Radical Angle Unit

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For parameter \(0.0 < t < 1.0\):

\[ \mathrm{rsin}(t) \;=\; \frac{t}{\sqrt{\,1.0 - 2.0t + 2.0t^{2.0}\,}} \]

\[ \mathrm{rcos}(t) \;=\; \frac{1.0 - t}{\sqrt{\,1.0 - 2.0t + 2.0t^{2.0}\,}} \]

\[ \mathrm{rtan}(t) \;=\; \frac{t}{1.0 - t} \]

Vector Info

Conversion Reference

Introduction

Quadrant-aware modular arithmetic RAU maps a linear parameter (0.0–4.0) to circle using integer and fractional parts.

t parameter: 0.00

u length:

120

u rotate:

30°

v length:

100

v rotate:

0°