That complex number arithmetic represents operations in 2D space. Quaternion arithmetic can represent operations in 3D space in a similar way Therefore Axis and Angle is not a very good notation to use when combining Valid to say that the total rotation is the sum of the individual rotations, When applying one rotation and then applying another rotation, it is not.The space where the normal rules don't apply. The 'gimbal lock' problem, there are singularities at certain points in.When an object is rotating it suddenly jumps from 360 degrees back to zero.Notations like euler angles and Axis and Angle are intuitive easy to understand, In keyframing, we may want to generate in-between frames so we need to interpolate We need toĭo things like, working out the effect of 2 or more subsequent rotations, also, These means of specifying rotations have different pros and cons. Representing Rotation with Translation (isometry).Rotation about origin (orthogonal transformation).There are different ways to specify and perform this rotation, these methods One method of holding this information is not suitable for all needs, therefore Rotational quantities are more difficult to represent than linear quantities, We have a reference orientation we can always define orientation as a rotation However both rotation and orientation can be defined in the same way, provided Takes a starting orientation and turns it into a possibly different orientation. I think of orientationĪs the current angular position of an object and rotation as an operation which The orientation and subsequent rotations of the object. When simulating solid 3D objects we need a way to specify, store and calculate
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