Mercurial > repos > public > sbplib
annotate +grid/Curve.m @ 86:3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
| author | Martin Almquist <martin.almquist@it.uu.se> |
|---|---|
| date | Sun, 29 Nov 2015 14:28:53 +0100 |
| parents | 48b6fb693025 |
| children | 0a29a60e0b21 |
| rev | line source |
|---|---|
| 0 | 1 classdef Curve |
| 2 properties | |
| 3 g | |
| 4 gp | |
| 5 transformation | |
| 6 end | |
| 7 methods | |
| 8 %TODO: | |
| 9 % Errors or FD if there is no derivative function added. | |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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10 % -semi-done |
| 0 | 11 |
| 12 % Concatenation of curves | |
| 13 % Subsections of curves | |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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14 % Stretching of curve paramter - semi-done |
| 0 | 15 % Curve to cell array of linesegments |
| 16 | |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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17 % Should supply either derivative or a difference operator D1 |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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18 function obj = Curve(g,gp,transformation,D1) |
| 0 | 19 default_arg('gp',[]); |
| 20 default_arg('transformation',[]); | |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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21 default_arg('D1',[]); |
| 0 | 22 p_test = g(0); |
| 23 assert(all(size(p_test) == [2,1]), 'A curve parametrization must return a 2x1 vector.'); | |
| 24 | |
|
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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25 if(isempty(gp) && isempty(D1)); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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26 % Should be error instead of disp. |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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27 disp(['You really should supply either the exact derivative ',... |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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28 'or a suitable difference operator to compute it.']); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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29 elseif(isempty(gp)) |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
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30 gp = grid.Curve.numerical_derivative(g,D1); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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31 end |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
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32 |
| 0 | 33 if ~isempty(transformation) |
| 34 transformation.base_g = g; | |
| 35 transformation.base_gp = gp; | |
| 36 [g,gp] = grid.Curve.transform_g(g,gp,transformation); | |
| 37 end | |
| 38 | |
| 39 obj.g = g; | |
| 40 obj.gp = gp; | |
| 41 obj.transformation = transformation; | |
| 42 end | |
|
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
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changeset
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43 |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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diff
changeset
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44 % Length of arc from parameter t0 to t1 (which may be vectors). |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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45 % Computed using derivative. |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
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46 function L = arc_length(obj,t0,t1) |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
diff
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47 deriv = obj.gp; |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
diff
changeset
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48 speed = @(t) sp(deriv(t)); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
diff
changeset
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49 |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
diff
changeset
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50 function s = sp(deriv) |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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changeset
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51 s = sqrt(sum(deriv.^2,1)); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
diff
changeset
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52 end |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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53 L = util.integral_vec(speed,t0,t1); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
0
diff
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54 end |
| 0 | 55 |
| 56 % Made up length calculation!! Science this before actual use!! | |
| 57 % Calculates the length of the curve. Makes sure the longet segment used is shorter than h_max. | |
| 58 function [L,t] = curve_length(C,h_max) | |
