如何参数化弯曲圆柱体? [英] How to parameterize a curved cylinder?

问题描述

我想生成一个弯曲的圆柱体.例如，轴为正弦曲线或圆.

I want to generate a curved cylinder. For example, with axis being a sine curve or a circle.

我可以得到一个笔直的圆柱体

I can get a straight cylinder as follows

% Parameters
r=5; l=5; nTheta=100;

theta = 2*pi*(linspace(0,1,nTheta+1));
x = r * cos(theta);
x(end) = [];    % Last element is same as first. So, just remove it
y = r * sin(theta);
y(end) = [];
z = repmat((0:l-1)', 1, nTheta);

% Plot
surf(repmat(x,l,1),repmat(y,l,1),z); 

提供圆柱体，如果第9行更改为

gives a cylinder and if the 9th line is changed to

z = (0:l-1)' * sin(linspace(-pi,pi,nTheta));

我认为应该给我一个以正弦曲线为轴的圆柱体.但是，它给了我现在，我知道参数设置错误.将圆柱体沿正弦轴作为轴的正确参数设置是什么?

which I think should give me a cylinder with sine curve as axis. But, it gives me Now, I know that the parameterization is wrong. What would be the right parameterization to get a cylinder along a sine as axis?

推荐答案

首先，您应该指定圆柱轴的方向.现在，我将假定它指向z方向，并且仅沿x方向振动(即，轴的方程式为x = sin(z)和y=0).

First, you should specify the orientation of the axis of the cylinder. For now, I'm going to assume it's pointed in the z-direction, and that it's going to oscillate only in the x-direction (i.e. The equation of the axis is x = sin(z) and y=0 ).

如果圆柱体的轴随z改变，则圆柱体表面的x,y坐标也应为z的函数.为此，您可以像以前一样先计算直圆柱体的x,y点，然后添加一个依赖于本地z值的移位".

If the cylinder's axis changes with z, then the x,y coordinates of the cylinder's surface should also be functions of z. You can do this by first computing the x,y points for the straight cylinder like you have already done, and then adding a "shift" that depends on the local z value.

代码如下:

% Parameters
r=5; l=5; nTheta=100, nL = 20;

theta = linspace(0,2*pi,nTheta+1);
x = r * cos(theta);
y = r * sin(theta);

z = linspace(0,l,nL)';
xshift = repmat( sin(z), 1, nTheta+1); %this is a function of z

X = repmat(x,nL,1) + xshift;
Y = repmat(y,nL,1);
Z = repmat(z, 1, nTheta+1);

% Plot
surf(X,Y,Z)

如果圆柱体的轴在x和y方向上都发生振荡(或弯曲)，则还需要yshift.

You will also need a yshift if the axis of the cylinder oscillates (or curves) in both x- and y-directions.

这篇关于如何参数化弯曲圆柱体?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！