用MATLAB计算曲率

uperrua

曲率公式：
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6 D+ @, u- d  v5 n6 Y注意：
- `3 {7 c5 I% i①曲率半径为曲率的倒数
; f6 H% x* v* m, b" Q( I" _②如果是离散点，先用polyfit和polyval拟合出曲线

程序：

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clc; clear all; close all;
) ]6 Q3 U4 f/ v1 ?) rx0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
h = abs(diff([x0(2), x0(1)]));
% 模拟一阶导
  H6 a. q# E0 Pfigure; box on; hold on;
1 C  q* l5 v; ?ythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
yapp1 = gradient(y0, h); %matlab数值近似
plot(x0, ythe1, '.');
, n! h& v7 J  P* Z' O* A  R8 D* Tplot(x0, yapp1, 'r');
legend('理论值', '模拟值');
title('模拟一阶导');
2 j9 x' l% X. D5 h+ C; p9 q! `% 模拟二阶导
8 A! V+ x8 F/ J; ifigure; box on; hold on;
ythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
: k, r* Q; A6 s; ^0 Syapp2 = 2*2*del2(y0, h); %matlab数值近似
plot(x0, ythe2,'.');
. K4 Q+ C3 T. H: Jplot(x0, yapp2,'r');
) a0 w  q1 e: Z3 Y6 clegend('理论值', '模拟值');
* T" X0 o0 Q1 g- R. k6 |9 ptitle('模拟二阶导');
% 模拟曲率
% B* a. K( t) I+ X8 ~8 t  d$ m  esyms x y
y = sin(x)*cos(x);
# ]) _( Q& X  ?) }7 J+ U8 J  y( }yd2 = diff(y, 2);
yd1 = diff(y, 1);
. `. N% }* {" v4 Rk = 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, '.');
plot(x0, k2, 'r');
8 T" D! T0 F' J' G% H3 q& j5 i6 d% vlegend('理论值', '模拟值', 'Location', 'NorthWest');
title('模拟曲率');

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用MATLAB计算曲率

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用MATLAB计算曲率