Matlab向量矢量图

不念不忘少年蓝@ 2022-07-16 22:27 206阅读 0赞

# 前言 #

目前在做图像分割时，有相关向量场图的表示，顺便整理一下向量场图的matlab实现方法，整理自：胖大星越来越胖的微博，http://blog.sina.com.cn/s/blog\_5e3213f30102v3o8.html，谢谢。

# Two-dimensional Quiver Plots 二维向量场图 #

## Joukowski Airfoil Transformation ##

相关链接：http://www.mathworks.com/matlabcentral/fileexchange/8870-joukowski-airfoil-transformation

代码示例：

t=10*pi/180; u=0.1; v=0.1; r=1.1; tol=8e-2;
    s=u+i*v; k=2*r*sin(t); w=exp(i*t);
    [x,y]=meshgrid(-2.5:0.1:3.5,-3:0.1:3);
    z=x+i*y; z(abs(z-s)<r-tol)=NaN;
    f=w*z+exp(-i*t)*r^2./(z-s)+i*k*log(z);
    a=0:0.1:2*pi; zc=r*(cos(a)+i*sin(a))+s;
    c1=-1.5; c2=2.5; c3=c2-c1;
    c=contour(x,y,imag(f),c1:c3/16:c2);
    set(gca,'color',0.5*[1 1 1])
    hold on, daspect([1 1 1])
    fill(real(zc),imag(zc),'y'), colorbar
    map=get(gcf,'colormap');
    domain=0:1/(size(map,1)-1):1; m=1;
    while m<length(c), n=m+c(2,m);
    if c(2,m)>9, p=c(:,m+1:n)';
        if p(end,1)>p(1,1), p=flipud(p); end
        ndx=10:10:length(p);
        p2=p(ndx,:); p1=p(ndx-3,:);
        cc=interp1(domain,map,(c(1,m)-c1)/c3);
        set(gca,'ColorOrder',cc)
        arrow3(p1,p2,'0o',0.8)
    end, m=n+1;
    end, hold off

代码结果图：

![20160822101319705][]

## Surface Gradients ##

相关链接：http://www.mathworks.com/help/matlab/ref/quiver.html

代码示例：

[x,y]=meshgrid(-1:1/21:1);
    z=x.*exp(-x.^2-y.^2);
    [c,h]=contour(x,y,z);
    set(h,'EdgeColor',0.45*[1 1 1])
    ndx=1:3:length(x);
    x=x(ndx,ndx); y=y(ndx,ndx); z=z(ndx,ndx);
    [u,v]=gradient(z,1/7);
    p1=[x(:),y(:)]; u=u(:); v=v(:);
    m=abs(u+i*v); % gradient magnitude
    daspect([1 1 1]), set(gca,'color',0.3*[1 1 1])
    hold on, colormap hot, scale=0.4;
    arrow3(p1,p1+scale*[u,v],'|',min(1.25*m,0.85))
    hold off, h=colorbar;
    set(h,'YTickLabel',num2str(str2num(get(h,...
    'YTickLabel'))/scale))

代码结果图：

![20160822101531505][]

## Dual Colormap ##

代码示例：

[x,y,z]=peaks(-2:0.05:2);
    contour(x,y,z,10); h=gca;
    ndx=1:4:length(x);
    x=x(ndx,ndx); y=y(ndx,ndx); z=z(ndx,ndx);
    [u,v]=gradient(z,0.2);
    p1=[x(:),y(:)]; u=u(:); v=v(:);
    m=abs(u+i*v); % gradient magnitude
    hold on, daspect([1 1 1]), scale=0.025;
    arrow3(p1,p1+scale*[u,v],'|',0.9*m/max(m))
    hold off, title('Dual Colormap')
    h1=colorbar; h2=copyobj(h1,gcf);
    set(h,'color',0.4*[1 1 1],...
    'position',get(h,'position')+[0.05 0 0 0])
    % ----------------------------------------------------- Right Colorbar
    p=get(h1,'position');
    set(h1,'position',[0.87,p(2),0.05,p(4)],...
    'YTickLabel',num2str(str2num(get(h1,...
    'YTickLabel'))/scale))                               % freeze labels
    map=colormap; cdata=reshape(map,size(map,1),1,3);
    set(get(h1,'children'),'cdata',cdata)              % freeze colors
    set(get(h1,'title'),'string','Gradient')
    % ------------------------------------------------------ Left Colorbar
    caxis auto, colorbar, colormap autumn
    set(h2,'YAxisLocation','left',...
    'position',[0.08,p(2),0.05,p(4)])
    set(get(h2,'title'),'string','Contour')

