Mercurial > repos > public > sbplib
annotate +parametrization/Ti.m @ 1037:2d7ba44340d0 feature/burgers1d
Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Fri, 18 Jan 2019 09:02:02 +0100 |
| parents | edb1d60b0b77 |
| children |
| rev | line source |
|---|---|
| 0 | 1 classdef Ti |
| 2 properties | |
| 3 gs % {4}Curve | |
| 4 S % FunctionHandle(u,v) | |
| 5 end | |
| 6 | |
| 7 methods | |
| 8 % TODO function to label boundary names. | |
| 9 % function to find largest and smallest delta h in the grid. Maybe shouldnt live here | |
| 10 function obj = Ti(C1,C2,C3,C4) | |
| 11 obj.gs = {C1,C2,C3,C4}; | |
| 12 | |
| 13 g1 = C1.g; | |
| 14 g2 = C2.g; | |
| 15 g3 = C3.g; | |
| 16 g4 = C4.g; | |
| 17 | |
| 18 A = g1(0); | |
| 19 B = g2(0); | |
| 20 C = g3(0); | |
| 21 D = g4(0); | |
| 22 | |
| 23 function o = S_fun(u,v) | |
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24 if isrow(u) && isrow(v) |
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25 flipped = false; |
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26 else |
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27 flipped = true; |
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28 u = u'; |
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29 v = v'; |
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30 end |
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31 |
| 0 | 32 x1 = g1(u); |
| 33 x2 = g2(v); | |
| 34 x3 = g3(1-u); | |
| 35 x4 = g4(1-v); | |
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36 |
| 0 | 37 o1 = (1-v).*x1(1,:) + u.*x2(1,:) + v.*x3(1,:) + (1-u).*x4(1,:) ... |
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38 -((1-u).*(1-v).*A(1,:) + u.*(1-v).*B(1,:) + u.*v.*C(1,:) + (1-u).*v.*D(1,:)); |
| 0 | 39 o2 = (1-v).*x1(2,:) + u.*x2(2,:) + v.*x3(2,:) + (1-u).*x4(2,:) ... |
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40 -((1-u).*(1-v).*A(2,:) + u.*(1-v).*B(2,:) + u.*v.*C(2,:) + (1-u).*v.*D(2,:)); |
| 0 | 41 |
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42 if ~flipped |
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43 o = [o1;o2]; |
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44 else |
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45 o = [o1'; o2']; |
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46 end |
| 0 | 47 end |
| 48 | |
| 49 obj.S = @S_fun; | |
| 50 end | |
| 51 | |
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52 % Does this funciton make sense? |
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53 % Should it always be eval? |
| 0 | 54 function [X,Y] = map(obj,u,v) |
| 55 default_arg('v',u); | |
| 56 | |
| 57 if isscalar(u) | |
| 58 u = linspace(0,1,u); | |
| 59 end | |
| 60 | |
| 61 if isscalar(v) | |
| 62 v = linspace(0,1,v); | |
| 63 end | |
| 64 | |
| 65 S = obj.S; | |
| 66 | |
| 67 nu = length(u); | |
| 68 nv = length(v); | |
| 69 | |
| 70 X = zeros(nv,nu); | |
| 71 Y = zeros(nv,nu); | |
| 72 | |
| 73 u = rowVector(u); | |
| 74 v = rowVector(v); | |
| 75 | |
| 76 for i = 1:nv | |
| 77 p = S(u,v(i)); | |
| 78 X(i,:) = p(1,:); | |
| 79 Y(i,:) = p(2,:); | |
| 80 end | |
| 81 end | |
| 82 | |
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83 % Evaluate S for each pair of u and v, |
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84 % Return same shape as u |
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85 function [x, y] = eval(obj, u, v) |
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86 x = zeros(size(u)); |
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87 y = zeros(size(u)); |
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88 |
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89 for i = 1:numel(u) |
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90 p = obj.S(u(i), v(i)); |
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91 x(i) = p(1,:); |
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92 y(i) = p(2,:); |
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93 end |
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94 end |
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95 |
| 0 | 96 function h = plot(obj,nu,nv) |
| 97 S = obj.S; | |
| 98 | |
| 99 default_arg('nv',nu) | |
| 100 | |
| 101 u = linspace(0,1,nu); | |
| 102 v = linspace(0,1,nv); | |
| 103 | |
| 104 m = 100; | |
| 105 | |
| 106 X = zeros(nu+nv,m); | |
| 107 Y = zeros(nu+nv,m); | |
| 108 | |
| 109 | |
| 110 t = linspace(0,1,m); | |
| 111 for i = 1:nu | |
| 112 p = S(u(i),t); | |
| 113 X(i,:) = p(1,:); | |
| 114 Y(i,:) = p(2,:); | |
| 115 end | |
| 116 | |
| 117 for i = 1:nv | |
| 118 p = S(t,v(i)); | |
| 119 X(i+nu,:) = p(1,:); | |
| 120 Y(i+nu,:) = p(2,:); | |
| 121 end | |
| 122 | |
| 123 h = line(X',Y'); | |
| 124 end | |
| 125 | |
| 126 | |
| 127 function h = show(obj,nu,nv) | |
| 128 default_arg('nv',nu) | |
| 129 S = obj.S; | |
| 130 | |
| 131 if(nu>2 || nv>2) | |
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132 h.grid = obj.plot(nu,nv); |
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133 set(h.grid,'Color',[0 0.4470 0.7410]); |
| 0 | 134 end |
| 135 | |
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136 h.border = obj.plot(2,2); |
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137 set(h.border,'Color',[0.8500 0.3250 0.0980]); |
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138 set(h.border,'LineWidth',2); |
