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