代码结果图：

![20160822102257156][]

# Three-dimensional Quiver Plots三维向量场图 #

## 三维向量场或速度箭图 ##

相关链接：http://www.mathworks.com/help/matlab/ref/quiver3.html

代码示例：

[x,y]=meshgrid(-2:0.25:2,-1:0.25:1);
    z=x.*exp(-x.^2-y.^2);
    surf(x,y,z,'EdgeColor','none')
    axis([-2.5 2.5 -1.5 1.5 -1 1]), daspect([1 1 1])
    set(gca,'CameraViewAngle',7)
    [u,v,w]=surfnorm(x,y,z);
    p1=[x(:),y(:),z(:)]; N=[u(:),v(:),w(:)];
    hold on
    arrow3(p1,p1+0.5*N,'1.5_b')
    hold off, colormap spring
    light('position',[-1 -1 -1],'style','local')
    light('position',[0 1 1]), lighting gouraud

代码结果图：

![20160822102430095][]

## 速度向量图 ##

代码示例：

vx=2; vy=3; vz=10; a=-32; t=(0:.1:1)';
    x=vx*t; y=vy*t; z=vz*t+1/2*a*t.^2;
    r=[x,y,z]; v=gradient(r')';
    axis([0 3 0 4 -10 2]), pbaspect([2 1 1])
    hold on, grid on, view([70 18])
    arrow3(r,r+v,'b',0.9)
    hold off

代码结果图：

![20160822102823819][]

# Cone Plots 圆锥箭图 #

## 风速和方向 ##

代码示例：

load wind, wind_speed=sqrt(u.^2+v.^2+w.^2);
    xmin=min(x(:)); xmax=max(x(:));
    ymin=min(y(:)); ymax=max(y(:));
    zmin=min(z(:));
    hsurfaces=slice(x,y,z,wind_speed,[xmin,xmax],ymax,zmin);
    set(hsurfaces,'FaceColor','interp','EdgeColor','none',...
                  'AmbientStrength',0.6)
    hold on, daspect([2,2,1]), view(30,40), axis tight
    xrange=linspace(xmin,xmax,8);
    yrange=linspace(ymin,ymax,8);
    [cx cy cz]=meshgrid(xrange,yrange,3:4:15);
    ui=interp3(x,y,z,u,cx,cy,cz);
    vi=interp3(x,y,z,v,cx,cy,cz);
    wi=interp3(x,y,z,w,cx,cy,cz);
    m=sqrt(ui.^2+vi.^2+wi.^2); m=m(:)/30;
    p1=[cx(:),cy(:),cz(:)]; p2=[ui(:),vi(:),wi(:)];
    hcones=arrow3(p1,p2,'r',m,3*m,'cone');
    set(hcones,'DiffuseStrength',0.8)
    hold off, axis off
    camproj perspective, camzoom(1.2)
    camlight right, lighting phong

代码结果图：

![20160822103655694][]

