There are also n directional derivative constraints in n arbitrary directions.
An algebraic formula for such a function would be beneficial.
The function is 2D function on the domain [0,1]x[0,1]
Hi, you can also use a function written under the following form:
f(x,y)=exp(-k*((x-x0)^2+(y-y0)^2)
where k>0. The maximum of this function is centered at (x0,y0) and the function decreases more or less rapidly depending on the value of k. This function is also smooth.
@Iago Augusto Carvalho, it is an excellent suggestion. I can add coefficients to set the directional derivatives and add a constant to shift the value.
But, I would be happy if something like this could be done with the Gaussian function.
Hi, you can also use a function written under the following form:
f(x,y)=exp(-k*((x-x0)^2+(y-y0)^2)
where k>0. The maximum of this function is centered at (x0,y0) and the function decreases more or less rapidly depending on the value of k. This function is also smooth.
@Richard Epenoy, Thank you very much for the excellent suggestion. I can introduce different gradients for both x and y by modifying the formula:
f(x,y)=exp(-k1*(x-x0)^2+k2*(y-y0)^2)
Can I introduce dependence on the directional derivatives other than the x and y. I know that some how we need to constrain the k1 and k2 to get the desired slope.
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