| 59 default_arg('h_max',0.001); | |
| 60 g = C.g; | |
| 61 h = 0.1; | |
| 62 m = 1/h+1; | |
| 63 t = linspace(0,1,m); | |
| 64 | |
| 65 [p,d] = get_d(t,g); | |
| 66 | |
| 67 while any(d>h_max) | |
| 68 I = find(d>h_max); | |
| 69 | |
| 70 % plot(p(1,:),p(2,:),'.') | |
| 71 % waitforbuttonpress | |
| 72 | |
| 73 new_t = []; | |
| 74 for i = I | |
| 75 new_t(end +1) = (t(i)+t(i+1))/2; | |
| 76 end | |
| 77 t = [t new_t]; | |
| 78 t = sort(t); | |
| 79 | |
| 80 [p,d] = get_d(t,g); | |
| 81 end | |
| 82 | |
| 83 L = sum(d); | |
| 84 | |
| 85 function [p,d] = get_d(t,g) | |
| 86 n = length(t); | |
| 87 | |
| 88 p = zeros(2,n); | |
| 89 for i = 1:n | |
| 90 p(:,i) = g(t(i)); | |
| 91 end | |
| 92 | |
| 93 d = zeros(1,n-1); | |
| 94 for i = 1:n-1 | |
| 95 d(i) = norm(p(:,i) - p(:,i+1)); | |
| 96 end | |
| 97 end | |
| 98 end | |
| 99 | |
| 100 function n = normal(obj,t) | |
| 101 deriv = obj.gp(t); | |
| 102 normalization = sqrt(sum(deriv.^2,1)); | |
| 103 n = [-deriv(2,:)./normalization; deriv(1,:)./normalization]; | |
| 104 end | |
| 105 | |
| 106 | |
| 107 % Plots a curve g(t) for 0<t<1, using n points. Retruns a handle h to the plotted curve. | |
| 108 % h = plot_curve(g,n) | |
| 109 function h = plot(obj,n) | |
| 110 default_arg('n',100); | |
| 111 | |
| 112 t = linspace(0,1,n); | |
| 113 | |
| 114 p = obj.g(t); | |
| 115 | |
| 116 h = line(p(1,:),p(2,:)); | |
| 117 end | |
| 118 | |
| 119 function h= plot_normals(obj,l,n,m) | |
| 120 default_arg('l',0.1); | |
| 121 default_arg('n',10); | |
| 122 default_arg('m',100); | |
| 123 t_n = linspace(0,1,n); | |
| 124 | |
| 125 normals = obj.normal(t_n)*l; | |
| 126 | |
| 127 n0 = obj.g(t_n); | |
| 128 n1 = n0 + normals; | |
| 129 | |
| 130 h = line([n0(1,:); n1(1,:)],[n0(2,:); n1(2,:)]); | |
| 131 set(h,'Color',Color.red); | |
| 132 obj.plot(m); | |
| 133 end | |
| 134 | |
| 135 function h= show(obj,name) | |
| 136 p = obj.g(1/2); | |
| 137 n = obj.normal(1/2); | |
| 138 p = p + n*0.1; | |
| 139 | |
| 140 % Add arrow | |
| 141 | |
| 142 h = text(p(1),p(2),name); | |
| 143 h.HorizontalAlignment = 'center'; | |
| 144 h.VerticalAlignment = 'middle'; | |
| 145 | |
| 146 obj.plot(); | |
| 147 end | |
| 148 % Shows curve with name and arrow for direction. | |
| 149 | |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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150 |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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151 % Should this be in the transformation method? |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
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152 function curve = stretch_parameter(obj,type) |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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153 default_arg('type','arc_length'); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
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154 switch type |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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155 % Arc length parameterization. WARNING: slow. |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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156 case 'arc_length' |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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157 arcLength = @(t) obj.arc_length(0,t); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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158 arcPar = @(t) util.fzero_vec(@(s)arcLength(s) - t*arcLength(1),0); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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159 g_new = @(t)obj.g(arcPar(t)); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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160 gp_old = obj.gp; |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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161 gp_new = @(t) normalize(gp_old(arcPar(t))); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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parents:
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162 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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163 curve = grid.Curve(g_new,gp_new); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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164 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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165 otherwise |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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166 error('That stretching is not implemented.'); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
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167 end |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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168 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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169 end |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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170 |
