Mercurial > repos > public > sbplib
annotate +parametrization/Curve.m @ 333:0fd4b259af9e feature/beams
Fixed some bugs in parametrization.Curve.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 04 Oct 2016 11:43:35 +0200 |
| parents | 81e0ead29431 |
| children | 0776fa4754ff |
| 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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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).
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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) | |
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71 default_arg('name', '') |
| 0 | 72 p = obj.g(1/2); |
| 73 n = obj.normal(1/2); | |
| 74 p = p + n*0.1; | |
| 75 | |
| 76 % Add arrow | |
| 77 | |
| 78 | |
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79 if ~isempty(name) |
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80 h = text(p(1),p(2),name); |
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81 h.HorizontalAlignment = 'center'; |
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82 h.VerticalAlignment = 'middle'; |
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83 end |
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84 |
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85 h = obj.plot(); |
| 0 | 86 end |
| 87 % Shows curve with name and arrow for direction. | |
| 88 | |
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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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89 % 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.
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90 % 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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91 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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92 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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93 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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94 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.
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95 end |
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96 |
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97 % Creates the arc length parameterization of a curve. |
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98 % N -- number of points used to approximate the arclength function |
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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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99 function curve = arcLengthParametrization(obj,N) |
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98
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100 default_arg('N',100); |
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101 assert(~isempty(obj.gp),'Curve has no derivative!'); |
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102 |
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103 % Construct arcLength function using splines |
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104 tvec = linspace(0,1,N); |
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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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105 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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106 tFunc = spline(arcVec,tvec); % t as a function of arcLength |
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107 L = obj.arcLength(0,1); |
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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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108 arcPar = @(s) tFunc(s*L); |
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109 |
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110 % New function and derivative |
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111 g_new = @(t)obj.g(arcPar(t)); |
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112 gp_new = @(t) normalize(obj.gp(arcPar(t))); |
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113 curve = parametrization.Curve(g_new,gp_new); |
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114 |
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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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115 end |
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116 |
| 0 | 117 % how to make it work for methods without returns |
| 118 function p = subsref(obj,S) | |
| 119 %Should i add error checking here? | |
| 120 %Maybe if you want performance you fetch obj.g and then use that | |
| 121 switch S(1).type | |
| 122 case '()' | |
| 123 p = obj.g(S.subs{1}); | |
| 124 % case '.' | |
| 125 | |
| 126 % p = obj.(S.subs); | |
| 127 otherwise | |
| 128 p = builtin('subsref',obj,S); | |
| 129 % error() | |
| 130 end | |
| 131 end | |
| 132 | |
| 133 | |
| 134 %% TRANSFORMATION OF A CURVE | |
| 135 function D = reverse(C) | |
| 136 % g = C.g; | |
| 137 % gp = C.gp; | |
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138 % D = parametrization.Curve(@(t)g(1-t),@(t)-gp(1-t)); |
| 0 | 139 D = C.transform([],[],-1); |
| 140 end | |
| 141 | |
