Mercurial > repos > public > sbplib
annotate +parametrization/Curve.m @ 1088:acf19ecd1338 feature/dataspline
Turn the helper function spline into a static method in the Curve class.
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Thu, 04 Apr 2019 17:55:57 -0700 |
| parents | 0776fa4754ff |
| children | 3c187e639dfa |
| 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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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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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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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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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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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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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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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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106 tFunc = parametrization.Curve.spline(arcVec,tvec); % t as a function of arcLength |
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104
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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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107 L = obj.arcLength(0,1); |
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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) | |
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184 assertSize(a,[2,1]); |
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185 assertSize(b,[2,1]); |
| 0 | 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) | |
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222 assertSize(a, [2,1]); |
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223 assertSize(rad, [1,1]); |
| 0 | 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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261 |
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262 gp1_fun = parametrization.Curve.spline(t,gpVec(1,:)); |
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263 gp2_fun = parametrization.Curve.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 | |
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282 % Returns a function handle to the spline. |
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283 function f = spline(tval,fval,spline_order) |
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284 default_arg('spline_order',4); |
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285 [m,~] = size(tval); |
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286 assert(m==1,'Need row vectors.'); |
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287 |
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288 f_spline = spapi( optknt(tval,spline_order), tval, fval ); |
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289 f = @(t) fnval(f_spline,t); |
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290 end |
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291 |
| 0 | 292 function obj = circle(c,r,phi) |
| 293 default_arg('phi',[0; 2*pi]) | |
| 294 default_arg('c',[0; 0]) | |
| 295 default_arg('r',1) | |
| 296 | |
| 297 function v = g_fun(t) | |
| 298 w = phi(1)+t*(phi(2)-phi(1)); | |
| 299 v(1,:) = c(1) + r*cos(w); | |
| 300 v(2,:) = c(2) + r*sin(w); | |
| 301 end | |
| 302 | |
| 303 function v = g_fun_deriv(t) | |
| 304 w = phi(1)+t*(phi(2)-phi(1)); | |
| 305 v(1,:) = -(phi(2)-phi(1))*r*sin(w); | |
| 306 v(2,:) = (phi(2)-phi(1))*r*cos(w); | |
| 307 end | |
| 308 | |
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309 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 310 end |
| 311 | |
| 312 function obj = bezier(p0, p1, p2, p3) | |
| 313 function v = g_fun(t) | |
| 314 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); | |
| 315 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); | |
| 316 end | |
| 317 | |
| 318 function v = g_fun_deriv(t) | |
| 319 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)); | |
| 320 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)); | |
| 321 end | |
| 322 | |
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323 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 324 end |
| 325 | |
| 326 | |
| 327 function [g_out,gp_out] = transform_g(g,gp,tr) | |
| 328 A = tr.A; | |
| 329 b = tr.b; | |
| 330 flip = tr.flip; | |
| 331 | |
| 332 function v = g_fun_noflip(t) | |
| 333 % v = A*g + b | |
| 334 x = g(t); | |
| 335 | |
| 336 v(1,:) = A(1,:)*x+b(1); | |
| 337 v(2,:) = A(2,:)*x+b(2); | |
| 338 end | |
| 339 | |
| 340 function v = g_fun_flip(t) | |
| 341 % v = A*g + b | |
| 342 x = g(1-t); | |
| 343 | |
| 344 v(1,:) = A(1,:)*x+b(1); | |
| 345 v(2,:) = A(2,:)*x+b(2); | |
| 346 end | |
| 347 | |
| 348 | |
| 349 switch flip | |
| 350 case 1 | |
| 351 g_out = @g_fun_noflip; | |
| 352 gp_out = @(t)A*gp(t); | |
| 353 case -1 | |
| 354 g_out = @g_fun_flip; | |
| 355 gp_out = @(t)-A*gp(1-t); | |
| 356 end | |
| 357 end | |
| 358 | |
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359 end |
| 0 | 360 end |
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361 |
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362 |
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363 |
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364 function g_norm = normalize(g0) |
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365 g1 = g0(1,:); |
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366 g2 = g0(2,:); |
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367 normalization = sqrt(sum(g0.^2,1)); |
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368 g_norm = [g1./normalization; g2./normalization]; |
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369 end |
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370 |
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371 function I = integral_vec(f,a,b) |
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372 % Wrapper around the built-in function integral that |
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373 % handles multiple limits. |
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374 |
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375 Na = length(a); |
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376 Nb = length(b); |
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377 assert(Na == 1 || Nb == 1 || Na==Nb,... |
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378 'a and b must have same length, unless one is a scalar.'); |
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379 |
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380 if(Na>Nb); |
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381 I = zeros(size(a)); |
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382 for i = 1:Na |
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383 I(i) = integral(f,a(i),b); |
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384 end |
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385 elseif(Nb>Na) |
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386 I = zeros(size(b)); |
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387 for i = 1:Nb |
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388 I(i) = integral(f,a,b(i)); |
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389 end |
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390 else |
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391 I = zeros(size(b)); |
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392 for i = 1:Nb |
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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
|
393 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
|
394 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
|
395 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
|
396 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
|
397 |