Derivative instruction details (ddx ddy or dFdx dFdy etc.)?

http://www.gamedev.net/topic/478820-derivative-instruction-details-ddx-ddy-or-dfdx-dfdy-etc/

Hi All, From my understanding the derivative instructions ddx,ddy,fwidth etc. Use 2x2 blocks of pixels to compute the derivative. Can someone please explain: 1.) What happens on triangle boundaries where a triangle only intersects one or 2 pixels of the 2x2 region 2.) The exact formula for the derivatives for each pixel in the 2x2 block. For example, given the block: a b c d the ddx derivative for pixel a/b/c/d could be ((b-a)+(d-c))/2 or it could be b-a for a/b and d-c for c/d. I have scoured the net and haven't found a good reference for this. I have found that if I draw a box and take the derivative of a complicated calculated value that *sometimes* i get artifacts on the border of the box's polygons. I imagine this is due to how it is computed on polygon boundaries. Any help would be appreciated. Cheers! Eric [Edited by - WizardOfOzzz on January 9, 2008 8:16:57 PM] 

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Posted 09 January 2008 - 02:42 PM

Quote:

Original post by WizardOfOzzz From my understanding the derivative instructions ddx,ddy,fwidth etc. Use 2x2 blocks of pixels to compute the derivative.

That's correct.

Quote:

Original post by WizardOfOzzz 1.) What happens on triangle boundaries where a triangle only intersects one or 2 pixels of the 2x2 region

The shader is evaluated for all of the pixels in the 2x2 "quad", even if some of them fall outside of the triangle.

Quote:

Original post by WizardOfOzzz 2.) The exact formula for the derivatives for each pixel in the 2x2 block. For example, given the block: a b c d

IIRC the ddx(a) and ddx(b) will be (b-a), ddy(a) and ddy© will be (c-a) and so on.

Quote:

Original post by WizardOfOzzz I have found that if I draw a box and take the derivative of a complicated calculated value that *sometimes* i get artifacts on the border of the box's polygons.

This problem can indeed occur if you're computing some function that is undefined or otherwise not well-behaved outside of the normal triangle interpolant range. Similar problems can occur with multi-sampling, but there you can often solve them using "centroid" interpolation. I don't recall exactly how derivatives interact with centroid interpolation but I wouldn't be surprised if it is implementation-dependent.