Mercurial > repos > public > sbplib
annotate +parametrization/old/triang_interp.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 | 81e0ead29431 |
| children |
| rev | line source |
|---|---|
| 0 | 1 classdef triang_interp |
| 2 properties | |
| 3 g1, g2 ,g3 % Curves encirling the tirangle in the positive direction. | |
| 4 A,B,C % The corners of the triangle | |
| 5 Sa, Sb, Sc % Mappings from square with different sides collapsed | |
| 6 end | |
| 7 | |
| 8 methods | |
| 9 function o = triang_interp(g1,g2,g3) | |
| 10 o.g1 = g1; | |
| 11 o.g2 = g2; | |
| 12 o.g3 = g3; | |
| 13 o.A = g1(0); | |
| 14 o.B = g2(0); | |
| 15 o.C = g3(0); | |
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16 o.Sa = parametrization.triang_interp.square_to_triangle_interp(g2,g3,g1); |
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17 o.Sb = parametrization.triang_interp.square_to_triangle_interp(g3,g1,g2); |
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18 o.Sc = parametrization.triang_interp.square_to_triangle_interp(g1,g2,g3); |
| 0 | 19 end |
| 20 | |
| 21 | |
| 22 function show(o,N) | |
| 23 % Show the mapped meridians of the triangle. | |
| 24 % Might be used for the barycentric coordinates. | |
| 25 ma = @(t)o.Sa(1/2,1-t); | |
| 26 mb = @(t)o.Sb(1/2,1-t); | |
| 27 mc = @(t)o.Sc(1/2,1-t); | |
| 28 | |
| 29 na = @(t)o.Sa(t,1/2); | |
| 30 | |
| 31 ka = @(t)(o.g1(1-t)+o.g2(t))/2; | |
| 32 | |
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33 h = parametrization.plot_curve(ma); |
| 0 | 34 h.Color = Color.blue; |
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35 h = parametrization.plot_curve(mb); |
| 0 | 36 h.Color = Color.blue; |
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37 h = parametrization.plot_curve(mc); |
| 0 | 38 h.Color = Color.blue; |
| 39 | |
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40 h = parametrization.plot_curve(na); |
| 0 | 41 h.Color = Color.red; |
| 42 | |
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43 h = parametrization.plot_curve(ka); |
| 0 | 44 h.Color = Color.red; |
| 45 | |
| 46 [a(1),a(2)] = ma(1/3); | |
| 47 [b(1),b(2)] = mb(1/3); | |
| 48 [c(1),c(2)] = mc(1/3); | |
| 49 | |
| 50 d = ka(1-1/3); | |
| 51 | |
| 52 | |
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53 parametrization.label_pt(a,b,c,d); |
| 0 | 54 |
| 55 | |
| 56 % t = linspace(0,1,N); | |
| 57 % for i = 1:N | |
| 58 % sa = @(s)o.Sa(s,t(i)); | |
| 59 % sb = @(s)o.Sb(s,t(i)); | |
| 60 % sc = @(s)o.Sc(s,t(i)); | |
| 61 | |
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62 % h = parametrization.plot_curve(sa); |
| 0 | 63 % h.Color = Color.blue; |
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64 % h = parametrization.plot_curve(sb); |
| 0 | 65 % h.Color = Color.blue; |
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66 % h = parametrization.plot_curve(sc); |
| 0 | 67 % h.Color = Color.blue; |
| 68 % end | |
| 69 | |
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70 h = parametrization.plot_curve(o.g1); |
| 0 | 71 h.LineWidth = 2; |
| 72 h.Color = Color.red; | |
| 73 | |
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74 h = parametrization.plot_curve(o.g2); |
| 0 | 75 h.LineWidth = 2; |
| 76 h.Color = Color.red; | |
| 77 | |
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78 h = parametrization.plot_curve(o.g3); |
| 0 | 79 h.LineWidth = 2; |
| 80 h.Color = Color.red; | |
| 81 | |
| 82 end | |
| 83 | |
| 84 | |
| 85 end | |
| 86 | |
| 87 methods(Static) | |
| 88 % Makes a mapping from the unit square to a triangle by collapsing | |
| 89 % one of the sides of the squares to a corner on the triangle | |
| 90 % The collapsed side is mapped to the corner oposite to g1. | |
| 91 % This is done such that for S(s,t), S(s,1) = g1(s) | |
| 92 function S = square_to_triangle_interp(g1,g2,g3) | |
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93 corner = parametrization.line_segment(g3(0),g3(0)); |
|
81e0ead29431
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Jonatan Werpers <jonatan@werpers.com>
parents:
151
diff
changeset
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94 S = parametrization.transfinite_interp(corner,g3,f(g1),f(g2)) |
| 0 | 95 |
| 96 % Function to flip a curve | |
| 97 function h = f(g) | |
| 98 h = @(t)g(1-t); | |
| 99 end | |
| 100 end | |
| 101 end | |
| 102 | |
| 103 end | |
| 104 | |
| 105 % % Return a mapping from u.v to x,y of the domain encircled by g1 g2 g3 in the the positive direction. created be using transfinite interpolation. | |
| 106 % function S = triang_interp(g1,g2,g3) | |
| 107 % A = g1(0) | |
| 108 % B = g2(0) | |
| 109 % C = g3(0) | |
| 110 | |
| 111 % function [x,y] = S_fun(u,v) | |
| 112 % w = sqrt((u-1)^2+v^2)/sqrt(2); % Parameter for g3 | |
| 113 % v = v*(1-u-v)*g1(u) + u*(1-u-v)*g2(v) + u*v*g3(w) ... | |
| 114 % +(1-u)*(1-v)*A+u*(1-v)*B + (1-u)*v*C; | |
| 115 % x = v(1); | |
| 116 % y = v(2); | |
| 117 % end | |
| 118 % S = @S_fun; | |
| 119 % end | |
| 120 | |
| 121 | |
| 122 | |
| 123 % function subsref(obj,S) | |
| 124 % if ~all(isnumeric(S.subs{:})) | |
| 125 % error('Only supports calling object with number') | |
| 126 % end | |
| 127 % if numel(S.subs{:}) > 1 | |
| 128 % disp('You''ve called the object with more than one argument'); | |
| 129 % else | |
| 130 % disp(['You called the object with argument = ',num2str(S.subs{:})]); | |
| 131 % end | |
| 132 % end |