| 142 function D = transform(C,A,b,flip) | |
| 143 default_arg('A',[1 0; 0 1]); | |
| 144 default_arg('b',[0; 0]); | |
| 145 default_arg('flip',1); | |
| 146 if isempty(C.transformation) | |
| 147 g = C.g; | |
| 148 gp = C.gp; | |
| 149 transformation.A = A; | |
| 150 transformation.b = b; | |
| 151 transformation.flip = flip; | |
| 152 else | |
| 153 g = C.transformation.base_g; | |
| 154 gp = C.transformation.base_gp; | |
| 155 A_old = C.transformation.A; | |
| 156 b_old = C.transformation.b; | |
| 157 flip_old = C.transformation.flip; | |
| 158 | |
| 159 transformation.A = A*A_old; | |
| 160 transformation.b = A*b_old + b; | |
| 161 transformation.flip = flip*flip_old; | |
| 162 end | |
| 163 | |
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164 D = parametrization.Curve(g,gp,transformation); |
| 0 | 165 |
| 166 end | |
| 167 | |
| 168 function D = translate(C,a) | |
| 169 g = C.g; | |
| 170 gp = C.gp; | |
| 171 | |
| 172 % function v = g_fun(t) | |
| 173 % x = g(t); | |
| 174 % v(1,:) = x(1,:)+a(1); | |
| 175 % v(2,:) = x(2,:)+a(2); | |
| 176 % end | |
| 177 | |
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178 % D = parametrization.Curve(@g_fun,gp); |
| 0 | 179 |
| 180 D = C.transform([],a); | |
| 181 end | |
| 182 | |
| 183 function D = mirror(C, a, b) | |
| 184 assert_size(a,[2,1]); | |
| 185 assert_size(b,[2,1]); | |
| 186 | |
| 187 g = C.g; | |
| 188 gp = C.gp; | |
| 189 | |
| 190 l = b-a; | |
| 191 lx = l(1); | |
| 192 ly = l(2); | |
| 193 | |
| 194 | |
| 195 % fprintf('Singular?\n') | |
| 196 | |
| 197 A = [lx^2-ly^2 2*lx*ly; 2*lx*ly ly^2-lx^2]/(l'*l); | |
| 198 | |
| 199 % function v = g_fun(t) | |
| 200 % % v = a + A*(g(t)-a) | |
| 201 % x = g(t); | |
| 202 | |
| 203 % ax1 = x(1,:)-a(1); | |
| 204 % ax2 = x(2,:)-a(2); | |
| 205 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 206 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 207 % end | |
| 208 | |
| 209 % function v = gp_fun(t) | |
| 210 % v = A*gp(t); | |
| 211 % end | |
| 212 | |
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213 % D = parametrization.Curve(@g_fun,@gp_fun); |
| 0 | 214 |
| 215 % g = A(g-a)+a = Ag - Aa + a; | |
| 216 b = - A*a + a; | |
| 217 D = C.transform(A,b); | |
| 218 | |
| 219 end | |
| 220 | |
| 221 function D = rotate(C,a,rad) | |
| 222 assert_size(a, [2,1]); | |
| 223 assert_size(rad, [1,1]); | |
| 224 g = C.g; | |
| 225 gp = C.gp; | |
| 226 | |
| 227 | |
| 228 A = [cos(rad) -sin(rad); sin(rad) cos(rad)]; | |
| 229 | |
| 230 % function v = g_fun(t) | |
| 231 % % v = a + A*(g(t)-a) | |
| 232 % x = g(t); | |
| 233 | |
| 234 % ax1 = x(1,:)-a(1); | |
| 235 % ax2 = x(2,:)-a(2); | |
| 236 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 237 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 238 % end | |
| 239 | |
| 240 % function v = gp_fun(t) | |
| 241 % v = A*gp(t); | |
| 242 % end | |
| 243 | |
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244 % D = parametrization.Curve(@g_fun,@gp_fun); |
| 0 | 245 |
| 246 | |
| 247 % g = A(g-a)+a = Ag - Aa + a; | |
| 248 b = - A*a + a; | |
| 249 D = C.transform(A,b); | |
| 250 end | |
| 251 end | |
| 252 | |
| 253 methods (Static) | |
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254 |
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255 % Computes the derivative of g: R -> R^2 using an operator D1 |
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256 function gp_out = numericalDerivative(g,D1) |
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257 m = length(D1); |
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258 t = linspace(0,1,m); |
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259 gVec = g(t)'; |
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260 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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261 |
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262 gp1_fun = spline(t,gpVec(1,:)); |
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263 gp2_fun = spline(t,gpVec(2,:)); |
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264 gp_out = @(t) [gp1_fun(t);gp2_fun(t)]; |
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265 end |
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266 |
| 0 | 267 function obj = line(p1, p2) |
| 268 | |
| 269 function v = g_fun(t) | |
| 270 v(1,:) = p1(1) + t.*(p2(1)-p1(1)); | |
| 271 v(2,:) = p1(2) + t.*(p2(2)-p1(2)); | |
| 272 end | |
| 273 | |
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274 function v = g_fun_deriv(t) |
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275 v(1,:) = t.*0 + (p2(1)-p1(1)); |
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276 v(2,:) = t.*0 + (p2(2)-p1(2)); |
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277 end |
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278 |
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279 obj = parametrization.Curve(@g_fun, @g_fun_deriv); |
| 0 | 280 end |
| 281 | |
| 282 function obj = circle(c,r,phi) | |
| 283 default_arg('phi',[0; 2*pi]) | |
| 284 default_arg('c',[0; 0]) | |
| 285 default_arg('r',1) | |
| 286 | |
| 287 function v = g_fun(t) | |
| 288 w = phi(1)+t*(phi(2)-phi(1)); | |
| 289 v(1,:) = c(1) + r*cos(w); | |
| 290 v(2,:) = c(2) + r*sin(w); | |
| 291 end | |
| 292 | |
| 293 function v = g_fun_deriv(t) | |
| 294 w = phi(1)+t*(phi(2)-phi(1)); | |
