Mercurial > repos > public > sbplib
annotate +parametrization/Curve.m @ 1097:eec03e78c6f2 feature/dataspline
Merge in default
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 08 Apr 2019 22:30:47 +0200 |
| parents | ad3089f04e0b |
| children | 36d092a00040 |
| 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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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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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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89 % Length of arc from parameter t0 to t1 (which may be vectors). |
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90 % Computed using derivative. |
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91 function L = arcLength(obj,t0,t1) |
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92 assert(~isempty(obj.gp),'Curve has no derivative!'); |
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93 speed = @(t) sqrt(sum(obj.gp(t).^2,1)); |
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94 L = integral_vec(speed,t0,t1); |
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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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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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105 arcVec = obj.arcLength(0,tvec); |
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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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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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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 function g_norm = normalize(g0) |
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353 g1 = g0(1,:); |
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354 g2 = g0(2,:); |
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355 normalization = sqrt(sum(g0.^2,1)); |
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356 g_norm = [g1./normalization; g2./normalization]; |
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357 end |
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358 |
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359 function I = integral_vec(f,a,b) |
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360 % Wrapper around the built-in function integral that |
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361 % handles multiple limits. |
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362 |
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363 Na = length(a); |
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364 Nb = length(b); |
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365 assert(Na == 1 || Nb == 1 || Na==Nb,... |
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366 'a and b must have same length, unless one is a scalar.'); |
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367 |
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368 if(Na>Nb); |
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369 I = zeros(size(a)); |
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370 for i = 1:Na |
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371 I(i) = integral(f,a(i),b); |
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372 end |
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373 elseif(Nb>Na) |
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374 I = zeros(size(b)); |
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375 for i = 1:Nb |
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376 I(i) = integral(f,a,b(i)); |
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377 end |
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378 else |
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379 I = zeros(size(b)); |
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380 for i = 1:Nb |
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381 I(i) = integral(f,a(i),b(i)); |
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382 end |
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383 end |
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384 end |
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385 |
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386 % Returns a function handle to the spline. |
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387 function f = spline(tval,fval,spline_order) |
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388 default_arg('spline_order',4); |
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389 [m,~] = size(tval); |
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Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
diff
changeset
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390 assert(m==1,'Need row vectors.'); |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
diff
changeset
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391 |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
diff
changeset
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392 f_spline = spapi( optknt(tval,spline_order), tval, fval ); |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
diff
changeset
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393 f = @(t) fnval(f_spline,t); |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
diff
changeset
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394 end |