用MATLAB计算曲率

uperrua

曲率公式：

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# R- h' r- e$ E2 _& n* a6 O①曲率半径为曲率的倒数
6 x& }9 J" R! ]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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% _* c+ e+ Y5 }7 U! nclc; clear all; close all;
1 L+ |/ ]/ O5 y1 s6 Ox0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
$ t; K! l( y$ Z1 i9 \h = abs(diff([x0(2), x0(1)]));
5 K7 M& G- Q: Y8 N5 f1 J/ J% 模拟一阶导
; l1 {5 o- w& ofigure; box on; hold on;
ythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
yapp1 = gradient(y0, h); %matlab数值近似
1 H# B: e0 {. F/ c. c/ Oplot(x0, ythe1, '.');
plot(x0, yapp1, 'r');
legend('理论值', '模拟值');
( K  F( }& A" M/ ptitle('模拟一阶导');
8 x7 x" T8 Z5 r! r& e* m) T: K% 模拟二阶导
figure; box on; hold on;
ythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导
0 s1 z7 X& T8 c, m9 P& b; hyapp2 = 2*2*del2(y0, h); %matlab数值近似
% d: {! @$ b; P: K. D# t' lplot(x0, ythe2,'.');
3 Z4 y# F6 Y( E  A' O5 P9 W/ Qplot(x0, yapp2,'r');
legend('理论值', '模拟值');
title('模拟二阶导');
! Y0 v; D0 }! K: g/ i; l0 ^% 模拟曲率
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3 W' L3 C" F& ~1 [) r8 ~* v) ^y = sin(x)*cos(x);
6 O3 A4 e- |: ?3 _( v" [# }yd2 = diff(y, 2);
' {4 }. ]1 q( Ryd1 = diff(y, 1);
k = abs(yd2)/(1+yd1^2)^(3/2);
5 `1 Z) a- Z7 c1 ~& h5 ~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');
( ~  b$ _' c7 Ulegend('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