Mercurial > repos > public > sbplib
annotate +parametrization/Curve.m @ 248:81e0ead29431 feature/beams
Fixed package names in +parametrization
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 05 Sep 2016 16:34:22 +0200 |
| parents | 3a3cf386bb7e |
| children | 0fd4b259af9e |
| rev | line source |
|---|---|
| 0 | 1 classdef Curve |
| 2 properties | |
| 3 g | |
| 4 gp | |
| 5 transformation | |
| 6 end | |
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7 |
| 0 | 8 methods |
| 9 %TODO: | |
| 10 % Concatenation of curves | |
| 11 % Subsections of curves | |
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12 % Stretching of curve parameter - done for arc length. |
| 0 | 13 % Curve to cell array of linesegments |
| 14 | |
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15 % Returns a curve object. |
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16 % g -- curve parametrization for parameter between 0 and 1 |
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17 % gp -- parametrization of curve derivative |
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103
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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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18 function obj = Curve(g,gp,transformation) |
| 0 | 19 default_arg('gp',[]); |
| 20 default_arg('transformation',[]); | |
| 21 p_test = g(0); | |
| 22 assert(all(size(p_test) == [2,1]), 'A curve parametrization must return a 2x1 vector.'); | |
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23 |
| 0 | 24 if ~isempty(transformation) |
| 25 transformation.base_g = g; | |
| 26 transformation.base_gp = gp; | |
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27 [g,gp] = parametrization.Curve.transform_g(g,gp,transformation); |
| 0 | 28 end |
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29 |
| 0 | 30 obj.g = g; |
| 31 obj.gp = gp; | |
| 32 obj.transformation = transformation; | |
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33 |
| 0 | 34 end |
| 35 | |
| 36 function n = normal(obj,t) | |
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37 assert(~isempty(obj.gp),'Curve has no derivative!'); |
| 0 | 38 deriv = obj.gp(t); |
| 39 normalization = sqrt(sum(deriv.^2,1)); | |
| 40 n = [-deriv(2,:)./normalization; deriv(1,:)./normalization]; | |
| 41 end | |
| 42 | |
| 43 | |
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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).
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44 % Plots a curve g(t) for 0<t<1, using n points. Returns a handle h to the plotted curve. |
| 0 | 45 % h = plot_curve(g,n) |
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Removed arclength property. Constructor compatible again. Translation and rotation are fast now, but ti is slow.
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46 function h = plot(obj,n) |
| 0 | 47 default_arg('n',100); |
| 48 | |
| 49 t = linspace(0,1,n); | |
| 50 p = obj.g(t); | |
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51 h = line(p(1,:),p(2,:)); |
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87
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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).
Martin Almquist <martin.almquist@it.uu.se>
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52 end |
| 0 | 53 |
| 54 function h= plot_normals(obj,l,n,m) | |
| 55 default_arg('l',0.1); | |
| 56 default_arg('n',10); | |
| 57 default_arg('m',100); | |
| 58 t_n = linspace(0,1,n); | |
| 59 | |
| 60 normals = obj.normal(t_n)*l; | |
| 61 | |
| 62 n0 = obj.g(t_n); | |
| 63 n1 = n0 + normals; | |
| 64 | |
| 65 h = line([n0(1,:); n1(1,:)],[n0(2,:); n1(2,:)]); | |
| 66 set(h,'Color',Color.red); | |
| 67 obj.plot(m); | |
| 68 end | |
| 69 | |
| 70 function h= show(obj,name) | |
| 71 p = obj.g(1/2); | |
| 72 n = obj.normal(1/2); | |
| 73 p = p + n*0.1; | |
| 74 | |
| 75 % Add arrow | |
| 76 | |
| 77 h = text(p(1),p(2),name); | |
| 78 h.HorizontalAlignment = 'center'; | |
| 79 h.VerticalAlignment = 'middle'; | |
| 80 | |
| 81 obj.plot(); | |
| 82 end | |
| 83 % Shows curve with name and arrow for direction. | |
| 84 | |
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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>
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85 % Length of arc from parameter t0 to t1 (which may be vectors). |
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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>
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86 % Computed using derivative. |
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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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87 function L = arcLength(obj,t0,t1) |
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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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88 assert(~isempty(obj.gp),'Curve has no derivative!'); |
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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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89 speed = @(t) sqrt(sum(obj.gp(t).^2,1)); |
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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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90 L = integral_vec(speed,t0,t1); |
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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>
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91 end |
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92 |
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93 % Creates the arc length parameterization of a curve. |
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94 % N -- number of points used to approximate the arclength function |
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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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95 function curve = arcLengthParametrization(obj,N) |
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98
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96 default_arg('N',100); |
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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.
