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How do you represent a 3D rotation?
The convention being used is usually indicated by specifying the axes about which the consecutive rotations (before being composed) take place, referring to them by index (1, 2, 3) or letter (X, Y, Z). The engineering and robotics communities typically use 3-1-3 Euler angles.
What is 3D orientation?
Euler’s rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of representing the orientation using an axis–angle representation. Other widely used methods include rotation quaternions, Euler angles, or rotation matrices.
Does rotation affect orientation?
The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its location does not change when it rotates. This gives one common way of representing the orientation using an axis–angle representation.
What’s the best way to rotate a 3D object?
Another popular way to handle rotating objects in 3D space is via the arcball rotation method popularized in a paper by Ken Shoemake. Map to sphere. Create a virtual sphere around the object you are trying to rotate.
How do you rotate an object in OpenGL?
To rotate a point on the sphere from start to current, you can think of it as a rotation of some degrees along some axis. Calculate this rotation/axis from the start/current positions. Update overall rotation. Update the overall rotation of the object with the current rotation in step 3.
How are quaternions used to rotate an object?
Quaternions can represent an axis and an angle of rotation around that axis. I.e. a quaternion can represent any rotation. Multiply quaternions = combine rotations. If you multiply two quaternions, they represent the combination of the rotations they represent.
Can a rotation matrix be used in 3D graphics?
Rotation Matrix Conventions. Mathematically speaking, all special orthogonal matrices can be used as rotation matrices. But by convention, when we do 3D graphics programming, we designate special properties to the rows and columns. In particular, we have names for the 3 rows of the rotation matrix.