在MATLAB中绘制椭圆和椭球

问题描述

如何使用MATLAB绘制椭圆和椭球?

How do I draw an ellipse and an ellipsoid using MATLAB?

(x^2/a^2)+(y^2/b^2)=1

n=40;
a=0;   b=2*pi;
c=0;   d=2*pi;
for i=1:n
    u=a+(b-a)*(i-1)/(n-1);
    for j=1:m
        v=a+(d-c)*(j-1)/(m-1);
        x(i,j)=sin(u)*cos(v);
        y(i,j)=sin(u)*sin(v);
        z(i,j)=cos(u);
    end
end
mesh(x,y,z);

但是我想要形状吗?

推荐答案

维基百科有一个简单的JavaScript代码来绘制椭圆.

Ellipse article on Wikipedia had a simple JavaScript code to draw ellipses.

它使用参数形式:

x(theta) = a0 + ax*sin(theta) + bx*cos(theta)
y(theta) = b0 + ay*sin(theta) + by*cos(theta)

其中

(a0,b0) is the center of the ellipse
(ax,ay) vector representing the major axis
(bx,by) vector representing the minor axis

我将代码翻译成MATLAB函数:

I translated the code into a MATLAB function:

function [X,Y] = calculateEllipse(x, y, a, b, angle, steps)
    %# This functions returns points to draw an ellipse
    %#
    %#  @param x     X coordinate
    %#  @param y     Y coordinate
    %#  @param a     Semimajor axis
    %#  @param b     Semiminor axis
    %#  @param angle Angle of the ellipse (in degrees)
    %#

    narginchk(5, 6);
    if nargin<6, steps = 36; end

    beta = -angle * (pi / 180);
    sinbeta = sin(beta);
    cosbeta = cos(beta);

    alpha = linspace(0, 360, steps)' .* (pi / 180);
    sinalpha = sin(alpha);
    cosalpha = cos(alpha);

    X = x + (a * cosalpha * cosbeta - b * sinalpha * sinbeta);
    Y = y + (a * cosalpha * sinbeta + b * sinalpha * cosbeta);

    if nargout==1, X = [X Y]; end
end

和测试示例:

%# ellipse centered at (0,0) with axes length
%# major=20, ,minor=10, rotated 50 degrees
%# (drawn using the default N=36 points)
p = calculateEllipse(0, 0, 20, 10, 50);
plot(p(:,1), p(:,2), '.-'), axis equal

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