Function that produce a spike in 3D

Question

I am looking for a function that would produce a spike, of any size, in the z-direction at a given x and y coordinate. A little bit like the https://en.wikipedia.org/wiki/Dirac_delta_function but that could be graphed in 3D.

I am not sure if those specifications are clear, if not please let me know I will clarify according to feedback.

Thanks a lot

score 1 · Accepted Answer · answered Jun 15 '20 at 12:15

1

There are a few ways of doing it, but a 'nice' way (continuous, infinitely differentiable) would be to consider a pulse as a normal distribution with close to zero variance, that is

$$z = A\exp\left(-\frac{(x-x_0)^2 + (y-y_0)^2}{2\sigma^2}\right)$$

You can keep taking variances smaller and smaller till you get the desired result

answered Jun 15 '20 at 12:15

Dhanvi Sreenivasan

5,637

Thanks Dhanvi, so something like this? https://www.geogebra.org/3d/rzh7bqms – silkAdmin Jun 15 '20 at 12:34
What is A here? Also, x_0 and y_0 are the desired coordinates right? – silkAdmin Jun 15 '20 at 12:34
A is a scaling factor, to get the height of the pulse – Dhanvi Sreenivasan Jun 15 '20 at 12:42
In the link, you need to eponentiate it. something like this: https://www.geogebra.org/3d/rzh7bqms – Dhanvi Sreenivasan Jun 15 '20 at 12:44
The smaller your variance, the sharper the pulse – Dhanvi Sreenivasan Jun 15 '20 at 12:44
Something like this https://www.geogebra.org/3d/rzh7bqms? (the that you shared didn't' update) – silkAdmin Jun 15 '20 at 12:50
Let us continue this discussion in chat. – silkAdmin Jun 15 '20 at 12:50

Function that produce a spike in 3D

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