formula for screen-space derivatives

[minxuanjun]

@s-laine Hello, I have difficulties understanding the following code about the barycentric differential interpolation,
" vec4 db0 = vec4(duvdx - dvwdx, duvdy - dvwdy, dvwdx, dvwdy); vec4 db1 = vec4(duwdx, duwdy, duvdx - duwdx, duvdy - duwdy); vec4 db2 = vec4(duwdx, duwdy, dvwdx, dvwdy); " could you help me out? Thank you!

_Originally posted by @minxuanjun in

[s-laine]

As a code comment states, du/dX = [d(u/w)/dX - u*d(1/w)/dX] * w, and here we set up the relevant constants, but I cannot recall the exact derivation. The formulas have been optimized quite a bit by grouping common subexpressions together, so there might not even be a simple geometrical meaning for the intermediate values in the code.

[minxuanjun]

Thank you very much!

At 2022-02-23 21:13:34, "Samuli Laine" @.***> wrote:

As a code comment states, du/dX = [d(u/w)/dX - ud(1/w)/dX] w, and here we set up the relevant constants, but I cannot recall the exact derivation. The formulas have been optimized quite a bit by grouping common subexpressions together, so there might not even be a simple geometrical meaning for the intermediate values in the code.

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