| 295 v(1,:) = -(phi(2)-phi(1))*r*sin(w); | |
| 296 v(2,:) = (phi(2)-phi(1))*r*cos(w); | |
| 297 end | |
| 298 | |
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299 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 300 end |
| 301 | |
| 302 function obj = bezier(p0, p1, p2, p3) | |
| 303 function v = g_fun(t) | |
| 304 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); | |
| 305 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); | |
| 306 end | |
| 307 | |
| 308 function v = g_fun_deriv(t) | |
| 309 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)); | |
| 310 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)); | |
| 311 end | |
| 312 | |
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313 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 314 end |
| 315 | |
| 316 | |
| 317 function [g_out,gp_out] = transform_g(g,gp,tr) | |
| 318 A = tr.A; | |
| 319 b = tr.b; | |
| 320 flip = tr.flip; | |
| 321 | |
| 322 function v = g_fun_noflip(t) | |
| 323 % v = A*g + b | |
| 324 x = g(t); | |
| 325 | |
| 326 v(1,:) = A(1,:)*x+b(1); | |
| 327 v(2,:) = A(2,:)*x+b(2); | |
| 328 end | |
| 329 | |
| 330 function v = g_fun_flip(t) | |
| 331 % v = A*g + b | |
| 332 x = g(1-t); | |
| 333 | |
| 334 v(1,:) = A(1,:)*x+b(1); | |
| 335 v(2,:) = A(2,:)*x+b(2); | |
| 336 end | |
| 337 | |
| 338 | |
| 339 switch flip | |
| 340 case 1 | |
| 341 g_out = @g_fun_noflip; | |
| 342 gp_out = @(t)A*gp(t); | |
| 343 case -1 | |
| 344 g_out = @g_fun_flip; | |
| 345 gp_out = @(t)-A*gp(1-t); | |
| 346 end | |
| 347 end | |
| 348 | |
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349 end |
| 0 | 350 end |
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351 |
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352 |
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353 |
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354 function g_norm = normalize(g0) |
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355 g1 = g0(1,:); |
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356 g2 = g0(2,:); |
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357 normalization = sqrt(sum(g0.^2,1)); |
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358 g_norm = [g1./normalization; g2./normalization]; |
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359 end |
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360 |
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361 function I = integral_vec(f,a,b) |
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362 % Wrapper around the built-in function integral that |
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363 % handles multiple limits. |
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364 |
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365 Na = length(a); |
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366 Nb = length(b); |
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367 assert(Na == 1 || Nb == 1 || Na==Nb,... |
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368 'a and b must have same length, unless one is a scalar.'); |
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369 |
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370 if(Na>Nb); |
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371 I = zeros(size(a)); |
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372 for i = 1:Na |
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373 I(i) = integral(f,a(i),b); |
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374 end |
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375 elseif(Nb>Na) |
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376 I = zeros(size(b)); |
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377 for i = 1:Nb |
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378 I(i) = integral(f,a,b(i)); |
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379 end |
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380 else |
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381 I = zeros(size(b)); |
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382 for i = 1:Nb |
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383 I(i) = integral(f,a(i),b(i)); |
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384 end |
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385 end |
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386 end |
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387 |
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388 % Returns a function handle to the spline. |
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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
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389 function f = spline(tval,fval,spline_order) |
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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
|
390 default_arg('spline_order',4); |
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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
|
391 [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
|
392 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
|
393 |
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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
|
394 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
|
395 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
|
396 end |