## 向量场的椎体箭图 ##

代码示例：

load wind, wind_speed=sqrt(u.^2+v.^2+w.^2);
    hiso=patch(isosurface(x,y,z,wind_speed,40),...
              'FaceColor','red','EdgeColor','none');
    isonormals(x,y,z,wind_speed,hiso)
    hcap=patch(isocaps(x,y,z,wind_speed,40),...
              'FaceColor','interp','EdgeColor','none',...
              'AmbientStrength',0.6);
    hold on, colormap hsv, daspect([1,1,1]), view(65,45)
    [f verts]=reducepatch(isosurface(x,y,z,wind_speed,30),0.07);
    cx=verts(:,1); cy=verts(:,2); cz=verts(:,3);
    ui=interp3(x,y,z,u,cx,cy,cz);
    vi=interp3(x,y,z,v,cx,cy,cz);
    wi=interp3(x,y,z,w,cx,cy,cz);
    m=sqrt(ui.^2+vi.^2+wi.^2); m=m(:)/40;
    p1=[cx(:),cy(:),cz(:)]; p2=[ui(:),vi(:),wi(:)];
    h1=arrow3(p1,p2,'b',m,3*m,'cone');
    xrange=linspace(min(x(:)),max(x(:)),10);
    yrange=linspace(min(y(:)),max(y(:)),10);
    [cx,cy,cz]=meshgrid(xrange,yrange,3:4:15);
    ui=interp3(x,y,z,u,cx,cy,cz);
    vi=interp3(x,y,z,v,cx,cy,cz);
    wi=interp3(x,y,z,w,cx,cy,cz);
    m=sqrt(ui.^2 + vi.^2 + wi.^2); m=m(:)/50;
    p1=[cx(:),cy(:),cz(:)]; p2=[ui(:),vi(:),wi(:)];
    h2=arrow3(p1,p2,'g',m,3*m,'cone');
    hold off, axis tight, box on
    set(gca,'xtick',[],'ytick',[],'ztick',[])
    camproj perspective, camzoom(1.2)
    camlight(-45,45), lighting phong

代码结果图：

![20160822103926196][]

# Feature Plots 特征图 #

## 特征图 ##

代码示例：

theta=(-90:10:90)'*pi/180;
    n=length(theta); p1=[1:n;zeros(1,n)]';
    r=2*ones(n,1); [u,v]=pol2cart(theta,r);
    plot([1 n],[0 0],'r')
    axis([0 20 -2 2]), daspect([8 2 1])
    hold on, grid on
    arrow3(p1,p1+[u,v],'r',0.9)
    hold off

代码结果图：

![20160822104038493][]

## 复杂数值图 ##

代码示例：

t=(0:0.5:10)'; s=0.05+i; Z=exp(-s*t);
    n=length(Z); p1=[1:n;zeros(1,n)]';
    plot([1 n],[0 0],'b')
    axis([0 22 -1 1]), daspect([8 1 1])
    hold on, grid on
    arrow3(p1,p1+[real(Z),imag(Z)],'b',0.8)
    hold off

代码结果图：

![20160822104132759][]

# 罗盘箭图 #

## 罗盘箭图 ##

代码示例：

wdir =[45 90 90 45 360 335 360 270 335 270 335 335];
    knots=[ 6 6 8 6   5   9   8   8   9 10 14 12];
    [x,y]=pol2cart(wdir*pi/180,knots);
    polar(0,15), axis(15.9*[-1 1 -1 1])
    hold on
    arrow3(zeros(length(x),2),[x',y'],'r',1.25)
    hold off

代码结果图：

![20160822104353260][]

## 罗盘箭图 ##

代码示例：

Z=eig(randn(20)); m=abs(Z);
    R=ceil(max(m)); r=R+0.3;
    polar(0,R), axis(r*[-1 1 -1 1])
    hold on
    arrow3(zeros(length(Z),2),[real(Z),imag(Z)],'b',1.75*m/R)
    hold off

代码结果图：

![20160822104440167][]

# 参考坐标系 #

## 坐标箭图 ##

代码示例：

p=[4 2 1]; axis([-6 6 0 5 -1 1])
    pbaspect([2 1.5 1]), view(55,15)
    hold on
    arrow3(repmat([p(1:2),0],4,1),...
    [0 p(2) 0;p(1) 0 0;p;0 0 0],'--o',0,0,0.5)
    arrow3(zeros(3),diag([7,5,1]),'o')
    arrow3([0 0 0],p,'2.5s',1.5,[],0)
    hold off, axis off, camlight left
    set(gca,'CameraViewAngle',4)
    text(7.1,0,0,'X'), text(0,5.05,0,'Y')
    text(0,0,1,'Z','VerticalAlignment','bottom',...
    'HorizontalAlignment','center')

代码结果图：

![20160822105026216][]

