Calculation/ Visualisation of circular planes in a 3D space

Hey @ all,

I have following problem: For a large number of points with x,y,z coordinates I want to calculate or at least visualize circles. The center of each circle is the respective point at x,y,z.

x: 1 y: 1 z: 1

The diameter of the circle is fixed to 0.25 m. Up to this point, all is fine. Now i want to orient the circular plane in the space based on the specific position vector of the point.

x_pvector: 0.008 y_pvector: -0.09 z_pvector: -0.339

The circular plane should be orthogonal to this vector. I found a way to calculate 3 points on the border of this plane and fit at circle afterwards - but this is really time-consuming and laborious.

Is there any elegant solution, that I might have overlooked? Thanks a lot for any comments! :)

R.

Answer 1

[Teja Muppirala]

Here are two possible ideas. Given a circle center and a normal vector:

R = 0.25; %Radius
xyz = randn(1,3); %Circle center
normalVec = randn(1,3); %Normal vector

Method 1: Use the ROTATE command

figure;
th = linspace(0,2*pi,100);
circ = bsxfun(@plus,xyz',R*[cos(th); sin(th); 0*th]);
h = plot3(circ(1,:),circ(2,:),circ(3,:));

RotationAxis = cross([0 0 1],normalVec);
if any(RotationAxis);
  RotationAngle = 180/pi*acos([0 0 1]*normalVec'/norm(normalVec));
rotate(h,RotationAxis,RotationAngle,xyz);
end;

hold on;
quiver3(xyz(1),xyz(2),xyz(3), normalVec(1),normalVec(2),normalVec(3),'r');
axis equal;

Method 2: Do it manually using the nullspace of the normal vector

th = linspace(0,2*pi,100);

P = null(normalVec);
circ = bsxfun(@plus,xyz',R*P*[cos(th); sin(th)]);

figure;
hold on;
plot3(circ(1,:),circ(2,:),circ(3,:));
quiver3(xyz(1),xyz(2),xyz(3), normalVec(1),normalVec(2),normalVec(3),'r');
axis equal;

Both methods will give you identical results.

[Reik]

Ah, you saved my day! (the rotation command was my missing link)

Method 1 is the perfect one. Thanks a lot, the result looks really nice!

:)

R.