Sebastian H. schrieb:
> Slime schrieb:
> 
>>> This worked nicely, thank you. A small tweak in the accuracy and
>>> max_gradient and I have this.
>>
>>
>>
>> Nice. You might even want to use this version:
>>
>> #local smoothfunc = function(x) {x*x*x*(10+x*(6*x-15))}
>>
>> Which also matches second derivatives, and will make the transition from
>> straight to curved even more invisible.
>>
> 
> Nice, how did you calculate it?
> Once I made some differential equations
> for this problem and solved them.
> It was a bit dirty and some paper sheets got lost.
> If I remember right the differential equations
> for a smooth transition from 0 to 1 were:
> 
> f(0) = 0
> f(1) = 1
> 
> df(0)/dx = 0   # match in first derivative
> df(1)/dx = 0
> 
> d^2f(0)/dx = 0 # match in second derivative
> d^2f(1)/dx = 0
> 
> An approximation method aka Taylor or
> something which could be used to get a match
> in even higher derivatives would be nicer
> but when I got f(x) for the second derivative
> I forgot thinking about it further.
> 

And here is my image from then.

Sebastian

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