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"computenormal": for the displaced surface?

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The help for "computenormal" (link below) reads: "However, when the VEX variables are changing with a high frequency (for example, a high frequency displacement map causing high frequency changes to the P variable) ... ". Since this mentions displacement, it suggests that "computenormal" (in a disp. shader) gives the normal to the displaced surface. It sounds too simple: to know this normal, the shader would need to know the partial derivatives of the disp. surface, i.e. for each shaded point, the shader would need to compute or "remember" two other shaded points. Is it really what's happening?

https://www.sidefx.com/docs/houdini/vex/functions/computenormal.html

 

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