| 0 | 171 % how to make it work for methods without returns |
| 172 function p = subsref(obj,S) | |
| 173 %Should i add error checking here? | |
| 174 %Maybe if you want performance you fetch obj.g and then use that | |
| 175 switch S(1).type | |
| 176 case '()' | |
| 177 p = obj.g(S.subs{1}); | |
| 178 % case '.' | |
| 179 | |
| 180 % p = obj.(S.subs); | |
| 181 otherwise | |
| 182 p = builtin('subsref',obj,S); | |
| 183 % error() | |
| 184 end | |
| 185 end | |
| 186 | |
| 187 | |
| 188 | |
| 189 | |
| 190 %% TRANSFORMATION OF A CURVE | |
| 191 function D = reverse(C) | |
| 192 % g = C.g; | |
| 193 % gp = C.gp; | |
| 194 % D = grid.Curve(@(t)g(1-t),@(t)-gp(1-t)); | |
| 195 D = C.transform([],[],-1); | |
| 196 end | |
| 197 | |
| 198 function D = transform(C,A,b,flip) | |
| 199 default_arg('A',[1 0; 0 1]); | |
| 200 default_arg('b',[0; 0]); | |
| 201 default_arg('flip',1); | |
| 202 if isempty(C.transformation) | |
| 203 g = C.g; | |
| 204 gp = C.gp; | |
| 205 transformation.A = A; | |
| 206 transformation.b = b; | |
| 207 transformation.flip = flip; | |
| 208 else | |
| 209 g = C.transformation.base_g; | |
| 210 gp = C.transformation.base_gp; | |
| 211 A_old = C.transformation.A; | |
| 212 b_old = C.transformation.b; | |
| 213 flip_old = C.transformation.flip; | |
| 214 | |
| 215 transformation.A = A*A_old; | |
| 216 transformation.b = A*b_old + b; | |
| 217 transformation.flip = flip*flip_old; | |
| 218 end | |
| 219 | |
| 220 D = grid.Curve(g,gp,transformation); | |
| 221 | |
| 222 end | |
| 223 | |
| 224 function D = translate(C,a) | |
| 225 g = C.g; | |
| 226 gp = C.gp; | |
| 227 | |
| 228 % function v = g_fun(t) | |
| 229 % x = g(t); | |
| 230 % v(1,:) = x(1,:)+a(1); | |
| 231 % v(2,:) = x(2,:)+a(2); | |
| 232 % end | |
| 233 | |
| 234 % D = grid.Curve(@g_fun,gp); | |
| 235 | |
| 236 D = C.transform([],a); | |
| 237 end | |
| 238 | |
| 239 function D = mirror(C, a, b) | |
| 240 assert_size(a,[2,1]); | |
| 241 assert_size(b,[2,1]); | |
| 242 | |
| 243 g = C.g; | |
| 244 gp = C.gp; | |
| 245 | |
| 246 l = b-a; | |
| 247 lx = l(1); | |
| 248 ly = l(2); | |
| 249 | |
| 250 | |
| 251 % fprintf('Singular?\n') | |
| 252 | |
| 253 A = [lx^2-ly^2 2*lx*ly; 2*lx*ly ly^2-lx^2]/(l'*l); | |
| 254 | |
| 255 % function v = g_fun(t) | |
| 256 % % v = a + A*(g(t)-a) | |
| 257 % x = g(t); | |
| 258 | |
| 259 % ax1 = x(1,:)-a(1); | |
| 260 % ax2 = x(2,:)-a(2); | |
| 261 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 262 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 263 % end | |
| 264 | |
| 265 % function v = gp_fun(t) | |
| 266 % v = A*gp(t); | |
| 267 % end | |
| 268 | |
| 269 % D = grid.Curve(@g_fun,@gp_fun); | |
| 270 | |
| 271 % g = A(g-a)+a = Ag - Aa + a; | |
| 272 b = - A*a + a; | |
| 273 D = C.transform(A,b); | |
| 274 | |
| 275 end | |
| 276 | |
| 277 function D = rotate(C,a,rad) | |
| 278 assert_size(a, [2,1]); | |
| 279 assert_size(rad, [1,1]); | |
| 280 g = C.g; | |
| 281 gp = C.gp; | |
| 282 | |
| 283 | |
| 284 A = [cos(rad) -sin(rad); sin(rad) cos(rad)]; | |
| 285 | |
| 286 % function v = g_fun(t) | |
| 287 % % v = a + A*(g(t)-a) | |
| 288 % x = g(t); | |
| 289 | |
| 290 % ax1 = x(1,:)-a(1); | |
| 291 % ax2 = x(2,:)-a(2); | |
| 292 % v(1,:) = a(1)+A(1,:)*[ax1;ax2]; | |
| 293 % v(2,:) = a(2)+A(2,:)*[ax1;ax2]; | |
| 294 % end | |
| 295 | |
| 296 % function v = gp_fun(t) | |
| 297 % v = A*gp(t); | |
| 298 % end | |
| 299 | |
| 300 % D = grid.Curve(@g_fun,@gp_fun); | |
| 301 | |
| 302 | |
| 303 % g = A(g-a)+a = Ag - Aa + a; | |
| 304 b = - A*a + a; | |
| 305 D = C.transform(A,b); | |
| 306 end | |
| 307 end | |
| 308 | |
| 309 methods (Static) | |
|
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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310 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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311 function gp_out = numerical_derivative(g,D1) |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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312 m = length(D1); L = 1; % Assume curve parameter from 0 to 1. |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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313 dt = L/(m-1); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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314 t = linspace(0,L,m); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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315 g = g(t)'; |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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316 gp = (D1*g)'; |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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317 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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318 % Make vectors longer to make sure splines are |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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319 % reasonable at 1+eps. |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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320 