Rotate 3D object with Direction and Axis

Question

I am working on showing a 3D model (IFC) in Java3D. I need to rotate the object with 2 vectors, a direction vector and a axis vector that are given by the IFC model.

But I can't figure out how to get the right angle.

Code:

// Create vectors
Vector3f directionVector = new Vector3f(dx, dy, dz);
Vector3f axisVector = new Vector3f(ax, ay, az);

//Calculate angle
float angle = axisVector.angle(directionVector);

//create AxisAngle4f
AxisAngle4f axisAngle = new AxisAngle4f(axisVector, angle);

The axisVector is always (0.0, 0.0, 1.0), so it needs to be rotated on the Z-axis

But when I calculate the angle it seems always 1.5707964 (90°):

Example 1:
dir:    (-1.0, 0.0, 0.0)
axis:   (0.0, 0.0, 1.0)
angle:  1.5707964 (90.00000250447816)
AA:     (0.0, 0.0, 1.0, 1.5707964)

Example 2:
dir:    (0.0, 1.0, 0.0)
axis:   (0.0, 0.0, 1.0)
angle:  1.5707964 (90.00000250447816)
AA:     (0.0, 0.0, 1.0, 1.5707964)

Example 3:
dir:    (1.0, 0.0, 0.0)
axis:   (0.0, 0.0, 1.0)
angle:  1.5707964 (90.00000250447816)
AA:     (0.0, 0.0, 1.0, 1.5707964)

I know through testing that -1.0 means inverted so 180°.

Can some one help me understanding what I am doing wrong?

Edit

Documentation for the placement object (Direction and axis)

Screenshots of the results:

• Orange: are the floors
• Green: is the roof
• Red: is de rotation point
• Left: Side perspective
• Right: Top perspective
• The group of 3 slabs have direction direction (0.0, 1.0, 0.0)
• The group of 2 slabs have direction direction (1.0, 0.0, 0.0)
• Roof has direction: (-1.0, 0.0, 0.0)

I did the *2 test to simulate the 180° of -1.0. as you can see in the last example the roof is correctly drawn.

Answer 1

You don't need the angle between the direction vector and the axis vector. Since your axis vector is always (0.0, 0.0, 1.0), you can define a constant vector of (1.0, 0.0, 0.0) to which you can compare the direction vector, i.e.:

// Create vectors
Vector3f directionVector = new Vector3f(dx, dy, dz);
Vector3f axisVector = new Vector3f(ax, ay, az);
Vector3f constantBaseVector = new Vector3f(1, 0, 0);

//Calculate angle
float angle = constantBaseVector.angle(directionVector);

//create AxisAngle4f
AxisAngle4f axisAngle = new AxisAngle4f(axisVector, angle);

Answer 2

I'm guessing that axisVector.angle(directionVector) returns the angle between the two vectors.

In all three of your examples you're comparing unit vectors on the base axes with the unit vector of the z-axis, which are perpendicular to each other by definition. What are you expecting to get?

To me the angle between -x and z is 90°, the angle between y and z is 90° and the angle between x and z is 90°. So all the data is correct, what are you expecting to get?

EDIT:

Example one: angle between (-1, 0, 0) and (0, 0, 1) = 90° Example two: angle between (0, 1, 0) and (0, 0, 1) = 90° Example three: angle between (1, 0, 0) and (0, 0, 1) = 90°

Please draw these vectors in a cartesian coordinate system and it should be clear. Also, please note that the angle between two vectors is the smallest angle on the plane that these two vectors define.

Answer 3

The angle between each axis should be 90°, and calculating the angle between any two vectors will only give values in the range 0° - 180°, rather than the 360° you need.

Also, if the zAxis is not (0, 0, 1), then you would need to calculate a rotation axis as well as the angle.

Instead, you can create a rotation matrix from the 3 axis directions, and create a transform object from that. The y-axis is the cross-product of the x and z axes:

// Given xAxis and zAxis.
Vector3f xAxis = new Vector3f(1, 0, 0);
Vector3f zAxis = new Vector3f(0, 0, 1);

// Create yAxis.
Vector3f yAxis = new Vector3f();
yAxis.cross(zAxis, xAxis);

// Create rotation matrix from axes.
Matrix4f rotationMatrix = new Matrix4f();
rotationMatrix.setRow(0, new Vector4f(xAxis));
rotationMatrix.setRow(1, new Vector4f(yAxis));
rotationMatrix.setRow(2, new Vector4f(zAxis));
rotationMatrix.setRow(3, new Vector4f(0, 0, 0, 1));

// Create transform.
Transform3D transform = new Transform3D(rotationMatrix);

// Transform points.
Vector3f vector = new Vector3f(0, 1, 0);
transform.transform(vector);
System.out.println(vector);