Matlab的离散点曲线导数曲率数值模拟方法
曲率公式：
模拟方法：
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代码:
clc; clear all; close all; x0 = linspace(0, 1); y0 = sin(x0).*cos(x0);
h = abs(diff([x0(2), x0(1)])); % 模拟一阶导
figure; 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 plot(x0, ythe1, '.'); plot(x0, yapp1, 'r');
legend('理论值', '模拟值'); title('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 yapp2 = 2*2*del2(y0, h); %matlab数值近似 plot(x0, ythe2,'.'); plot(x0, yapp2,'r');
legend('理论值', '模拟值'); title('模拟二阶导'); % 模拟曲率 syms x y
y = sin(x)*cos(x); yd2 = diff(y, 2); yd1 = diff(y, 1);
k = 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');
legend('理论值', '模拟值', 'Location', 'NorthWest'); title('模拟曲率'); 效果：