Matlab: 3D Plot in cartesian coordinates

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3D Grid/Gitter

(German) This plot is to generate a 3D-lattice for Matlab. In dependence of a few arguments you can use this function to plot easy 3D vectors and flats as seen in

function grid3D(startVec,stopVec,varargin)

With the variables startVec and stopVec you can specify the direction of the Cartesian grid that will be plotted. Optional arguments like color, thickness can be applied as described in the function.

figure;hold on;axis off;
grid3D([0,0,0], [1,1,1], 'Amount', [4,4,4], 'Axes', gca, 'MinorGrid','Arrow');

P = [0.5,0.5,1];
Q = [1,0.5,1];
point3D([0,0,0],P,'Marker','arrow','Label','P(0.5|0.5|1)','Color',[0.7 0.5 0]);
point3D([0,0,0],Q,'Marker','arrow','Label','Q(1|0.5|1)','Color',[0.0 0.4 0.74],'Deviation',[0,0,0.1]);



In addition, the grid can also be rotated. For example, a projection of two coordinate systems can be displayed:

figure;hold on;axis off;
grid3D([0,0,0], [1,1,1], 'Amount', [4,4,4], 'Axes', gca, 'MinorGrid','Arrow','AxTicks',[{['']},{['']},{['']}],...
    'AxLabels',["";"";""]);

P = [0.5,0.5,1];
Q = [1,0.5,1];
point3D([0,0,0],P,'Marker','arrow','Label','P(0.5|0.5|1)','Color',[0.7 0.5 0]);
point3D([0,0,0],Q,'Marker','arrow','Label','Q(1|0.5|1)','Color',[0.0 0.4 0.74],'Deviation',[0,0,0.1]);

gridStart = [2,1,1];gridEnd = [3,2,2];
arg = grid3D(gridStart, gridEnd, 'Amount', [4,4,4], 'Axes', gca, 'MinorGrid','Arrow','AxTicks',[{['']},{['']},{['']}],...
    'AxLabels',["";"";""],'Rotate',[10, 10, 10]);
rotateMat = arg;

newP = gridStart+[rotateMat*P']';
newQ = gridStart+[rotateMat*Q']';

s = num2str(round(newP,1));
while contains(s, '  ')
    s = strrep(s, '  ', ' ');
end
PLabel = replace(s,' ','|');

s = num2str(round(newQ,1));
while contains(s, '  ')
    s = strrep(s, '  ', ' ');
end
QLabel = replace(s,' ','|');

point3D(gridStart,newP,'Marker','arrow','Label',PLabel,'Color',[0.7 0.5 0]);
point3D(gridStart,newQ,'Marker','arrow','Label',QLabel,'Color',[0.0 0.4 0.74],'Deviation',[0,0,0.1]);




Source code:

function varargout = grid3D(startVec,stopVec,varargin)
% Input arguments:
% startVec ... input vector of the beginning of the point in [x,y,z]
% stopVec ... input vector of the ending of the point in [x,y,z]
%
% Optional input argument (varargin):
% 'Arrow' ... plots an arrow to the axes
% 'Axes',ax ... define the axes where it should be plotted.
% 'Amount',amout ... a vector that defines the amount of grids per axes
% 'AxLabels',axlabels ... defines the labels of the axes
% 'AxTicks',axticks ... defines the ticks of the axes
% 'Offset',offset ... defines the offset of the axis labels and ticks
% (Default:15)
% 'Rotate',rotateAng ... defines the angles in x, y and z for the rotation
%
% Optional output argument:
% rotate ... Corresponding Rotation Matrix [RotateMat]
    if isempty(varargin)
        varargin{1} = '';
    end
    
    [x] = stopVec(1); 
    [y] = stopVec(2); 
    [z] = stopVec(3); 
    x2 = startVec(1);
    y2 = startVec(2);
    z2 = startVec(3);
    
