Mercurial > repos > public > sbplib
annotate +parametrization/Curve.m @ 1299:73e52c74baac feature/boundary_optimized_grids
Closed branch feature/boundary_optimized_grids
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Wed, 08 Jul 2020 18:20:57 +0200 |
| parents | 7f4aae76e06a |
| children | 60c875c18de3 |
| 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 |
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107 % t as a function of arcLength. Monotonicity-preserving cubic splines. |
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108 tFunc = @(arcLen) pchip(arcVec,tvec,arcLen); |
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109 |
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110 L = obj.arcLength(0,1); |
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111 arcPar = @(s) tFunc(s*L); |
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112 |
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113 % New function and derivative |
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114 g_new = @(t)obj.g(arcPar(t)); |
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115 gp_new = @(t) normalize(obj.gp(arcPar(t))); |
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116 curve = parametrization.Curve(g_new,gp_new); |
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117 |
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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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118 end |
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119 |
| 0 | 120 % how to make it work for methods without returns |
| 121 function p = subsref(obj,S) | |
| 122 %Should i add error checking here? | |
| 123 %Maybe if you want performance you fetch obj.g and then use that | |
| 124 switch S(1).type | |
| 125 case '()' | |
| 126 p = obj.g(S.subs{1}); | |
| 127 % case '.' | |
| 128 | |
| 129 % p = obj.(S.subs); | |
| 130 otherwise | |
| 131 p = builtin('subsref',obj,S); | |
| 132 % error() | |
| 133 end | |
| 134 end | |
| 135 | |
| 136 | |
| 137 %% TRANSFORMATION OF A CURVE | |
| 138 function D = reverse(C) | |
| 139 % g = C.g; | |
| 140 % gp = C.gp; | |
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141 % D = parametrization.Curve(@(t)g(1-t),@(t)-gp(1-t)); |
| 0 | 142 D = C.transform([],[],-1); |
| 143 end | |
| 144 | |
| 145 function D = transform(C,A,b,flip) | |
| 146 default_arg('A',[1 0; 0 1]); | |
| 147 default_arg('b',[0; 0]); | |
| 148 default_arg('flip',1); | |
| 149 if isempty(C.transformation) | |
| 150 g = C.g; | |
| 151 gp = C.gp; | |
| 152 transformation.A = A; | |
| 153 transformation.b = b; | |
| 154 transformation.flip = flip; | |
| 155 else | |
| 156 g = C.transformation.base_g; | |
| 157 gp = C.transformation.base_gp; | |
| 158 A_old = C.transformation.A; | |
| 159 b_old = C.transformation.b; | |
| 160 flip_old = C.transformation.flip; | |
| 161 | |
| 162 transformation.A = A*A_old; | |
| 163 transformation.b = A*b_old + b; | |
| 164 transformation.flip = flip*flip_old; | |
| 165 end | |
| 166 | |
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167 D = parametrization.Curve(g,gp,transformation); |
| 0 | 168 |
| 169 end | |
| 170 | |
| 171 function D = translate(C,a) | |
| 172 g = C.g; | |
| 173 gp = C.gp; | |
| 174 | |
| 175 % function v = g_fun(t) | |
| 176 % x = g(t); | |
| 177 % v(1,:) = x(1,:)+a(1); | |
| 178 % v(2,:) = x(2,:)+a(2); | |
| 179 % end | |
| 180 | |
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181 % D = parametrization.Curve(@g_fun,gp); |
| 0 | 182 |
| 183 D = C.transform([],a); | |
| 184 end | |
| 185 | |
| 186 function D = mirror(C, a, b) | |
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187 assertSize(a,[2,1]); |
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188 assertSize(b,[2,1]); |
| 0 | 189 |
| 190 g = C.g; | |
| 191 gp = C.gp; | |
| 192 | |
| 193 l = b-a; | |
| 194 lx = l(1); | |
| 195 ly = l(2); | |
| 196 | |
| 197 | |
| 198 % fprintf('Singular?\n') | |
| 199 | |
| 200 A = [lx^2-ly^2 2*lx*ly; 2*lx*ly ly^2-lx^2]/(l'*l); | |
| 201 | |
| 202 % function v = g_fun(t) | |
| 203 % % v = a + A*(g(t)-a) | |
| 204 % x = g(t); | |
| 205 | |
| 206 % ax1 = x(1,:)-a(1); | |
| 207 % ax2 = x(2,:)-a(2); | |
| 208 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 209 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 210 % end | |
| 211 | |
| 212 % function v = gp_fun(t) | |
| 213 % v = A*gp(t); | |
| 214 % end | |
| 215 | |
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216 % D = parametrization.Curve(@g_fun,@gp_fun); |
| 0 | 217 |
