VECTOR



NORMALIZE

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Result is a unit length vector, a vector of magnitude 1,
in the same direction as input A.

TRANSFORM

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This function transforms the input point, PP from the "FROM" 
coordinate system into the "TO" coordinate system.
The available coordinate systems are: "world", "camera",
"object", "shader", "screen", "NDC" and "raster".

NTRANSFORM

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This function transforms the input normal, NN from the "FROM" 
coordinate system into the "TO" coordinate system.
The available coordinate systems are: "world", "camera",
"object", "shader", "screen", "NDC" and "raster".

VTRANSFORM

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This function transforms the input vector, V from the "FROM" 
coordinate system into the "TO" coordinate system.
The available coordinate systems are: "world", "camera",
"object", "shader", "screen", "NDC" and "raster".

DOTPRODUCT

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This function returns a float derived by multiplying 
the corresponding components of A and B and then summing the products.
A.B = |A||B|cos@, where @ is the angle between A and B.

FACEFORWARD

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Result is NN, if NN and II form an acute angle when placed head to tail,
otherwise the result is -NN.
refer to page 328 in the RenderMan Companion.

CROSSPRODUCT

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Result is the vector perpendicular to both A and B.
|AxB| = |A||B|sin@, where @ is the angle between A and B.

CALCULATENORMAL

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Result is the normal vector associated with point PP.
OUT = dPdu ^ dPdv.

AREA

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Result is the area of point PP in pixels, the screen space PP occupies.
This function is valuable in calculating 
anti-aliasing filters and maximum noise frequencies.

DEPTH

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This function returns the distance in z of point PP from the camera.
The results are normalize such that points on the near clipping 
plane are 0, and those on the far clipping plane are 1.
refer to page 330 in the RenderMan Companion.

LENGTH

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This function returns the length of vector A. 

ROTATE

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This is a transformation function which rotates the input point, Q 
by the angle A radians about the axis described by points P0 and P1.

DISTANCE

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This function returns the distance between A and B. 

PTLINEDISTANCE

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This function returns the perpendicular distance 
between point Q and the line defined by A and B. 

RANDOMV

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The result is a random point between point(0,0,0) and point(1,1,1);