曲率公式：
注意：
①曲率半徑為曲率的倒數
②如果是離散點，先用polyfit和polyval拟合出曲線
程式：
clc; clear all; close all;
x0 = linspace(0, 1);
y0 = sin(x0).*cos(x0);
h = abs(diff([x0(2), x0(1)]));
% 模拟一階導
figure; box on; hold on;
ythe1 = cos(x0).^2 - sin(x0).^2; %理論一階導
yapp1 = gradient(y0, h); %matlab數值近似
plot(x0, ythe1, ‘.’);
plot(x0, yapp1, ‘r’);
legend(‘理論值’, ‘模拟值’);
title(‘模拟一階導’);
% 模拟二階導
figure; box on; hold on;
ythe2 = (-4)cos(x0).sin(x0); %理論二階導
yapp2 = 22del2(y0, h); %matlab數值近似
plot(x0, ythe2,’.’);
plot(x0, yapp2,‘r’);
legend(‘理論值’, ‘模拟值’);
title(‘模拟二階導’);
% 模拟曲率
syms x y
y = sin(x)*cos(x);
yd2 = diff(y, 2);
yd1 = diff(y, 1);
k = abs(yd2)/(1+yd12)(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’);
legend(‘理論值’, ‘模拟值’, ‘Location’, ‘NorthWest’);
title(‘模拟曲率’);
