如何在 MATLAB 或 Python 中生成 3D 螺旋线？

Question

我编写了一个代码来生成螺旋的 x、y、z 点并得到了这个结果：

代码：

clear all; delete all, clc;
% Spiral constants
THETA_0 = 5; % constant
THETA_1 = 10.3; % starting angle
A = 3.762;
B = 0.001317;
C = 7.967;
D = 0.1287;
E = 0.003056;

s=2;
% Calculate (x,y,z) coordinates of points defining the spiral path
theta = THETA_1:.1:910.3;  % range, starting degree angle:final degree angle
for i = 1:length(theta)
    if (theta(i)<=99.9)
        R(i) = C*(1-D*log(theta(i)-THETA_0));
    else
%       theta_mod = 0.0002*theta(i)^2+.98*theta(i);
        R(i) = A*exp(-B*theta(i));
    end
    % scaling 
    x(i) = s*R(i)*cosd(theta(i));
    y(i) = s*R(i)*sind(theta(i));
    z(i) = s*E*(theta(i)-THETA_1);
end

helix=animatedline('LineWidth',2);
axis equal;
axis vis3d;
% set (gca,'XLim', [-5 5],'YLim', [-10 10], 'ZLim',[0 6])
view(43,24);
hold on;
for i=1:length(z)
    addpoints(helix, x(i),y(i),z(i));
    head=scatter3 (x(i),y(i),z(i));
    drawnow
%   pause(0.01);
    delete(head);
end

我想要一个类似于这个的螺旋结构

Answer 1

你的第二张照片给你：

x、y 和 z 的参数方程。
对u和v的限制

您已具备创建几何图形所需的所有信息：

%plot the mesh
u=linspace(0,4*pi,50);
v=linspace(0,2*pi,50);
[u,v]=meshgrid(u,v);
x=(1.2+0.5*cos(v)).*cos(u);
y=(1.2+0.5*cos(v)).*sin(u);
z=0.5*sin(v)+u/pi;
surf(x,y,z)
hold on

%plot the 3d line
u = linspace(0,4*pi,40)
x=1.2.*cos(u);
y=1.2.*sin(u);
z=u/pi;
plot3(x,y,z,'r');

axis equal

现在您只需调整参数方程以适合您的线。

编辑： 要将相同的解决方案应用于您的特定情况，您只需在 meshgrid 函数中将 u 和 v 替换为您的 theta 和 R 变量：

THETA_0 = 5; % constant
THETA_1 = 10.3; % starting angle
A = 3.762;
B = 0.001317;
C = 7.967;
D = 0.1287;
E = 0.003056;

s=2;
% Calculate (x,y,z) coordinates of points defining the spiral path
theta = THETA_1:5:910.3;
for i = 1:length(theta)
    if (theta(i)<=99.9)
        R(i) = s*C*(1-D*log(theta(i)-THETA_0));
    else
        R(i) = s*A*exp(-B*theta(i));
    end

end

x = R.*cosd(theta);
y = R.*sind(theta);
z = E.*(theta-THETA_1);
plot3(x,y,z,'r','linewidth',2)

hold on
[u,v]=meshgrid(theta,R);
x=(R+0.5*cos(v)).*cosd(u);
y=(R+0.5*cos(v)).*sind(u);
z=0.5*sin(v)+E.*(u-THETA_1);
mesh(x,y,z,'facecolor','none')

axis equal

结果：

顺便说一句，我不太喜欢在同一个脚本中混合使用 cosd 和 cos，但随心所欲。

Answer 2

花了一些时间寻找这个，并想分享一份代码副本，并对每个变量的作用进行更多评论。如果我说错了，请纠正我，但我已经玩过代码，这似乎是正确的。希望这能帮助那些最终寻找更多细节的人，因为微积分 III 已经有一段时间了:)

    %% 3D Helical Curve
    % tested on MATLAB R2018a
    % See also 
    % See also 
    %
    % Code is in the state used to obtain the second of the two images shown below
    clear, clc, close all
    format compact
    
    %% Input Parameters
    res = 25;   % plot resolution; higher -> finer resolution
    R = 0.15;   % wire radius
    r = 4;      % radius to wire centerline
    t = 3;      % number of coils
    
    %% Surface of the wire
    a = 3;  % scalar for resolutoin for surface.u to make it look nicer
    b = 2;  % Set to 2 for upper and lower surfaces. Set to 1 for upper surface only
    
    surface.u = linspace(0, t*2*pi, a*res); % Path of the wire surface
    surface.v = linspace(0, b*pi, res);     % Wire surface
    [surface.u, surface.v] = meshgrid(surface.u, surface.v);
    
    surface.x = (r + R*cos(surface.v)).*cos(surface.u);
    surface.y = (r + R*cos(surface.v)).*sin(surface.u);
    surface.z = R*sin(surface.v) + surface.u/pi;
    
    %% Center line of the wire
    c = a;  % scalar for resolution for line.u to make it look nicer
    
    line.u = linspace(0, t*2*pi, c*res);
    line.x = r.*cos(line.u);
    line.y = r.*sin(line.u);
    line.z = line.u/pi;
    
    %% Plotting
    f = figure();
    grid on
    hold on
    plot3(line.x, line.y, line.z, 'r');
    surf(surface.x, surface.y, surface.z)
    view(45, 12);   % Azimuth = 45, Elevation = 12
    axis equal

样本（假设单位为毫米）：

输入：R = 0.25、r = 1、t = 1、res = 25

线径，R，为0.25mm
线圈半径，r，为1mm
圈数，t，为1（无量纲）
绘图分辨率，res，为 25（无单位）

输入：R = 0.15、r = 4、t = 3、res = 25

线径，R，为0.15mm
线圈半径，r，为4mm
圈数，t，为3（无量纲）
绘图分辨率，res，为 25（无单位）

如何在 MATLAB 或 Python 中生成 3D 螺旋线？

How to generate 3D helix in MATLAB or Python?

python

3d

matlab

figure

helix