|
|
EDA365欢迎您登录！
您需要 登录 才可以下载或查看，没有帐号？注册
x
曲率公式：
* z( q; |$ S8 Q, O
- N2 P$ C" Z- ~: Q6 O
注意：
9 }7 b9 J' @* e①曲率半径为曲率的倒数9 ]( q6 T4 O7 ?: j; T
②如果是离散点，先用polyfit和polyval拟合出曲线
8 `; f: M# g# Q9 G/ O
- c* m: O- D; i2 Y/ r; f; G. [程序：& \/ {# n$ i9 u1 I& \3 ^! e
3 e3 ]' D: r2 A7 x/ n 0 Q+ j7 X- U/ x6 r8 F+ i, [
clc; clear all; close all;, v6 V' l$ V0 y$ n- D+ r) } t
x0 = linspace(0, 1);
$ N% J$ c7 V) |$ j8 l9 o# Ey0 = sin(x0).*cos(x0);1 u' B$ x4 q2 Z0 W6 p* R0 S/ H
h = abs(diff([x0(2), x0(1)]));
/ R8 q) [" h N" x" o# y6 k% 模拟一阶导% W: n, j0 J+ m e. M- b1 [
figure; box on; hold on;
+ g) v8 o i I* @& kythe1 = cos(x0).^2 - sin(x0).^2; %理论一阶导
7 Z# x4 n/ X; o3 @yapp1 = gradient(y0, h); %matlab数值近似1 y! W7 r f; q, b% `
plot(x0, ythe1, '.');
+ @$ Q6 G; c. R, Cplot(x0, yapp1, 'r');
/ K5 ]) E* d# mlegend('理论值', '模拟值');
5 R6 L% o @' \9 G D) A- {8 p Xtitle('模拟一阶导');1 X7 j1 N$ z" i2 E
% 模拟二阶导% _/ D* q z, n0 v/ V6 A
figure; box on; hold on;
0 t6 O) Z5 m1 g) sythe2 = (-4)*cos(x0).*sin(x0); %理论二阶导6 M& ~* B* g' R
yapp2 = 2*2*del2(y0, h); %matlab数值近似
& u* w& G# ]/ d5 E' ?9 Z( iplot(x0, ythe2,'.');
+ h4 K$ p+ ~. G1 j* Qplot(x0, yapp2,'r');
2 s% @2 f! P, B5 h: [legend('理论值', '模拟值');+ L( B+ }6 l* g
title('模拟二阶导');
! H+ ]! ? p7 S, p% \% 模拟曲率: R( G* [/ m, e
syms x y
! d- U4 d) u* x6 J @4 ]7 T6 h# ly = sin(x)*cos(x);
# s& v0 A3 i) M A! Cyd2 = diff(y, 2);( T" n! U7 N) g: z$ Y
yd1 = diff(y, 1);4 m5 d4 g, N. @( m# c
k = abs(yd2)/(1+yd1^2)^(3/2);
- t9 y4 W: p/ D6 C" B H: g, U4 }k1 = subs(k, x, x0);
( k1 h! A# F8 @3 K: F8 hk2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
' t. h3 t6 m( J" Vfigure; box on; hold on;, {! a# [( `& r2 h
plot(x0, k1, '.');: D3 b8 w. d& Y, }) s- e9 ]6 _3 G
plot(x0, k2, 'r');
' \( b$ |# ?3 x# k1 [; ~ ~* Hlegend('理论值', '模拟值', 'Location', 'NorthWest');! x7 y7 ~1 M6 h" U( A+ K* x
title('模拟曲率');# ]! K3 Q0 j, ?9 Y0 I
( R9 I0 Q% z8 b' o( n5 L
0 t' L$ M7 Y; z- V% V, g
# R( ^+ K* b0 d+ L! t$ \: c) F0 E) m) `( \! ~8 a+ b8 \$ G% w
, z; L4 k0 B& a: u& h7 o) n
, ? f& d& z+ b/ ~, C2 ?6 ?2 w0 D( e5 ~+ z% H* U
& Z) a7 B' x+ y% B, X0 [4 [8 i* @
! _- f, `( D3 }1 [# i6 Q& [% C
|
|
/1 
发表于 2020-4-21 10:44
收藏
淘帖
支持！
反对！