t_l = linspace(0,L+dt,m+1); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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321 gp_l = [gp,gp(:,end)+gp(:,end)-gp(:,end-1)]; |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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322 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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323 % 4:th order splines. |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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324 spline_order = 4; |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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325 gp1 = spapi( optknt(t_l,spline_order), t_l, gp_l(1,:) ); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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326 gp2 = spapi( optknt(t_l,spline_order), t_l, gp_l(2,:) ); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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327 gp1_fun = @(t) fnval(gp1,t); gp2_fun = @(t) fnval(gp2,t); |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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328 gp_out = @(t) [gp1_fun(t);gp2_fun(t)]; |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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329 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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330 end |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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331 |
| 0 | 332 function obj = line(p1, p2) |
| 333 | |
| 334 function v = g_fun(t) | |
| 335 v(1,:) = p1(1) + t.*(p2(1)-p1(1)); | |
| 336 v(2,:) = p1(2) + t.*(p2(2)-p1(2)); | |
| 337 end | |
| 338 g = @g_fun; | |
| 339 | |
| 340 obj = grid.Curve(g); | |
| 341 end | |
| 342 | |
| 343 function obj = circle(c,r,phi) | |
| 344 default_arg('phi',[0; 2*pi]) | |
| 345 default_arg('c',[0; 0]) | |
| 346 default_arg('r',1) | |
| 347 | |
| 348 function v = g_fun(t) | |
| 349 w = phi(1)+t*(phi(2)-phi(1)); | |
| 350 v(1,:) = c(1) + r*cos(w); | |
| 351 v(2,:) = c(2) + r*sin(w); | |
| 352 end | |
| 353 | |
| 354 function v = g_fun_deriv(t) | |
| 355 w = phi(1)+t*(phi(2)-phi(1)); | |
| 356 v(1,:) = -(phi(2)-phi(1))*r*sin(w); | |
| 357 v(2,:) = (phi(2)-phi(1))*r*cos(w); | |
| 358 end | |
| 359 | |
| 360 obj = grid.Curve(@g_fun,@g_fun_deriv); | |
| 361 end | |
| 362 | |
| 363 function obj = bezier(p0, p1, p2, p3) | |
| 364 function v = g_fun(t) | |
| 365 v(1,:) = (1-t).^3*p0(1) + 3*(1-t).^2.*t*p1(1) + 3*(1-t).*t.^2*p2(1) + t.^3*p3(1); | |
| 366 v(2,:) = (1-t).^3*p0(2) + 3*(1-t).^2.*t*p1(2) + 3*(1-t).*t.^2*p2(2) + t.^3*p3(2); | |
| 367 end | |
| 368 | |
| 369 function v = g_fun_deriv(t) | |
| 370 v(1,:) = 3*(1-t).^2*(p1(1)-p0(1)) + 6*(1-t).*t*(p2(1)-p1(1)) + 3*t.^2*(p3(1)-p2(1)); | |
| 371 v(2,:) = 3*(1-t).^2*(p1(2)-p0(2)) + 6*(1-t).*t*(p2(2)-p1(2)) + 3*t.^2*(p3(2)-p2(2)); | |
| 372 end | |
| 373 | |
| 374 obj = grid.Curve(@g_fun,@g_fun_deriv); | |
| 375 end | |
| 376 | |
| 377 | |
| 378 function [g_out,gp_out] = transform_g(g,gp,tr) | |
| 379 A = tr.A; | |
| 380 b = tr.b; | |
| 381 flip = tr.flip; | |
| 382 | |
| 383 function v = g_fun_noflip(t) | |
| 384 % v = A*g + b | |
| 385 x = g(t); | |
| 386 | |
| 387 v(1,:) = A(1,:)*x+b(1); | |
| 388 v(2,:) = A(2,:)*x+b(2); | |
| 389 end | |
| 390 | |
| 391 function v = g_fun_flip(t) | |
| 392 % v = A*g + b | |
| 393 x = g(1-t); | |
| 394 | |
| 395 v(1,:) = A(1,:)*x+b(1); | |
| 396 v(2,:) = A(2,:)*x+b(2); | |
| 397 end | |
| 398 | |
| 399 | |
| 400 switch flip | |
| 401 case 1 | |
| 402 g_out = @g_fun_noflip; | |
| 403 gp_out = @(t)A*gp(t); | |
| 404 case -1 | |
| 405 g_out = @g_fun_flip; | |
| 406 gp_out = @(t)-A*gp(1-t); | |
| 407 end | |
| 408 end | |
| 409 | |
|
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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410 end |
| 0 | 411 end |
|
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
412 |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
413 function g_norm = normalize(g0) |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
414 g1 = g0(1,:); g2 = g0(2,:); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
415 normalization = sqrt(sum(g0.^2,1)); |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
416 g_norm = [g1./normalization; g2./normalization]; |
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3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
417 end |
|
3c39dd714fb6
In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
418 |
|
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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419 |
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In Curve: Added numerical FD differentiation if derivative is not supplied. Added arc length computation based on the derivative. Added arc length parameterization (but this function is very slow.). In +util: Added fzero_vec.m and integral_vec.m, which call fzero and integral but take vector arguments.
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|
420 |