comments.
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parents: 104
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12 % Stretching of curve parameter - done for arc length.
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13 % Curve to cell array of linesegments
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14
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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15 % The curve parameter t must be in [0,1].
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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16 % Can supply derivative.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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17 function obj = Curve(g,gp,transformation)
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18 default_arg('gp',[]);
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19 default_arg('transformation',[]);
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20 p_test = g(0);
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21 assert(all(size(p_test) == [2,1]), 'A curve parametrization must return a 2x1 vector.');
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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22
0
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23 if ~isempty(transformation)
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24 transformation.base_g = g;
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25 transformation.base_gp = gp;
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26 [g,gp] = grid.Curve.transform_g(g,gp,transformation);
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27 end
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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28
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29 obj.g = g;
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30 obj.gp = gp;
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31 obj.transformation = transformation;
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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33 end
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34
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35 function n = normal(obj,t)
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1df4f3704b76 Added error checking for all methods that use the derivative gp. Removed that from the to do list. Updated some comments.
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36 assert(~isempty(obj.gp),'Curve has no derivative!');
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37 deriv = obj.gp(t);
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38 normalization = sqrt(sum(deriv.^2,1));
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39 n = [-deriv(2,:)./normalization; deriv(1,:)./normalization];
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40 end
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41
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42
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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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43 % 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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44 % h = plot_curve(g,n)
98
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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45 function h = plot(obj,n)
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46 default_arg('n',100);
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47
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48 t = linspace(0,1,n);
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49 p = obj.g(t);
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50 h = line(p(1,:),p(2,:));
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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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51 end
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52
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53 function h= plot_normals(obj,l,n,m)
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54 default_arg('l',0.1);
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55 default_arg('n',10);
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56 default_arg('m',100);
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57 t_n = linspace(0,1,n);
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58
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59 normals = obj.normal(t_n)*l;
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60
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61 n0 = obj.g(t_n);
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62 n1 = n0 + normals;
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63
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64 h = line([n0(1,:); n1(1,:)],[n0(2,:); n1(2,:)]);
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65 set(h,'Color',Color.red);
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66 obj.plot(m);
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67 end
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68
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69 function h= show(obj,name)
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70 p = obj.g(1/2);
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71 n = obj.normal(1/2);
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72 p = p + n*0.1;
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73
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74 % Add arrow
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75
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76 h = text(p(1),p(2),name);
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77 h.HorizontalAlignment = 'center';
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78 h.VerticalAlignment = 'middle';
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79
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80 obj.plot();
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81 end
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82 % Shows curve with name and arrow for direction.
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83
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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84 % Length of arc from parameter t0 to t1 (which may be vectors).
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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85 % Computed using derivative.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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86 function L = arcLength(obj,t0,t1)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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87 assert(~isempty(obj.gp),'Curve has no derivative!');
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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88 speed = @(t) sqrt(sum(obj.gp(t).^2,1));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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89 L = integral_vec(speed,t0,t1);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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90 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
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91
98
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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92 % Arc length parameterization.
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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93 function curve = arcLengthParametrization(obj,N)
98
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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94 default_arg('N',100);
105
1df4f3704b76 Added error checking for all methods that use the derivative gp. Removed that from the to do list. Updated some comments.
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parents: 104
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95 assert(~isempty(obj.gp),'Curve has no derivative!');
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
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96
98
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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97 % Construct arcLength function using splines
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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98 tvec = linspace(0,1,N);
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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99 arcVec = obj.arcLength(0,tvec);
104
ffd9e68f63cc Splined in the other direction! Works great. Runs faster. Removed ugly fix outside [0,1] in spline(). Camelcased numerical_derivative().
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parents: 103
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100 tFunc = spline(arcVec,tvec); % t as a function of arcLength
ffd9e68f63cc Splined in the other direction! Works great. Runs faster. Removed ugly fix outside [0,1] in spline(). Camelcased numerical_derivative().
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parents: 103
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101 L = obj.arcLength(0,1);
ffd9e68f63cc Splined in the other direction! Works great. Runs faster. Removed ugly fix outside [0,1] in spline(). Camelcased numerical_derivative().
Martin Almquist <martin.almquist@it.uu.se>
parents: 103
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102 arcPar = @(s) tFunc(s*L);
98
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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103
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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104 % New function and derivative
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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105 g_new = @(t)obj.g(arcPar(t));
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
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106 gp_new = @(t) normalize(obj.gp(arcPar(t)));
98
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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107 curve = grid.Curve(g_new,gp_new);
b30f3d8845f4 Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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parents: 87
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108
86
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Martin Almquist <martin.almquist@it.uu.se>
parents: 0
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109 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.
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parents: 0
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110
0
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111 % how to make it work for methods without returns
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112 function p = subsref(obj,S)
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113 %Should i add error checking here?
