Timeline for computing derivatives of sampled data
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2019 at 19:45 | comment | added | ali | Perfect. It's all clear now. I had missed the capital F function. | |
| Nov 8, 2019 at 17:44 | history | edited | Simon F | CC BY-SA 4.0 |
Further remarks
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| Nov 8, 2019 at 17:22 | comment | added | Simon F | But you are building a surface in 3D. I'll add another note | |
| Nov 8, 2019 at 14:24 | comment | added | ali | "but for a surface, if a given first (partial) derivative is non-zero then it also is locally tangential...". I am not making a fuss :) but your argument already assumes partial derivative to be a vector(otherwise it won't be tangential) whereas I think it is scalar. | |
| Nov 8, 2019 at 11:05 | history | edited | Simon F | CC BY-SA 4.0 |
Added some more explanatory notes
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| Nov 8, 2019 at 10:56 | comment | added | Simon F | "I thought derivative is the rate of change of "function value" with respect to one of its arguments" That is indeed correct. But for a surface, if a given first (partial) derivative is non-zero (which is guaranteed in your case because of the way you construct the surface), then it also is locally tangential to the surface. Further, we know your two partial derivates aren't parallel, so the cross product will construct a valid normal. (FWIW For some arrangements of control points, in more general use cases, you can get so-called 'degenerate' surfaces, but you're safe here) | |
| Nov 7, 2019 at 22:43 | comment | added | ali | Thanks for the update. My math is not very good. I thought derivative is the rate of change of "function value" with respect to one of its arguments(unless it is a vector-valued function and you are assuming that the point S(x,y,z) is the function value); the gradient is a vector but not the partial derivatives, is that correct? | |
| Nov 7, 2019 at 22:15 | vote | accept | ali | ||
| Nov 7, 2019 at 11:03 | history | edited | Simon F | CC BY-SA 4.0 |
Responded to comment
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| Nov 6, 2019 at 23:41 | comment | added | ali | Thanks Simon. You mentioned that both partial derivatives are vectors(in i,j directions). could you write each vector components plz. | |
| Nov 6, 2019 at 14:59 | history | answered | Simon F | CC BY-SA 4.0 |