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97 assert(~isempty(obj.gp),'Curve has no derivative!'); |
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98 |
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99 % Construct arcLength function using splines |
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100 tvec = linspace(0,1,N); |
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103
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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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101 arcVec = obj.arcLength(0,tvec); |
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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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102 tFunc = spline(arcVec,tvec); % t as a function of arcLength |
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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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103 L = obj.arcLength(0,1); |
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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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104 arcPar = @(s) tFunc(s*L); |
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105 |
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106 % New function and derivative |
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107 g_new = @(t)obj.g(arcPar(t)); |
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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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108 gp_new = @(t) normalize(obj.gp(arcPar(t))); |
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109 curve = parametrization.Curve(g_new,gp_new); |
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110 |
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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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111 end |
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112 |
| 0 | 113 % how to make it work for methods without returns |
| 114 function p = subsref(obj,S) | |
| 115 %Should i add error checking here? | |
| 116 %Maybe if you want performance you fetch obj.g and then use that | |
| 117 switch S(1).type | |
| 118 case '()' | |
| 119 p = obj.g(S.subs{1}); | |
| 120 % case '.' | |
| 121 | |
| 122 % p = obj.(S.subs); | |
| 123 otherwise | |
| 124 p = builtin('subsref',obj,S); | |
| 125 % error() | |
| 126 end | |
| 127 end | |
| 128 | |
| 129 | |
| 130 %% TRANSFORMATION OF A CURVE | |
| 131 function D = reverse(C) | |
| 132 % g = C.g; | |
| 133 % gp = C.gp; | |
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134 % D = parametrization.Curve(@(t)g(1-t),@(t)-gp(1-t)); |
| 0 | 135 D = C.transform([],[],-1); |
| 136 end | |
| 137 | |
| 138 function D = transform(C,A,b,flip) | |
| 139 default_arg('A',[1 0; 0 1]); | |
| 140 default_arg('b',[0; 0]); | |
| 141 default_arg('flip',1); | |
| 142 if isempty(C.transformation) | |
| 143 g = C.g; | |
| 144 gp = C.gp; | |
| 145 transformation.A = A; | |
| 146 transformation.b = b; | |
| 147 transformation.flip = flip; | |
| 148 else | |
| 149 g = C.transformation.base_g; | |
| 150 gp = C.transformation.base_gp; | |
| 151 A_old = C.transformation.A; | |
| 152 b_old = C.transformation.b; | |
| 153 flip_old = C.transformation.flip; | |
| 154 | |
| 155 transformation.A = A*A_old; | |
| 156 transformation.b = A*b_old + b; | |
| 157 transformation.flip = flip*flip_old; | |