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114 %Maybe if you want performance you fetch obj.g and then use that
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115 switch S(1).type
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116 case '()'
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117 p = obj.g(S.subs{1});
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118 % case '.'
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119
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120 % p = obj.(S.subs);
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121 otherwise
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122 p = builtin('subsref',obj,S);
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123 % error()
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124 end
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125 end
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126
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127
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128 %% TRANSFORMATION OF A CURVE
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129 function D = reverse(C)
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130 % g = C.g;
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131 % gp = C.gp;
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132 % D = grid.Curve(@(t)g(1-t),@(t)-gp(1-t));
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133 D = C.transform([],[],-1);
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134 end
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135
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136 function D = transform(C,A,b,flip)
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137 default_arg('A',[1 0; 0 1]);
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138 default_arg('b',[0; 0]);
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139 default_arg('flip',1);
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140 if isempty(C.transformation)
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141 g = C.g;
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142 gp = C.gp;
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143 transformation.A = A;
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144 transformation.b = b;
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145 transformation.flip = flip;
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146 else
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147 g = C.transformation.base_g;
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148 gp = C.transformation.base_gp;
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149 A_old = C.transformation.A;
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150 b_old = C.transformation.b;
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151 flip_old = C.transformation.flip;
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152
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153 transformation.A = A*A_old;
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154 transformation.b = A*b_old + b;
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155 transformation.flip = flip*flip_old;
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156 end
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157
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158 D = grid.Curve(g,gp,transformation);
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159
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160 end
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161
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162 function D = translate(C,a)
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163 g = C.g;
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164 gp = C.gp;
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165
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166 % function v = g_fun(t)
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167 % x = g(t);
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168 % v(1,:) = x(1,:)+a(1);
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169 % v(2,:) = x(2,:)+a(2);
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170 % end
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171
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172 % D = grid.Curve(@g_fun,gp);
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173
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174 D = C.transform([],a);
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175 end
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176
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177 function D = mirror(C, a, b)
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178 assert_size(a,[2,1]);
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179 assert_size(b,[2,1]);
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180
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181 g = C.g;
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182 gp = C.gp;
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183
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184 l = b-a;
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185 lx = l(1);
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186 ly = l(2);
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187
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188
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189 % fprintf('Singular?\n')
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190
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191 A = [lx^2-ly^2 2*lx*ly; 2*lx*ly ly^2-lx^2]/(l'*l);
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192
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193 % function v = g_fun(t)
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194 % % v = a + A*(g(t)-a)
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195 % x = g(t);
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196
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197 % ax1 = x(1,:)-a(1);
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198 % ax2 = x(2,:)-a(2);
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199 % v(1,:) = a(1)+A(1,:)*[ax1;ax2];
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200 % v(2,:) = a(2)+A(2,:)*[ax1;ax2];
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201 % end
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202
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203 % function v = gp_fun(t)
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204 % v = A*gp(t);
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205 % end
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206
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207 % D = grid.Curve(@g_fun,@gp_fun);
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208
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209 % g = A(g-a)+a = Ag - Aa + a;
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210 b = - A*a + a;
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211 D = C.transform(A,b);
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212
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213 end
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214
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215 function D = rotate(C,a,rad)
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216 assert_size(a, [2,1]);
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217 assert_size(rad, [1,1]);
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218 g = C.g;
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219 gp = C.gp;
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220
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221
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222 A = [cos(rad) -sin(rad); sin(rad) cos(rad)];
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223
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224 % function v = g_fun(t)
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225 % % v = a + A*(g(t)-a)
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226 % x = g(t);
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227
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228 % ax1 = x(1,:)-a(1);
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229 % ax2 = x(2,:)-a(2);
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230 % v(1,:) = a(1)+A(1,:)*[ax1;ax2];
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231 % v(2,:) = a(2)+A(2,:)*[ax1;ax2];
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232 % end
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233
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234 % function v = gp_fun(t)
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235 % v = A*gp(t);
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236 % end
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237
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238 % D = grid.Curve(@g_fun,@gp_fun);
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239
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240
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241 % g = A(g-a)+a = Ag - Aa + a;
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242 b = - A*a + a;
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243 D = C.transform(A,b);
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244 end
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245 end
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246
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247 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.
Martin Almquist <martin.almquist@it.uu.se>
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248
104
ffd9e68f63cc Splined in the other direction! Works great. Runs faster. Removed ugly fix outside [0,1] in spline(). Camelcased numerical_derivative().
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parents: 103
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249
ffd9e68f63cc Splined in the other direction! Works great. Runs faster. Removed ugly fix outside [0,1] in spline(). Camelcased numerical_derivative().
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parents: 103
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250 function gp_out = numericalDerivative(g,D1)
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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parents: 0
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251 m = length(D1); L = 1; % Assume curve parameter from 0 to 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.
