3-D Rotation¶
From jME3 wiki
This is an excerpt from the jME3 wiki, check the original article for more details: 3D Rotation
3D rotation is a mathematical operation where all vertices of your object are multiplied by four floating point numbers. This multiplication is called concatenation. The array of four numbers {x, y, z, w} is known as a quaternion. Don’t worry—your 3D engine handles the hard part. All you need to know:
The Quaternion is an object that can "deep-freeze" and store a rotation which can then be applied to a 3D object.
Using Quaternions for Rotation¶
To store a rotation in a quaternion, you must specify:
- The angle (as a multiple of π)
- The axis (as a vector—think pitch, yaw, roll)
Example:
/* This quaternion stores a 180 degree rolling rotation */
Quaternion roll180 = new Quaternion();
roll180.fromAngleAxis(FastMath.PI, new Vector3f(0,0,1));
/* Apply the rotation */
thingamajig.setLocalRotation(roll180);
Cheat-Sheet: Quaternion Axis Vectors¶
| Rotation around Axis? | Use this Axis Vector! | Examples |
|---|---|---|
| X axis | (1, 0, 0) | A plane pitches, nodding your head |
| Y axis | (0, 1, 0) | A plane yaws, vehicle turns, shaking your head |
| Z axis | (0, 0, 1) | A plane rolls or banks, cocking your head |
Note
These are common examples—you can rotate around any axis expressed by a vector.
Cheat-Sheet: Angle to Radian Conversion¶
| Angle | Radian Value | Examples |
|---|---|---|
| 45° | FastMath.PI / 4 |
Eighth of a circle |
| 90° | FastMath.PI / 2 |
Quarter circle (3 o'clock) |
| 180° | FastMath.PI |
Half circle (6 o'clock) |
| 270° | FastMath.PI * 3 / 2 |
Three-quarter circle (9 o'clock) |
| 360° | FastMath.PI * 2 |
Full circle (12 o'clock 😉) |
g degrees |
FastMath.PI * g / 180 |
Any angle g |
Warning
You must specify angles in radians. Using degrees will lead to incorrect results.
Steps to Specify a Rotation¶
- Choose the axis vector.
- Choose the radians value.
- Create a quaternion:
fromAngleAxis(radians, vector) - Apply it to your object:
setLocalRotation(...)
Give your quaternion variables meaningful names like roll90, pitch45, yaw180.
More on Using Quaternions
Code Sample¶
/* Start with a horizontal object */
Cylinder cylinder = new Cylinder("post", 10, 10, 1, 10);
cylinder.setModelBound(new BoundingBox());
/* Create a 90-degree pitch rotation */
Quaternion pitch90 = new Quaternion();
pitch90.fromAngleAxis(FastMath.PI / 2, new Vector3f(1, 0, 0));
/* Apply the rotation */
cylinder.setLocalRotation(pitch90);
/* Update the model */
cylinder.updateModelBound();
cylinder.updateGeometry();
Interpolating Rotations¶
You can interpolate between two rotations:
Quaternion.slerp()stores a step between two rotations See com.jme3.math.Quaternion
Adding Rotations¶
Concatenation (adding rotations):
Quaternion myRotation = pitch90.mult(roll45); // pitch and roll
Troubleshooting Rotations¶
If your object ends up in the wrong orientation:
- Order matters! 3D transformations are non-commutative. Rotation before translation ≠ translation before rotation.
- Pivot points: Want to rotate around a pivot not at the origin? Create a parent pivot node, attach your object to it, and rotate the parent.
- Radians vs degrees: The engine expects radians. Convert degrees:
g° = FastMath.PI * g / 180 - Do not modify constants!