用MATLAB计算曲率

uperrua

曲率公式：
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注意：
' K8 @) M" g$ ~" L- u* [' n①曲率半径为曲率的倒数
7 n7 c7 X" ~, w" n/ N% Y% E②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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- a4 X3 O8 m% |clc; clear all; close all;
x0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
  O8 y% t) n: t; p$ Bh = abs(diff([x0(2), x0(1)]));
% 模拟一阶导
figure; box on; hold on;
1 x- B8 v% W0 e. \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');
7 y7 B5 x3 ?" k: Rlegend('理论值', '模拟值');
& w, Y5 l* y7 }  otitle('模拟一阶导');
% 模拟二阶导
figure; box on; hold on;
ythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
1 p" L) p9 Q7 q0 j7 @yapp2 = 2*2*del2(y0, h); %matlab数值近似
& N9 |9 T: o5 H8 N( dplot(x0, ythe2,'.');
: ~) ^4 f5 I  h. G7 Tplot(x0, yapp2,'r');
legend('理论值', '模拟值');
" c9 z" f+ h, n4 ftitle('模拟二阶导');
8 X* q! L  F8 o$ T% 模拟曲率
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y = sin(x)*cos(x);
yd2 = diff(y, 2);
/ y2 Y$ _/ z0 o% v7 I3 oyd1 = diff(y, 1);
k = abs(yd2)/(1+yd1^2)^(3/2);
k1 = subs(k, x, x0);
" g6 m1 o$ U4 r+ h$ Q7 N( ]" \9 k# ck2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
; h4 t: T. L$ _6 G# n& kfigure; box on; hold on;
plot(x0, k1, '.');
plot(x0, k2, 'r');
legend('理论值', '模拟值', 'Location', 'NorthWest');
! Z! s- m8 i% y# Y0 ]title('模拟曲率');
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CCxiaom

用MATLAB计算曲率

NingW

用MATLAB计算曲率