![]() ![]() ![]() William Rowan Hamilton Plaque on Broome Bridge on the Royal Canal commemorating his discovery of the fundamental formula for quaternion multiplication. Hamilton was on his way to the Royal Irish Academy with his wife and as he was passing over the Royal Canal on the Brougham Bridge he made a dramatic realization that he immediately carved into the stone of the bridge. The concept of quaterinions was realized by the Irish mathematician Sir William Rowan Hamilton on Monday October 16th 1843 in Dublin, Ireland. In this article, I want to discuss an alternative method of describing the orientation of an object (rotation) in space using quaternions. For a detailed description of transformation matrices, you can refer to my previous article titled Matrices. In this article, I will not discuss the details of transformation matrices. We can think of this transformation matrix as a “basis space” where if you multiply a vector or a point (or even another matrix) by a transformation matrix you “transform” that vector, point or matrix into the space represented by that matrix. Optionally, a single transformation matrix can also be used to express the scale or “shear” of an object. In computer graphics, we use transformation matrices to express a position in space (translation) as well as its orientation in space (rotation). This article is extremely math intensive and is not intended for the weak-hearted. You cannot fully understand quaternions in just 45 minutes. 7.1.3 Fractional Difference of Quaternions.5.5 Multiplying a Quaternion by a Scalar.2.2 Multiply a Complex Number by a Scalar.2.1 Adding and Subtracting Complex Numbers. ![]()
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