用MATLAB计算曲率

uperrua

曲率公式：

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- p8 r8 I* P7 e* E# }①曲率半径为曲率的倒数
1 v, l7 ^& Z- m& V②如果是离散点，先用polyfit和polyval拟合出曲线
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程序：

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clc; clear all; close all;
x0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
h = abs(diff([x0(2), x0(1)]));
% 模拟一阶导
figure; box on; hold on;
1 X% [& M( w/ o! vythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
yapp1 = gradient(y0, h); %matlab数值近似
- z/ H8 j  e/ zplot(x0, ythe1, '.');
+ h$ ]. C4 J  d' P& lplot(x0, yapp1, 'r');
legend('理论值', '模拟值');
title('模拟一阶导');
' R# `0 r- m( ~1 M) k- `; \% W% 模拟二阶导
figure; box on; hold on;
! S) D* |% F9 u# p3 {; ^, k  }ythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
0 Y8 G2 B% e1 {: F& y$ a7 zyapp2 = 2*2*del2(y0, h); %matlab数值近似
, ?9 I2 N  F! B" v) u3 mplot(x0, ythe2,'.');
9 V0 M9 R; X6 }. Kplot(x0, yapp2,'r');
# X, R$ h8 I7 [5 [# m5 T, ?0 Mlegend('理论值', '模拟值');
, V5 I9 d: d- R, ntitle('模拟二阶导');
% 模拟曲率
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2 e3 L! }, T" U: gy = sin(x)*cos(x);
0 n3 x# f5 |$ U5 V5 z) G4 Q1 W. Kyd2 = diff(y, 2);
* b( a8 _5 |' \, E) l2 [) myd1 = diff(y, 1);
# W, m! J- P9 s- `0 zk = abs(yd2)/(1+yd1^2)^(3/2);
) \: {5 ~1 x/ b0 `& jk1 = subs(k, x, x0);
6 ^2 F4 o0 ]( W& p: wk2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
* B. z, q/ f, _; c. ]figure; box on; hold on;
2 g( e1 A. j7 }) g! Cplot(x0, k1, '.');
( H" b* T. B/ |/ {$ tplot(x0, k2, 'r');
" v  J. C1 n# J$ H8 Z% Vlegend('理论值', '模拟值', 'Location', 'NorthWest');
title('模拟曲率');

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CCxiaom

用MATLAB计算曲率

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用MATLAB计算曲率