| 218 % g = A(g-a)+a = Ag - Aa + a; | |
| 219 b = - A*a + a; | |
| 220 D = C.transform(A,b); | |
| 221 | |
| 222 end | |
| 223 | |
| 224 function D = rotate(C,a,rad) | |
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225 assertSize(a, [2,1]); |
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226 assertSize(rad, [1,1]); |
| 0 | 227 g = C.g; |
| 228 gp = C.gp; | |
| 229 | |
| 230 | |
| 231 A = [cos(rad) -sin(rad); sin(rad) cos(rad)]; | |
| 232 | |
| 233 % function v = g_fun(t) | |
| 234 % % v = a + A*(g(t)-a) | |
| 235 % x = g(t); | |
| 236 | |
| 237 % ax1 = x(1,:)-a(1); | |
| 238 % ax2 = x(2,:)-a(2); | |
| 239 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 240 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 241 % end | |
| 242 | |
| 243 % function v = gp_fun(t) | |
| 244 % v = A*gp(t); | |
| 245 % end | |
| 246 | |
|
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247 % D = parametrization.Curve(@g_fun,@gp_fun); |
| 0 | 248 |
| 249 | |
| 250 % g = A(g-a)+a = Ag - Aa + a; | |
| 251 b = - A*a + a; | |
| 252 D = C.transform(A,b); | |
| 253 end | |
| 254 end | |
| 255 | |
| 256 methods (Static) | |
|
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257 |
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258 % Computes the derivative of g: R -> R^2 using an operator D1 |
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259 function gp_out = numericalDerivative(g,D1) |
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260 m = length(D1); |
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261 t = linspace(0,1,m); |
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262 gVec = g(t)'; |
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263 gpVec = (D1*gVec)'; |
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264 |
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265 gp1_fun = spline(t,gpVec(1,:)); |
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266 gp2_fun = spline(t,gpVec(2,:)); |
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267 gp_out = @(t) [gp1_fun(t);gp2_fun(t)]; |
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268 end |
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269 |
| 0 | 270 function obj = line(p1, p2) |
| 271 | |
| 272 function v = g_fun(t) | |
| 273 v(1,:) = p1(1) + t.*(p2(1)-p1(1)); | |
| 274 v(2,:) = p1(2) + t.*(p2(2)-p1(2)); | |
| 275 end | |
| 276 | |
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277 function v = g_fun_deriv(t) |
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278 v(1,:) = t.*0 + (p2(1)-p1(1)); |
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279 v(2,:) = t.*0 + (p2(2)-p1(2)); |
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280 end |
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281 |
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282 obj = parametrization.Curve(@g_fun, @g_fun_deriv); |
| 0 | 283 end |
| 284 | |
| 285 function obj = circle(c,r,phi) | |
| 286 default_arg('phi',[0; 2*pi]) | |
| 287 default_arg('c',[0; 0]) | |
| 288 default_arg('r',1) | |
| 289 | |
| 290 function v = g_fun(t) | |
| 291 w = phi(1)+t*(phi(2)-phi(1)); | |
| 292 v(1,:) = c(1) + r*cos(w); | |
| 293 v(2,:) = c(2) + r*sin(w); | |
| 294 end | |
| 295 | |
| 296 function v = g_fun_deriv(t) | |
| 297 w = phi(1)+t*(phi(2)-phi(1)); | |
| 298 v(1,:) = -(phi(2)-phi(1))*r*sin(w); | |
| 299 v(2,:) = (phi(2)-phi(1))*r*cos(w); | |
| 300 end | |
| 301 | |
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302 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 303 end |
| 304 | |
| 305 function obj = bezier(p0, p1, p2, p3) | |
| 306 function v = g_fun(t) | |
| 307 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); | |
| 308 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); | |
| 309 end | |
| 310 | |
| 311 function v = g_fun_deriv(t) | |
| 312 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)); | |
| 313 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)); | |
| 314 end | |
| 315 | |
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316 obj = parametrization.Curve(@g_fun,@g_fun_deriv); |
| 0 | 317 end |
| 318 | |
| 319 | |
| 320 function [g_out,gp_out] = transform_g(g,gp,tr) | |
| 321 A = tr.A; | |
| 322 b = tr.b; | |
| 323 flip = tr.flip; | |
| 324 | |
| 325 function v = g_fun_noflip(t) | |
| 326 % v = A*g + b | |
| 327 x = g(t); | |
| 328 | |
| 329 v(1,:) = A(1,:)*x+b(1); | |
| 330 v(2,:) = A(2,:)*x+b(2); | |
| 331 end | |
| 332 | |
| 333 function v = g_fun_flip(t) | |
| 334 % v = A*g + b | |
| 335 x = g(1-t); | |
| 336 | |
| 337 v(1,:) = A(1,:)*x+b(1); | |
