Quaternions For Computer Graphics
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Quaternion - Wikipedia In mathematics, the quaternions are a number system that extends the complex numbers.They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.A feature of quaternions is that multiplication of two quaternions is noncommutative.Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional ... Quaternions and spatial rotation - Wikipedia Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock.Compared to rotation matrices they are more compact, more numerically stable, and more efficient.Quaternions have applications in computer ... Quaternion -- from Wolfram MathWorld The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along the Royal Canal on his way to a meeting of the Irish Academy, and Hamilton was so pleased with his discovery that he scratched the fundamental formula of quaternion algebra, i^2=j^2=k^2=ijk=-1, (1) into the stone of the ...
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