Mercurial > repos > public > sbplib
annotate +parametrization/old/triang_interp.m @ 1198:2924b3a9b921 feature/d2_compatible
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Fri, 16 Aug 2019 14:30:28 -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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parents:
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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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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 |