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The RenderMan Interface - Paul Bourke

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Appendix F<br />

STANDARD BASIS MATRICES<br />

In this section the required <strong>RenderMan</strong> <strong>Interface</strong> basis matrices (used for bicubic patches).<br />

RiBezierBasis =<br />

RiBSplineBasis = 1 6<br />

RiCatmullRomBasis = 1 2<br />

RiHermiteBasis =<br />

RiPowerBasis =<br />

⎡<br />

⎢<br />

⎣<br />

⎡<br />

⎢<br />

⎣<br />

⎡<br />

⎢<br />

⎣<br />

⎡<br />

⎢<br />

⎣<br />

⎡<br />

⎢<br />

⎣<br />

−1 3 −3 1<br />

3 −6 3 0<br />

−3 3 0 0<br />

1 0 0 0<br />

−1 3 −3 1<br />

3 −6 3 0<br />

−3 0 3 0<br />

1 4 1 0<br />

⎤<br />

⎥<br />

⎦<br />

⎤<br />

⎥<br />

⎦<br />

−1 3 −3 1<br />

2 −5 4 −1<br />

−1 0 1 0<br />

0 2 0 0<br />

2 1 −2 1<br />

−3 −2 3 −1<br />

0 1 0 0<br />

1 0 0 0<br />

1 0 0 0<br />

0 1 0 0<br />

0 0 1 0<br />

0 0 0 1<br />

⎤<br />

⎥<br />

⎦<br />

⎤<br />

⎥<br />

⎦<br />

⎤<br />

⎥<br />

⎦<br />

197

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