| 158 end | |
| 159 | |
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160 D = parametrization.Curve(g,gp,transformation); |
| 0 | 161 |
| 162 end | |
| 163 | |
| 164 function D = translate(C,a) | |
| 165 g = C.g; | |
| 166 gp = C.gp; | |
| 167 | |
| 168 % function v = g_fun(t) | |
| 169 % x = g(t); | |
| 170 % v(1,:) = x(1,:)+a(1); | |
| 171 % v(2,:) = x(2,:)+a(2); | |
| 172 % end | |
| 173 | |
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174 % D = parametrization.Curve(@g_fun,gp); |
| 0 | 175 |
| 176 D = C.transform([],a); | |
| 177 end | |
| 178 | |
| 179 function D = mirror(C, a, b) | |
| 180 assert_size(a,[2,1]); | |
| 181 assert_size(b,[2,1]); | |
| 182 | |
| 183 g = C.g; | |
| 184 gp = C.gp; | |
| 185 | |
| 186 l = b-a; | |
| 187 lx = l(1); | |
| 188 ly = l(2); | |
| 189 | |
| 190 | |
| 191 % fprintf('Singular?\n') | |
| 192 | |
| 193 A = [lx^2-ly^2 2*lx*ly; 2*lx*ly ly^2-lx^2]/(l'*l); | |
| 194 | |
| 195 % function v = g_fun(t) | |
| 196 % % v = a + A*(g(t)-a) | |
| 197 % x = g(t); | |
| 198 | |
| 199 % ax1 = x(1,:)-a(1); | |
| 200 % ax2 = x(2,:)-a(2); | |
| 201 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 202 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 203 % end | |
| 204 | |
| 205 % function v = gp_fun(t) | |
| 206 % v = A*gp(t); | |
| 207 % end | |
| 208 | |
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209 % D = parametrization.Curve(@g_fun,@gp_fun); |
| 0 | 210 |
| 211 % g = A(g-a)+a = Ag - Aa + a; | |
| 212 b = - A*a + a; | |
| 213 D = C.transform(A,b); | |
| 214 | |
| 215 end | |
| 216 | |
| 217 function D = rotate(C,a,rad) | |
| 218 assert_size(a, [2,1]); | |
| 219 assert_size(rad, [1,1]); | |
| 220 g = C.g; | |
| 221 gp = C.gp; | |
| 222 | |
| 223 | |
| 224 A = [cos(rad) -sin(rad); sin(rad) cos(rad)]; | |
| 225 | |
| 226 % function v = g_fun(t) | |
| 227 % % v = a + A*(g(t)-a) | |
| 228 % x = g(t); | |
| 229 | |
| 230 % ax1 = x(1,:)-a(1); | |
| 231 % ax2 = x(2,:)-a(2); | |
| 232 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 233 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 234 % end | |
| 235 | |
| 236 % function v = gp_fun(t) | |
| 237 % v = A*gp(t); | |
| 238 % end | |
| 239 | |
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240 % D = parametrization.Curve(@g_fun,@gp_fun); |
| 0 | 241 |
| 242 | |
| 243 % g = A(g-a)+a = Ag - Aa + a; | |
| 244 b = - A*a + a; | |
| 245 D = C.transform(A,b); | |
| 246 end | |
| 247 end | |
| 248 | |
| 249 methods (Static) | |
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250 |
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251 % Computes the derivative of g: R -> R^2 using an operator D1 |
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Splined in the other direction! Works great. Runs faster. Removed ugly fix outside [0,1] in spline(). Camelcased numerical_derivative().
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252 function gp_out = numericalDerivative(g,D1) |
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253 m = length(D1); |
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254 t = linspace(0,1,m); |
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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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255 gVec = g(t)'; |
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256 gpVec = (D1*gVec)'; |
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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).
