Ive spent all day on this, driving me nuts, Im hoping someone has a simple solution.
I have a sigmoid curve speed function (attached pic) in my Time machine that allows smooth transitions between speed steps.
I need to distort the curve in some way to increase/decrease the area under the curve (distance) without changing the start/end speed or time .
I would like to scale the vertical axis in a non linear fashion to squash/expand the end or start curves to increase the area because the curve is in form of a look up table with a vertical speed axis resolution of 0 to 65000 (word) and horizonal time axis of 0 to 255 (byte), so the verticle axis would seem to be the one to scale.
What scale formula can I apply to the look up table speed values to smoothly change the area (distance)?.
The PIC im useing only allows integer math and its math functions such as sin/cos/log are very basic and low res, so im hoping to avoid them.
I am no expert on what you are trying to do here but here goes.
If the function for the Sigmoid is similar to y=x/SQRT(a+x^2)
Where a is normally 1
Although I am guessing your graph has X and Y offsets in the formula.
eg Y-c = (x-b)/sqrt(1+(x-b)^2)
Where c = 1 to offset Y into positive territory and b = some value to shift X into positive territory - say 2
Substitute some other value for a, try lower value like 0.5 for more area under the curve.
Alternatively just change the values in the look up table manually
Thanks Rally, the sigmoid formula I used in exell to build the table was 1/(1+EXP(-x)), buts its irrelavent , now its just a simple look up table in the PIC mem I need to scale. An integer PIC cant do any of the functions you describe to recalculate the curve live.
The problem exactly is I need to ramp from a given speed to zero in a set time and distance. This means a non linear speed profile hence the need to distort the lookup table curve. Lookup tables for every distance variation is not viable.
Im thinking a simple non linear offset to the vertical scale would be the go, but I just cant find it testing in excel, Im missing something very basic...................
Pity you don't have Matlab, Fred. That'd handle that problem easily. Excel was made for business in mind, not so much scientific spreadsheet graphing and its functions belie that heritage. It's pretty basic, even though it'll handle most jobs OK.
I think I misunderstood the nature of your problem
If I understand it - The curve is not computed, it's locked into memory as a lookup table that was computed on some other device and cannot be changed, so all you can do is change the values as they are read out
What can it do ?
I simply added to your provided formula with a multiplication function.
BTW I tested both my examples before posting, they seem to do what I think you need.
Would a Flux Capacitor do the trick?
MMMMM Guess its not practical cause its not real
Bartman
sorry just putting a bit of light in a heavy subject
Bartman
Sorry if this is inappropriate.....but I just know a great joke about something driving somebody nuts.
I have a remedy........ PM me if you want to know......
hehehehe once again sorry for distracting from an interesting yet baffling ( for me) subject.
Bartman
Sorry if this is inappropriate.....but I just know a great joke about something driving somebody nuts.
I have a remedy........ PM me if you want to know......
hehehehe once again sorry for distracting from an interesting yet baffling ( for me) subject.
Bartman
No, thats OK, so long as you have an actual solution?
the sigmoid curve speed function can be extended and smoothed with little, but useful, distortion of the curve but the 3N-dimensional configuration must be balanced thus:
i \hbar {\partial \over \partial t} \Psi(x_1,...,x_n,t) = \hbar^2 (-{\nabla_1^2\over 2m_1} - {\nabla_2^2 \over 2m_2} ... - {\nabla_N^2\over 2m_N} ) \Psi(x_1,...,x_n,t) + V(x_1,..,x_n,t)\Psi(x_1,...,x_n,t). \,
but to be Time independent, you cannot use Rally's suggestion of Y-c = (x-b)/sqrt(1+(x-b)^2).
To be Time independent AND achieve proper smooth transitions between speed steps this must be the resultant configuration:
\psi_{-|E|}(x) = C_1 e^{\sqrt{2m|E|/\hbar^2}\,x} + C_2 e^{-\sqrt{2m|E|/\hbar^2}\,x}.\,
If you end up with a backwash effect from any form of Time dilation you will need to run a discrete delta potential method scenario to test it.
Here is how:
Φ(s) = ∑ G(s,ai)V(ai)Φ(ai) + γ(s)
Good luck.
Glad to see you have plenty of time on your hands to attempt this project
With all this rain, I suppose there's not much else to do
the sigmoid curve speed function can be extended and smoothed with little, but useful, distortion of the curve but the 3N-dimensional configuration must be balanced thus:
i \hbar {\partial \over \partial t} \Psi(x_1,...,x_n,t) = \hbar^2 (-{\nabla_1^2\over 2m_1} - {\nabla_2^2 \over 2m_2} ... - {\nabla_N^2\over 2m_N} ) \Psi(x_1,...,x_n,t) + V(x_1,..,x_n,t)\Psi(x_1,...,x_n,t). \,
but to be Time independent, you cannot use Rally's suggestion of Y-c = (x-b)/sqrt(1+(x-b)^2).
To be Time independent AND achieve proper smooth transitions between speed steps this must be the resultant configuration:
\psi_{-|E|}(x) = C_1 e^{\sqrt{2m|E|/\hbar^2}\,x} + C_2 e^{-\sqrt{2m|E|/\hbar^2}\,x}.\,
If you end up with a backwash effect from any form of Time dilation you will need to run a discrete delta potential method scenario to test it.
Here is how:
Φ(s) = ∑ G(s,ai)V(ai)Φ(ai) + γ(s)
Good luck.
Glad to see you have plenty of time on your hands to attempt this project
With all this rain, I suppose there's not much else to do
I think I just stepped into an agument in a Greek Bar ...
Thanks Ken. I banged all of that into the PIC and ran it. Its still running I think, Im not hopefull ;-).
I found the answer in another place actually.
"If you want to modify just the red portion, then break it in 3: first and third curves from a lookup table, the second (red) is a linear function ds/dt = constant".
yar, like I can use exp,or brackets, or 1/ with integer math on a PIC 
.
