Mercurial > repos > public > sbplib
annotate +parametrization/old/triang_interp.m @ 774:66eb4a2bbb72 feature/grids
Remove default scaling of the system.
The scaling doens't seem to help actual solutions. One example that fails in the flexural code.
With large timesteps the solutions seems to blow up. One particular example is profilePresentation
on the tdb_presentation_figures branch with k = 0.0005
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Wed, 18 Jul 2018 15:42:52 -0700 |
| 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)); |
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81e0ead29431
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parents:
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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 |