用MATLAB计算曲率

uperrua

曲率公式：
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注意：
7 F3 T# ^/ o* M- z. _①曲率半径为曲率的倒数
$ P, o9 C4 ~7 |; I②如果是离散点，先用polyfit和polyval拟合出曲线
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# W% k7 n7 h. |( s) N2 d8 u程序：

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* y* f+ n5 l! E; U3 a; z0 Y. Uclc; clear all; close all;
/ @# U/ Z/ J/ ux0 = linspace(0, 1);
* D/ ~/ r8 c% oy0 = sin(x0).*cos(x0);
h = abs(diff([x0(2), x0(1)]));
% 模拟一阶导
figure; box on; hold on;
) d6 @: o/ s0 V0 r+ V, p+ n' D0 zythe1 = 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');
3 x0 _! A5 o7 }legend('理论值', '模拟值');
6 J' J8 z; V; w4 btitle('模拟一阶导');
% 模拟二阶导
figure; box on; hold on;
) H/ W" F6 D5 Sythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
6 N6 w$ v6 A- h6 hyapp2 = 2*2*del2(y0, h); %matlab数值近似
plot(x0, ythe2,'.');
7 k+ A% G& J, G; c; Z% O+ Rplot(x0, yapp2,'r');
1 b9 x( {3 }' Y4 Q& r; a! Q' P! flegend('理论值', '模拟值');
- J7 p1 M7 w2 X' K, z6 a! Ptitle('模拟二阶导');
% 模拟曲率
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, o, G# Y/ C! t  `y = sin(x)*cos(x);
yd2 = diff(y, 2);
+ ?* S: }/ Y9 v! j/ v% Z+ Kyd1 = diff(y, 1);
! {# ]' p0 y: Q7 y, Z5 yk = abs(yd2)/(1+yd1^2)^(3/2);
+ u' l5 M- r  p! |& ak1 = subs(k, x, x0);
3 `1 N+ K( ?8 O/ ?0 f9 Ik2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
% {; ?6 N& G# l  W: r8 T/ Ifigure; box on; hold on;
$ P3 J$ A* f+ \+ uplot(x0, k1, '.');
/ d: c+ h. R$ c8 G3 O2 E3 cplot(x0, k2, 'r');
/ e* ?& g& ?: O5 I, |legend('理论值', '模拟值', 'Location', 'NorthWest');
title('模拟曲率');


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NingW

用MATLAB计算曲率

CCxiaom

用MATLAB计算曲率