“Recursive wave”的意思、由来-开放百科全书

词条

Recursive wave

释义

A recursive wave is a self-similar curve in three-dimensional space that is constructed by iteratively adding a helix around the previous curve.

Construction

A recursive wave of depth can be constructed as following:

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where

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and

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Each wave at non-zero depth is described by an amplitude , frequency and phase offset .

represents a unit vector that is perpendicular to the previous curve at . An arbitrary vector is chosen to be the fixed "rag" vector.

is a function that rotates a vector around an axis defined by a vector by degrees. In this case it is expressed with quaternions.