Mercurial > repos > public > sbplib
comparison testArcLength.m @ 87:0a29a60e0b21
In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
| author | Martin Almquist <martin.almquist@it.uu.se> |
|---|---|
| date | Sun, 29 Nov 2015 22:23:09 +0100 |
| parents | |
| children |
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| 86:3c39dd714fb6 | 87:0a29a60e0b21 |
|---|---|
| 1 m = 201; L = 1; order = 4; | |
| 2 close all; | |
| 3 tic | |
| 4 | |
| 5 g1 = @(t) 2*pi*t.*sin(2*pi*t); | |
| 6 g2 = @(t) 2*pi*t.*cos(2*pi*t); | |
| 7 g = @(t) [g1(t);g2(t)]; | |
| 8 | |
| 9 t = linspace(0,L,m)'; dt = L/(m-1); | |
| 10 ops = sbp.Ordinary(m,dt,order); | |
| 11 D = ops.derivatives.D1; | |
| 12 | |
| 13 C = grid.Curve(g,[],[],D); | |
| 14 | |
| 15 % Function | |
| 16 figure; | |
| 17 C.plot([],'bo'); | |
| 18 hold on | |
| 19 plot(g1(t),g2(t),'r-'); | |
| 20 drawnow | |
| 21 | |
| 22 % Derivative | |
| 23 figure | |
| 24 C.plot_derivative([],'bo'); | |
| 25 hold on; | |
| 26 plot(2*pi*sin(2*pi*t) + (2*pi)^2*t.*cos(2*pi*t),... | |
| 27 2*pi*cos(2*pi*t) - (2*pi)^2*t.*sin(2*pi*t),'r-') | |
| 28 drawnow | |
| 29 | |
| 30 % Arc length | |
| 31 L = C.arc_length_fun(t); | |
| 32 figure; | |
| 33 plot(t,L) | |
| 34 drawnow | |
| 35 | |
| 36 % Stretch curve | |
| 37 C2 = C.stretch_parameter(); | |
| 38 z = linspace(0,1,m); | |
| 39 gnew = C2.g(z); | |
| 40 gpnew = C2.gp(z); | |
| 41 | |
| 42 % Compare stretched and unstretched curves. | |
| 43 figure | |
| 44 plot(g1(t),g2(t),'b*',gnew(1,:),gnew(2,:),'ro'); | |
| 45 | |
| 46 % Compare stretched and unstretched derivatives. | |
| 47 figure | |
| 48 theta = linspace(0,2*pi,100); | |
| 49 plot(cos(theta),sin(theta),'-b',gpnew(1,:),gpnew(2,:),'rx'); | |
| 50 | |
| 51 toc | |
| 52 | |
| 53 | |
| 54 | |
| 55 |