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257 |
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258 gp1_fun = spline(t,gpVec(1,:)); |
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259 gp2_fun = spline(t,gpVec(2,:)); |
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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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260 gp_out = @(t) [gp1_fun(t);gp2_fun(t)]; |
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261 end |
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262 |
| 0 | 263 function obj = line(p1, p2) |
| 264 | |
| 265 function v = g_fun(t) | |
| 266 v(1,:) = p1(1) + t.*(p2(1)-p1(1)); | |
| 267 v(2,:) = p1(2) + t.*(p2(2)-p1(2)); | |
| 268 end | |
| 269 g = @g_fun; | |
| 270 | |
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271 obj = parametrization.Curve(g); |
| 0 | 272 end |
| 273 | |
| 274 function obj = circle(c,r,phi) | |
| 275 default_arg('phi',[0; 2*pi]) | |
| 276 default_arg('c',[0; 0]) | |
| 277 default_arg('r',1) | |
| 278 | |
| 279 function v = g_fun(t) | |
| 280 w = phi(1)+t*(phi(2)-phi(1)); | |
| 281 v(1,:) = c(1) + r*cos(w); | |
| 282 v(2,:) = c(2) + r*sin(w); | |
| 283 end | |
| 284 | |
| 285 function v = g_fun_deriv(t) | |
| 286 w = phi(1)+t*(phi(2)-phi(1)); | |
| 287 v(1,:) = -(phi(2)-phi(1))*r*sin(w); | |
| 288 v(2,:) = (phi(2)-phi(1))*r*cos(w); | |
| 289 end | |
| 290 | |
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291 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 292 end |
| 293 | |
| 294 function obj = bezier(p0, p1, p2, p3) | |
| 295 function v = g_fun(t) | |
| 296 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); | |
| 297 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); | |
| 298 end | |
| 299 | |
| 300 function v = g_fun_deriv(t) | |
| 301 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)); | |
| 302 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)); | |
| 303 end | |
| 304 | |
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305 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 306 end |
| 307 | |
| 308 | |
| 309 function [g_out,gp_out] = transform_g(g,gp,tr) | |
| 310 A = tr.A; | |
| 311 b = tr.b; | |
| 312 flip = tr.flip; | |
| 313 | |
| 314 function v = g_fun_noflip(t) | |
| 315 % v = A*g + b | |
| 316 x = g(t); | |
| 317 | |
| 318 v(1,:) = A(1,:)*x+b(1); | |
| 319 v(2,:) = A(2,:)*x+b(2); | |
| 320 end | |
| 321 | |
| 322 function v = g_fun_flip(t) | |
| 323 % v = A*g + b | |
| 324 x = g(1-t); | |
| 325 | |
| 326 v(1,:) = A(1,:)*x+b(1); | |
| 327 v(2,:) = A(2,:)*x+b(2); | |
| 328 end | |
| 329 | |
| 330 | |
| 331 switch flip | |
| 332 case 1 | |
| 333 g_out = @g_fun_noflip; | |
| 334 gp_out = @(t)A*gp(t); | |
| 335 case -1 | |
| 336 g_out = @g_fun_flip; | |
| 337 gp_out = @(t)-A*gp(1-t); | |
| 338 end | |
| 339 end | |
| 340 | |
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341 end |
| 0 | 342 end |
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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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343 |
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344 |
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345 |
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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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346 function g_norm = normalize(g0) |
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347 g1 = g0(1,:); |
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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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348 g2 = g0(2,:); |
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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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349 normalization = sqrt(sum(g0.^2,1)); |
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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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350 g_norm = [g1./normalization; g2./normalization]; |
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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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351 end |
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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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352 |
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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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353 function I = integral_vec(f,a,b) |
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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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354 % Wrapper around the built-in function integral that |
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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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355 % handles multiple limits. |
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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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356 |
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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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357 Na = length(a); |
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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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358 Nb = length(b); |
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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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359 assert(Na == 1 || Nb == 1 || Na==Nb,... |
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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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360 'a and b must have same length, unless one is a scalar.'); |
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361 |
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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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362 if(Na>Nb); |
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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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363 I = zeros(size(a)); |
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364 for i = 1:Na |
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365 I(i) = integral(f,a(i),b); |
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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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366 end |
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367 elseif(Nb>Na) |
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368 I = zeros(size(b)); |
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369 for i = 1:Nb |
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370 I(i) = integral(f,a,b(i)); |
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371 end |
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372 else |
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373 I = zeros(size(b)); |
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374 for i = 1:Nb |
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375 I(i) = integral(f,a(i),b(i)); |
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376 end |
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377 end |
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378 end |
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379 |
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380 % Returns a function handle to the spline. |
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381 function f = spline(tval,fval,spline_order) |
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382 default_arg('spline_order',4); |
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383 [m,~] = size(tval); |
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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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384 assert(m==1,'Need row vectors.'); |
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385 |
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386 f_spline = spapi( optknt(tval,spline_order), tval, fval ); |
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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
|
387 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
|
388 end |