    [logic, index] = max(strcmp(varargin,'Rotate'));
    if logic
        rotateAngles = varargin{index+1};
        phix = rotateAngles(1)/180*pi;phiy = rotateAngles(2)/180*pi;phiz = rotateAngles(3)/180*pi;
    else
        phix = 0;phiy = 0;phiz = 0;
    end
    % turn the signs for saving
    Rx = [1 0 0; 0 cos(-phix) -sin(-phix); 0 sin(-phix) cos(-phix)];
    Ry = [cos(-phiy) 0 sin(-phiy); 0 1 0; -sin(-phiy) 0 cos(-phiy)];
    Rz = [cos(-phiz) -sin(-phiz) 0; sin(-phiz) cos(-phiz) 0; 0 0 1];
    varargout{1} = Rx*Ry*Rz;
    
    Rx = [1 0 0; 0 cos(phix) -sin(phix); 0 sin(phix) cos(phix)];
    Ry = [cos(phiy) 0 sin(phiy); 0 1 0; -sin(phiy) 0 cos(phiy)];
    Rz = [cos(phiz) -sin(phiz) 0; sin(phiz) cos(phiz) 0; 0 0 1];
    RotateMat = Rx*Ry*Rz;
    GridMat = [x-x2 0 0;0 y-y2 0;0 0 z-z2];
    RotGridMat = RotateMat * GridMat;
    
    [logic, index] = max(strcmp(varargin,'Offset'));
    if logic
        offset = varargin{index+1};
    else
        offset = 15;
    end
    [logic, index] = max(strcmp(varargin,'Amount'));
    if logic
        amount = varargin{index+1};
        amountx = amount(1);
        amounty = amount(2);
        amountz = amount(3);
    else
        amountx = 1;
        amounty = 1;
        amountz = 1;
    end
    
    xrange = x-x2;
    yrange = y-y2;
    zrange = z-z2;
    dx = xrange/offset;
    dy = yrange/offset;
    dz = zrange/offset;

    [logic, index] = max(strcmp(varargin,'Axes'));
    if logic 
        ax = varargin{index+1};
%         set(ax,'visible','off')
    else
        ax = gca;
        hold on;
        set(ax,'visible','off')
    end
    xvx1 = linspace(0,RotGridMat(1,1),amountx+2)+x2;xvx1 = xvx1';
    xvy1 = linspace(0,RotGridMat(1,2),amountx+2)+y2;xvy1 = xvy1';
    xvz1 = linspace(0,RotGridMat(1,3),amountx+2)+z2;xvz1 = xvz1';
    yvx1 = linspace(0,RotGridMat(2,1),amountx+2)+x2;yvx1 = yvx1';
    yvy1 = linspace(0,RotGridMat(2,2),amountx+2)+y2;yvy1 = yvy1';
    yvz1 = linspace(0,RotGridMat(2,3),amountx+2)+z2;yvz1 = yvz1';
    zvx1 = linspace(0,RotGridMat(3,1),amountx+2)+x2;zvx1 = zvx1';
    zvy1 = linspace(0,RotGridMat(3,2),amountx+2)+y2;zvy1 = zvy1';
    zvz1 = linspace(0,RotGridMat(3,3),amountx+2)+z2;zvz1 = zvz1';
    
    [logic, ~] = max(strcmp(varargin,'MinorGrid'));
    if logic
        view(120,25)
        plot3(ax,[0+yvx1 RotGridMat(1,1)+yvx1]',[0+yvy1 RotGridMat(1,2)+yvy1]',[0+yvz1 RotGridMat(1,3)+yvz1]','Color',[0.8 0.8 0.8]);
        plot3(ax,[0+zvx1 RotGridMat(1,1)+zvx1]',[0+zvy1 RotGridMat(1,2)+zvy1]',[0+zvz1 RotGridMat(1,3)+zvz1]','Color',[0.8 0.8 0.8]);
        plot3(ax,[0+xvx1 RotGridMat(2,1)+xvx1]',[0+xvy1 RotGridMat(2,2)+xvy1]',[0+xvz1 RotGridMat(2,3)+xvz1]','Color',[0.8 0.8 0.8]);
        plot3(ax,[0+zvx1 RotGridMat(2,1)+zvx1]',[0+zvy1 RotGridMat(2,2)+zvy1]',[0+zvz1 RotGridMat(2,3)+zvz1]','Color',[0.8 0.8 0.8]);
        plot3(ax,[0+yvx1 RotGridMat(3,1)+yvx1]',[0+yvy1 RotGridMat(3,2)+yvy1]',[0+yvz1 RotGridMat(3,3)+yvz1]','Color',[0.8 0.8 0.8]);
        plot3(ax,[0+xvx1 RotGridMat(3,1)+xvx1]',[0+xvy1 RotGridMat(3,2)+xvy1]',[0+xvz1 RotGridMat(3,3)+xvz1]','Color',[0.8 0.8 0.8]);
    end
    
