用MATLAB计算曲率

uperrua

曲率公式：

& X+ c. p; Q3 O; G: o9 j" D注意：
# k$ H+ _8 e5 k4 d4 V( E0 |①曲率半径为曲率的倒数
②如果是离散点，先用polyfit和polyval拟合出曲线

程序：
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6 G8 K  {! {- d! uclc; clear all; close all;
x0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
) n8 r0 K, w3 }+ t2 O% zh = abs(diff([x0(2), x0(1)]));
% 模拟一阶导
figure; box on; hold on;
ythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
yapp1 = gradient(y0, h); %matlab数值近似
plot(x0, ythe1, '.');
plot(x0, yapp1, 'r');
, e1 y# R7 {- b0 b1 b% xlegend('理论值', '模拟值');
title('模拟一阶导');
! w% i5 h/ L# ^5 O! n* ~# Z" c4 s% 模拟二阶导
figure; box on; hold on;
. J9 Q( q, t- D$ T6 d$ r/ kythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
yapp2 = 2*2*del2(y0, h); %matlab数值近似
plot(x0, ythe2,'.');
8 I4 F( T6 Q* K8 g7 B% V( bplot(x0, yapp2,'r');
legend('理论值', '模拟值');
/ h* s1 H# X! w" ztitle('模拟二阶导');
: |1 L! T. t! A  n% 模拟曲率
syms x y
y = sin(x)*cos(x);
: y, S0 r; u9 m- l) S. Lyd2 = diff(y, 2);
yd1 = diff(y, 1);
& L1 \: K# X, M5 y4 uk = abs(yd2)/(1+yd1^2)^(3/2);
k1 = subs(k, x, x0);
k2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
' W& B' U- @! Q4 ]9 Bfigure; box on; hold on;
' p/ o4 T3 P4 e" e1 P3 pplot(x0, k1, '.');
+ p' c% u0 c. F4 ]2 N/ N# tplot(x0, k2, 'r');
  w6 T& r3 x9 _( K- Y- s2 Blegend('理论值', '模拟值', 'Location', 'NorthWest');
, h- e% z0 W& _title('模拟曲率');



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CCxiaom

用MATLAB计算曲率

NingW

用MATLAB计算曲率