| 338 v(2,:) = A(2,:)*x+b(2); | |
| 339 end | |
| 340 | |
| 341 | |
| 342 switch flip | |
| 343 case 1 | |
| 344 g_out = @g_fun_noflip; | |
| 345 gp_out = @(t)A*gp(t); | |
| 346 case -1 | |
| 347 g_out = @g_fun_flip; | |
| 348 gp_out = @(t)-A*gp(1-t); | |
| 349 end | |
| 350 end | |
| 351 | |
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352 end |
| 0 | 353 end |
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354 |
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355 function g_norm = normalize(g0) |
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356 g1 = g0(1,:); |
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357 g2 = g0(2,:); |
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358 normalization = sqrt(sum(g0.^2,1)); |
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359 g_norm = [g1./normalization; g2./normalization]; |
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360 end |
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361 |
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362 function I = integral_vec(f,a,b) |
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363 % Wrapper around the built-in function integral that |
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364 % handles multiple limits. |
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365 |
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366 Na = length(a); |
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367 Nb = length(b); |
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368 assert(Na == 1 || Nb == 1 || Na==Nb,... |
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369 'a and b must have same length, unless one is a scalar.'); |
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370 |
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371 if(Na>Nb); |
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372 I = zeros(size(a)); |
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373 for i = 1:Na |
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374 I(i) = integral(f,a(i),b); |
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375 end |
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376 elseif(Nb>Na) |
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377 I = zeros(size(b)); |
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378 for i = 1:Nb |
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379 I(i) = integral(f,a,b(i)); |
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380 end |
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381 else |
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382 I = zeros(size(b)); |
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383 for i = 1:Nb |
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384 I(i) = integral(f,a(i),b(i)); |
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385 end |
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386 end |
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387 end |
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388 |
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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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389 % Returns a function handle to the spline. |
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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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390 function f = spline(tval,fval,spline_order) |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
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changeset
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391 default_arg('spline_order',4); |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
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392 [m,~] = size(tval); |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
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changeset
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393 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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394 |
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ad3089f04e0b
Revert changes in Curve so that spline() is not a static method.
Martin Almquist <malmquist@stanford.edu>
parents:
1090
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395 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
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396 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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397 end |