3.10 Discontinuities

There are several functions which “clamp” their inputs in various ways, i.e. potentially lose some information in their inputs and introduce discontinuities. These are documented in Tables 3.21, 3.22, and 3.23. The first set of functions are sharp discontinuities, the second supports smoothed discontinuities, as required in shaders for antialiasing. The smoothed version of a function typically has smooth in front of the name and an extra parameter for setting the width of the transition region.

Operation  r a,b,c,... Description abs   N N Componentwise absolute value ceil   N N Componentwise ceiling / clamp   N N,N,N Componentwise clamping of ai between bi and ci / clamp   N N,1,1 Componentwise clamping of ai between bi and ci floor   N N Componentwise floor / frac   N N Componentwise fractional part / mod   N N,N Componentwise floating-point modulus / round   N N Componentwise nearest integer / sign   N N Componentwise sign   Table 3.21: Clamping functions. These operations all potentially lose information and introduce discontinuities.

Operation  r a,b,c,... Description max   N N,N Componentwise maximum / max   1 N Tuple maximum min   N N,N Componentwise minimum / min   1 N Tuple minimum pos   N N Componentwise maximum with 0 / sat   N N Componentwise minimum with 1   Table 3.22: Minimum and maximum functions.

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