Matlab: 3D Plot in kartesischem Koordinatensystem
3D Grid/Gitter
(English) In diesem Post stell ich mein 3D-Gitter für Matlab vor. Dieses erzeugt in Abhängigkeit verschiedener Parameter ein Gitter in Matlab. Dieses kann einfach genutzt werden, um Vektoren, Ebenen und Geraden im dreidimensionalen Darzustellen.
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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