用MATLAB计算曲率

uperrua

曲率公式：

# \" T& e9 T3 J/ A- x注意：
7 U% k5 S( y9 w, T) [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
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程序：
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9 C; F1 @; \. N7 o2 u$ Uclc; clear all; close all;
x0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
0 y$ c6 j. |. D* l9 v; i# [2 [h = abs(diff([x0(2), x0(1)]));
8 ]( F/ u5 M0 N3 D8 e% 模拟一阶导
6 Q! u6 u+ I8 Zfigure; box on; hold on;
ythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
& D) I7 ~& }& K" z$ u1 h$ r1 l! @! |yapp1 = gradient(y0, h); %matlab数值近似
plot(x0, ythe1, '.');
* P+ K* p" j0 Z9 P& `' s9 ]& \plot(x0, yapp1, 'r');
; k* A- D; f. r. |# nlegend('理论值', '模拟值');
' L: h! {. A3 I& }$ v) ttitle('模拟一阶导');
% 模拟二阶导
3 d; p% a. m/ r* u  t- Cfigure; box on; hold on;
ythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
  s$ s( v( |- Pyapp2 = 2*2*del2(y0, h); %matlab数值近似
7 e* z% r7 L1 H% Zplot(x0, ythe2,'.');
; H7 f: x/ ^, \( `- _plot(x0, yapp2,'r');
, C; ~: X! h6 w' n7 U9 g& c  s! Llegend('理论值', '模拟值');
, w9 s  C2 x5 Etitle('模拟二阶导');
: |  p. w5 m  V- J! ?% 模拟曲率
syms x y
" ]( O3 L- V7 T9 sy = sin(x)*cos(x);
yd2 = diff(y, 2);
yd1 = diff(y, 1);
6 B. X; j- E+ {. g4 b$ o" I' jk = abs(yd2)/(1+yd1^2)^(3/2);
k1 = subs(k, x, x0);
k2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
figure; box on; hold on;
plot(x0, k1, '.');
7 R! i" f4 O5 z1 T# A, k/ {0 Lplot(x0, k2, 'r');
6 n5 q& |; {, Mlegend('理论值', '模拟值', 'Location', 'NorthWest');
title('模拟曲率');

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CCxiaom

用MATLAB计算曲率

NingW

用MATLAB计算曲率