## 特征向量图 ##

代码示例：

n=500; % generate test data
    newz=[ 1 1 1]/sqrt(3);
    newy=[ 0 -1 1]/sqrt(2);
    newx=cross(newy,newz);
    R=[newx;newy;newz]; % rotation matrix
    U=randn(n,3)*diag([1,2,3])*R;
    u=U(:,1)+10; v=U(:,2)+20; w=U(:,3)+30;
    % plot eigenvectors with mean origin
    plot3(u,v,w,'r.')
    axis([0 20 10 29 20 40]), daspect([1 1 1])
    view([-70,15]), set(gca,'CameraViewAngle',8)
    hold on, grid on
    mu=repmat(mean([u,v,w]),3,1);
    [V,D]=eig(cov([u,v,w]));
    p=9*V'+mu;
    arrow3(mu,p,[],1.25,[],0)
    p=p+ones(3);
    text(p(1,1),p(1,2),p(1,3),'bfU')
    text(p(2,1),p(2,2),p(2,3),'bfV')
    text(p(3,1),p(3,2),p(3,3),'bfW')
    hold off

代码结果图：

![20160822105133287][]

## 弗朗内特标架图 ##

代码示例：

z=(0:2/99:2)'; t=2*pi*z; r=2+z;
    x=r.*cos(t); y=r.*sin(t);
    R=[x,y,z]; dR=gradient(R')';
    m=repmat(sqrt(sum(dR.*dR,2)),1,3);
    T=dR./m; dT=gradient(T')';
    m=repmat(sqrt(sum(dT.*dT,2)),1,3);
    N=dT./m; B=cross(T,N);
    plot3(x,y,z,'color',0.5*[1 1 1])
    axis([-4 4 -4 4 0 2.5])
    hold on, grid on, pbaspect([1 1 1])
    set(gca,'CameraViewAngle',7)
    plot3(0,0,0,'r'), plot3(0,0,0,'color',[0 0.5 0])
    plot3(0,0,0,'b')
    legend('Curve','Tangent','Normal','Binormal',2)
    ndx=1:4:length(x); R=R(ndx,:);
    arrow3(R,R+1.4*T(ndx,:),'r',0.9)
    arrow3(R,R+1.4*N(ndx,:),'e',0.9)
    arrow3(R,R+0.4*B(ndx,:),'b',0.9)
    hold off, view(-50,5)
    set(gcf,'renderer','zbuffer')

代码结果图：

![20160822105246507][]

# 命名颜色表 #

## 命名颜色表 ##

代码示例：

arrow3('colors',0.4) % 24 named colors with 44 adjustable shades

代码结果图：

![20160822105345571][]

![20160822105413947][]

[20160822101319705]: /images/20220717/e0e492c6719944b396a6a3d0f450753c.png
[20160822101531505]: /images/20220717/0732f39ed1bb47639fccbfb218ed2132.png
[20160822102257156]: /images/20220717/6f64c7c9a7ac4a2a83b6df08b878eec4.png
[20160822102430095]: /images/20220717/1910336c717c413b82d4b8cfc9b7a3f7.png
[20160822102823819]: /images/20220717/a81c261cf4ee43f09be016ceadd78c35.png
[20160822103655694]: /images/20220717/b8d2153167b64ffd8fcc830feffa37ae.png
[20160822103926196]: /images/20220717/8cc65c7b4ab444bfa43a72f53cafd45c.png
[20160822104038493]: /images/20220717/9d4c7a8e516f492d898e913314997c76.png
[20160822104132759]: /images/20220717/35e92647f92447c38181d2a54346b2a7.png
[20160822104353260]: /images/20220717/6faf5a4b2a4c43dea0207a572f6a0d19.png
[20160822104440167]: /images/20220717/f87f5f6b2df74514ba3adfe8f26e4d7d.png
[20160822105026216]: /images/20220717/a5f9f131f3cb4a0b81c77d46519fac65.png
[20160822105133287]: /images/20220717/6cfb2e412d88459cba8b0fee3d50ac70.png
[20160822105246507]: /images/20220717/b7cbfad9fdbb4264aa2fb94b3a4a601e.png
[20160822105345571]: /images/20220717/466fc1e3b0e547a7be655e1411ff8af8.png
[20160822105413947]: /images/20220717/a8e2aca79e5f4fc5b0c5b4433b3be82d.png