    plot3(ax,[0 RotGridMat(1,1)]+x2,[0 RotGridMat(1,2)]+y2,[0 RotGridMat(1,3)]+z2,'k');
    plot3(ax,[0 RotGridMat(2,1)]+x2,[0 RotGridMat(2,2)]+y2,[0 RotGridMat(2,3)]+z2,'k');
    plot3(ax,[0 RotGridMat(3,1)]+x2,[0 RotGridMat(3,2)]+y2,[0 RotGridMat(3,3)]+z2,'k');
    %arrows
    [logic, ~] = max(strcmp(varargin,'Arrow'));
    if logic
        thickx=(yrange+zrange)/(2*xrange);
        thicky=(xrange+zrange)/(2*yrange);
        thickz=(yrange+xrange)/(2*zrange);
        
        arrow3D(startVec+RotGridMat(1,:),startVec+(1+1/offset).*RotGridMat(1,:),'Length',1,'Thickness',thickx,'Color',[0 0 0],'Axes',ax);
        arrow3D(startVec+RotGridMat(2,:),startVec+(1+1/offset).*RotGridMat(2,:),'Length',1,'Thickness',thicky,'Color',[0 0 0],'Axes',ax);
        arrow3D(startVec+RotGridMat(3,:),startVec+(1+1/offset).*RotGridMat(3,:),'Length',1,'Thickness',thickz,'Color',[0 0 0],'Axes',ax);
    end
    
    
    %texte
    [logic, index] = max(strcmp(varargin,'AxLabels'));
    if logic 
        axLabels = varargin{index+1};
    else
        axLabels = ["x_1","x_2","x_3"];
    end
    text(ax,x,y2+dy,z2+dz,axLabels(1))
    text(ax,x2+dx,y,z2+dz,axLabels(2))
    text(ax,x2+dx,y2+dy,z,axLabels(3))
    zq = 0:1:amountz;
    yq = 0:1:amounty;
    xq = 0:1:amountx;
    xv1=x*ones(amountx+1,1)-(xq*xrange/amountx)';
    yv1=y*ones(amounty+1,1)-(yq*yrange/amounty)';
    zv1=z*ones(amountz+1,1)-(zq*zrange/amountz)';
    xv1(sum((xv1==0),2)>0,:)=[];
    yv1(sum((yv1==0),2)>0,:)=[];
    zv1(sum((zv1==0),2)>0,:)=[];
    
    %Ticks
    [logic, index] = max(strcmp(varargin,'AxTicks'));
    if logic 
        axTicks = varargin{index+1};
    else
        axTicks{1} = num2cell(round((xv1-x2)*100)/100);
        axTicks{2} = num2cell(round((yv1-y2)*100)/100);
        axTicks{3} = num2cell(round((zv1-z2)*100)/100);
    end
    text(ax,xv1,  -y/offset*ones(numel(xv1),1)+y2,  -z/offset*ones(numel(xv1),1)+z2,axTicks{1});
    text(ax,-x/offset*ones(numel(yv1),1)+x2,  yv1, -z/offset*ones(numel(yv1),1)+z2, axTicks{2} );
    text(ax,-x/offset*ones(numel(zv1),1)+x2,  -y/offset*ones(numel(zv1),1)+y2,  zv1, axTicks{3});
    %axis
    [logic, ~] = max(strcmp(varargin,'Axes'));
    if ~logic 
        view(120,25);
    end
    [logic, ~] = max(strcmp(varargin,'Axes'));
    if ~logic 
        set(ax,'ylim',[y2 y+dy]);
        set(ax,'xlim',[x2 x+dx]);
        set(ax,'zlim',[z2 z+dz]);
    end
end

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