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252 t = linspace(0,L,m);
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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253 gVec = g(t)';
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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254 gpVec = (D1*gVec)';
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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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255
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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256 gp1_fun = spline(t,gpVec(1,:));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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257 gp2_fun = spline(t,gpVec(2,:));
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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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parents: 0
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258 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.
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parents: 0
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259
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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260 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.
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261
0
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262 function obj = line(p1, p2)
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263
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264 function v = g_fun(t)
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265 v(1,:) = p1(1) + t.*(p2(1)-p1(1));
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266 v(2,:) = p1(2) + t.*(p2(2)-p1(2));
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267 end
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268 g = @g_fun;
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269
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270 obj = grid.Curve(g);
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271 end
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272
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273 function obj = circle(c,r,phi)
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274 default_arg('phi',[0; 2*pi])
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275 default_arg('c',[0; 0])
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276 default_arg('r',1)
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277
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278 function v = g_fun(t)
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279 w = phi(1)+t*(phi(2)-phi(1));
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280 v(1,:) = c(1) + r*cos(w);
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281 v(2,:) = c(2) + r*sin(w);
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282 end
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283
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284 function v = g_fun_deriv(t)
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285 w = phi(1)+t*(phi(2)-phi(1));
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286 v(1,:) = -(phi(2)-phi(1))*r*sin(w);
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287 v(2,:) = (phi(2)-phi(1))*r*cos(w);
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288 end
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289
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290 obj = grid.Curve(@g_fun,@g_fun_deriv);
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291 end
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292
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293 function obj = bezier(p0, p1, p2, p3)
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294 function v = g_fun(t)
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295 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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296 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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297 end
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298
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299 function v = g_fun_deriv(t)
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300 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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301 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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302 end
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303
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304 obj = grid.Curve(@g_fun,@g_fun_deriv);
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305 end
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306
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307
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308 function [g_out,gp_out] = transform_g(g,gp,tr)
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309 A = tr.A;
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310 b = tr.b;
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311 flip = tr.flip;
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312
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313 function v = g_fun_noflip(t)
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314 % v = A*g + b
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315 x = g(t);
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316
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317 v(1,:) = A(1,:)*x+b(1);
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318 v(2,:) = A(2,:)*x+b(2);
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319 end
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320
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321 function v = g_fun_flip(t)
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322 % v = A*g + b
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323 x = g(1-t);
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324
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325 v(1,:) = A(1,:)*x+b(1);
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326 v(2,:) = A(2,:)*x+b(2);
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327 end
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328
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329
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330 switch flip
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331 case 1
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332 g_out = @g_fun_noflip;
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333 gp_out = @(t)A*gp(t);
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334 case -1
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335 g_out = @g_fun_flip;
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336 gp_out = @(t)-A*gp(1-t);
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337 end
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338 end
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339
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
340 end
0
48b6fb693025 Initial commit.
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341 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
342
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
343 function g_norm = normalize(g0)
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
344 g1 = g0(1,:);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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345 g2 = g0(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
346 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
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347 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
348 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.
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parents: 0
diff changeset
349
103
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
350 function I = integral_vec(f,a,b)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
351 % Wrapper around the built-in function integral that
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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352 % handles multiple limits.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
353
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
354 Na = length(a);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
355 Nb = length(b);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
356 assert(Na == 1 || Nb == 1 || Na==Nb,...
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
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357 'a and b must have same length, unless one is a scalar.');
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
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parents: 99
diff changeset
358
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
359 if(Na>Nb);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
360 I = zeros(size(a));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
361 for i = 1:Na
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
362 I(i) = integral(f,a(i),b);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
363 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
364 elseif(Nb>Na)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
365 I = zeros(size(b));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
366 for i = 1:Nb
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
367 I(i) = integral(f,a,b(i));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
368 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
369 else
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
370 I = zeros(size(b));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
371 for i = 1:Nb
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
372 I(i) = integral(f,a(i),b(i));
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
373 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
374 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
375 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
376
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
377 % Returns a function handle to the spline.
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
378 function f = spline(tval,fval,spline_order)
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
379 default_arg('spline_order',4);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
380 [m,~] = size(tval);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
381 assert(m==1,'Need row vectors.');
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
382
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
383 f_spline = spapi( optknt(tval,spline_order), tval, fval );
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
384 f = @(t) fnval(f_spline,t);
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
385 end
bc5db54f9efd fzero_vec, integral_vec and spline are now local functions in Curve. Renamed arcLengthStretch to arcLengthParametrization. Removed plot_derivative. Added some comments and extra lines + removed unneccesary lines. arcLength is now a method and not static. Constructor does not accept difference operator anymore.
Martin Almquist <martin.almquist@it.uu.se>
parents: 99
diff changeset
386
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
387
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
388