在 MATLAB 中将 2D 向量的 3D 演化绘制为带状

Question

我想绘制二维矢量的幅度和方向如何随时间变化的图。为此，我想创建一个让人想起规范 E & 的图表。您可能还记得电学和磁学入门课程中的 B 场图。

具体来说，我想用丝带连接我的 2D 矢量点，以便它们很容易看到。在 MATLAB 中是否有一种简单的方法可以做到这一点？ quiver3 非常接近，但缺少功能区。也许某种参数化曲面？

Answer 1

您可以使用绘图函数 FILL3 和 QUIVER3 执行如下操作：

x = linspace(0,4*pi,30);  %# Create some x data
y1 = sin(x);              %# Create wave 1
y2 = sin(x-pi);           %# Create wave 2
u = zeros(size(x));       %# Create a vector of zeroes

hRibbon1 = fill3(x,y1,u,'r');     %# Plot wave 1 and fill underneath with color
set(hRibbon1,'EdgeColor','r',...  %# Change the edge color and
             'FaceAlpha',0.5);    %#   make the colored patch transparent
hold on;                          %# Add to the existing plot
quiver3(x,u,u,u,y1,u,0,'r');      %# Plot the arrows

hRibbon2 = fill3(x,u,y2,'b');     %# Plot wave 2 and fill underneath with color
set(hRibbon2,'EdgeColor','b',...  %# Change the edge color and
             'FaceAlpha',0.5);    %#   make the colored patch transparent
quiver3(x,u,u,u,u,y2,0,'b');      %# Plot the arrows
axis equal;                       %# Use equal axis scaling

这是结果图：

Answer 2

这是一个在 3D 空间中的任意两条线之间绘制一条丝带的解决方案。你可以在它上面绘制你的箭袋&使用 'FaceAlpha' 调整不透明度，就像 gnovice 的解决方案一样

为了使函数更清晰，我首先发布它，而不进行错误检查和调整函数大小（它们构成了函数主体的大部分并且不是特别有趣）

function h = filledRibbon (x,y,z,u,v,w,c, varargin)
%function filledRibbon (x,y,z,u,v,w,c, varargin)
%
%plots a ribbon spanning the area between the lines x,y,z and x+u,y+v,z+w
%in the color c
%varargin is passed directly to patch
%returns a handle to the patch graphic created

%make up a set of regions that span the space between the lines

xr = [x(1:end-1); x(1:end-1) + u(1:end-1); x(2:end) + u(2:end); x(2:end)];
yr = [y(1:end-1); y(1:end-1) + v(1:end-1); y(2:end) + v(2:end); y(2:end)];
zr = [z(1:end-1); z(1:end-1) + w(1:end-1); z(2:end) + w(2:end); z(2:end)];

%plot the regions with no edges
h = patch(xr,yr,zr,c, 'LineStyle','none', varargin{:});

使用这个实际代码中的错误检查版本：

function h = filledRibbon (x,y,z,u,v,w,c, varargin)
%function filledRibbon (x,y,z,u,v,w,c, varargin)
%
%plots a ribbon spanning the area between the lines x,y,z and x+u,y+v,z+w
%in the color c
%varargin is passed directly to patch
%returns a handle to the patch graphic created


if ~exist('w', 'var') || isempty(w)
    w = 0;
end
if ~exist('u', 'var') || isempty(u)
    u = 0;
end
if ~exist('v', 'var') || isempty(v)
    v = 0;
end
if ~exist('c', 'var') || isempty(c)
    c = 'b';
end


%make all vectors 1xN 
x = reshape(x,1,[]);
y = reshape(y,1,[]);
z = reshape(z,1,[]);

%if any offsets are scalar, expand to a vector
if all(size(u) == 1)
    u = repmat(u, size(x));
end

if all(size(v) == 1)
    v = repmat(v, size(x));
end
if all(size(w) == 1)
    w = repmat(w, size(x));
end

%make up a set of regions that span the space between the lines

xr = [x(1:end-1); x(1:end-1) + u(1:end-1); x(2:end) + u(2:end); x(2:end)];
yr = [y(1:end-1); y(1:end-1) + v(1:end-1); y(2:end) + v(2:end); y(2:end)];
zr = [z(1:end-1); z(1:end-1) + w(1:end-1); z(2:end) + w(2:end); z(2:end)];

%plot the regions with no edges
h = patch(xr,yr,zr,c, 'LineStyle','none', varargin{:});