Mercurial > repos > public > sbplib
annotate +parametrization/old/triang_interp.m @ 577:e45c9b56d50d feature/grids
Add an Empty grid class
The need turned up for the flexural code when we may or may not have a grid for the open water and want to plot that solution.
In case there is no open water we need an empty grid to plot the empty gridfunction against to avoid errors.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Thu, 07 Sep 2017 09:16:12 +0200 |
| 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 |