用MATLAB计算曲率

uperrua

曲率公式：
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注意：
2 u+ D# X2 U- a①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
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程序：


clc; clear all; close all;
+ M3 K  j- `' i, {x0 = linspace(0, 1);
! S" ^  L  Q+ z0 J6 \* |% ?7 Ly0 = sin(x0).*cos(x0);
h = abs(diff([x0(2), x0(1)]));
2 |; p. I& D  `1 \, o/ h* L% 模拟一阶导
figure; box on; hold on;
ythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
+ X+ e& n0 H8 eyapp1 = gradient(y0, h); %matlab数值近似
* e' w$ Z. P7 n  B/ r$ I3 l; splot(x0, ythe1, '.');
6 |$ r' V" d# `2 J1 V$ bplot(x0, yapp1, 'r');
legend('理论值', '模拟值');
title('模拟一阶导');
0 ]# X- W( V& [% [9 W' `: k% W% 模拟二阶导
) \5 k0 S- t/ H# p  ffigure; box on; hold on;
5 f2 S* X- w5 U8 d( gythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
yapp2 = 2*2*del2(y0, h); %matlab数值近似
; R9 `7 F5 z, Mplot(x0, ythe2,'.');
( i) d# R5 Y* qplot(x0, yapp2,'r');
legend('理论值', '模拟值');
title('模拟二阶导');
% 模拟曲率
syms x y
y = sin(x)*cos(x);
yd2 = diff(y, 2);
yd1 = diff(y, 1);
k = abs(yd2)/(1+yd1^2)^(3/2);
k1 = subs(k, x, x0);
9 @+ F4 v, h# O  B$ _4 n! kk2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
figure; box on; hold on;
plot(x0, k1, '.');
plot(x0, k2, 'r');
$ g7 X& l  X+ Elegend('理论值', '模拟值', 'Location', 'NorthWest');
# m4 Q' \- G# e2 o9 Z4 ttitle('模拟曲率');
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CCxiaom

用MATLAB计算曲率

NingW

用MATLAB计算曲率