R3 – Complex Rotations – Comparing Wave Numbers and Quaternion Efficiency
Introduction This comparison of Wave Numbers and Quaternions evaluates their efficiency based on the rotation operation due to its computational complexity. Computer games and other high quality graphics frequently use rotation operations to implement the physics of movement, making this an important consideration for performance. Unit of Rotation The magnitude and unit rotation of a […]
R3 – Rotication
This post defines the new concept of the R3 rotication operation. It also provides examples. What is Rotication in R3? The rotication operation is grounded in the principles outlined in its axioms. Rotication consists of two steps. The first step is identical to rotation, resulting in a circular movement of a point. The second step takes […]
R3 – Multiplication – Cross Product
Cross product multiplication in R3 uses the same approach as in classical mathematics. The cross product of the points and is written as and is given by the formula: Unlike for dot-product, the Opposite Signs are used in multiplication. For example: Conclusion Try this example of R3 cross product multiplication with our online calculator. […]
R3 – Complex Rotations – Example 1
Up to this point, we’ve focused on unitary rotations around a single axis on the unit sphere. Now, let’s delve into more complex rotations in R3, where the operand can be any combination of Opposite Values with any degree of rotation. This post introduces the Wave Number Rotation formula, based on Rodrigues’ formula for calculating […]