| 0 | 139 end |
| 140 | |
| 141 | |
| 142 % TRANSFORMATIONS | |
| 143 function ti = translate(obj,a) | |
| 144 gs = obj.gs; | |
| 145 | |
| 146 for i = 1:length(gs) | |
| 147 new_gs{i} = gs{i}.translate(a); | |
| 148 end | |
| 149 | |
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150 ti = parametrization.Ti(new_gs{:}); |
| 0 | 151 end |
| 152 | |
| 153 % Mirrors the Ti so that the resulting Ti is still left handed. | |
| 154 % (Corrected by reversing curves and switching e and w) | |
| 155 function ti = mirror(obj, a, b) | |
| 156 gs = obj.gs; | |
| 157 | |
| 158 new_gs = cell(1,4); | |
| 159 | |
| 160 new_gs{1} = gs{1}.mirror(a,b).reverse(); | |
| 161 new_gs{3} = gs{3}.mirror(a,b).reverse(); | |
| 162 new_gs{2} = gs{4}.mirror(a,b).reverse(); | |
| 163 new_gs{4} = gs{2}.mirror(a,b).reverse(); | |
| 164 | |
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165 ti = parametrization.Ti(new_gs{:}); |
| 0 | 166 end |
| 167 | |
| 168 function ti = rotate(obj,a,rad) | |
| 169 gs = obj.gs; | |
| 170 | |
| 171 for i = 1:length(gs) | |
| 172 new_gs{i} = gs{i}.rotate(a,rad); | |
| 173 end | |
| 174 | |
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175 ti = parametrization.Ti(new_gs{:}); |
| 0 | 176 end |
| 177 | |
| 178 function ti = rotate_edges(obj,n); | |
| 179 new_gs = cell(1,4); | |
| 180 for i = 0:3 | |
| 181 new_i = mod(i - n,4); | |
| 182 new_gs{new_i+1} = obj.gs{i+1}; | |
| 183 end | |
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184 ti = parametrization.Ti(new_gs{:}); |
| 0 | 185 end |
| 186 end | |
| 187 | |
| 188 methods(Static) | |
| 189 function obj = points(p1, p2, p3, p4) | |
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190 g1 = parametrization.Curve.line(p1,p2); |
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191 g2 = parametrization.Curve.line(p2,p3); |
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192 g3 = parametrization.Curve.line(p3,p4); |
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193 g4 = parametrization.Curve.line(p4,p1); |
| 0 | 194 |
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195 obj = parametrization.Ti(g1,g2,g3,g4); |
| 0 | 196 end |
| 197 | |
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198 function obj = rectangle(a, b) |
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199 p1 = a; |
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200 p2 = [b(1), a(2)]; |
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201 p3 = b; |
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202 p4 = [a(1), b(2)]; |
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203 |
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204 obj = parametrization.Ti.points(p1,p2,p3,p4); |
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205 end |
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206 |
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332
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207 % Like the constructor but allows inputing line curves as 2-cell arrays: |
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208 % example: parametrization.Ti.linesAndCurves(g1, g2, {a, b} g4) |
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209 function obj = linesAndCurves(C1, C2, C3, C4) |
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210 C = {C1, C2, C3, C4}; |
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211 c = cell(1,4); |
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212 |
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213 for i = 1:4 |
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214 if ~iscell(C{i}) |
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215 c{i} = C{i}; |
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216 else |
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217 c{i} = parametrization.Curve.line(C{i}{:}); |
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218 end |
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219 end |
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220 |
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221 obj = parametrization.Ti(c{:}); |
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222 end |
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223 |
| 0 | 224 function label(varargin) |
| 225 if nargin == 2 && ischar(varargin{2}) | |
| 226 label_impl(varargin{:}); | |
| 227 else | |
| 228 for i = 1:length(varargin) | |
| 229 label_impl(varargin{i},inputname(i)); | |
| 230 end | |
| 231 end | |
| 232 | |
| 233 | |
| 234 function label_impl(ti,str) | |
| 235 S = ti.S; | |
| 236 | |
| 237 pc = S(0.5,0.5); | |
| 238 | |
| 239 margin = 0.1; | |
| 240 pw = S( margin, 0.5); | |
| 241 pe = S(1-margin, 0.5); | |
| 242 ps = S( 0.5, margin); | |
| 243 pn = S( 0.5, 1-margin); | |
| 244 | |
| 245 | |
| 246 ti.show(2,2); | |
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247 parametrization.place_label(pc,str); |
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248 parametrization.place_label(pw,'w'); |
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249 parametrization.place_label(pe,'e'); |
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250 parametrization.place_label(ps,'s'); |
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251 parametrization.place_label(pn,'n'); |
| 0 | 252 end |
| 253 end | |
| 254 end | |
| 255 end |