I'm sorry but I'm too rusted to solve this alone. If anyone can help me :)
It’s a physical problem, I have a plastic pipe coming out vertically from an inlet. At the same time the end of the pipe is tied to a wire that is coming out below.
The speed of the output of the plastic pipe and of the wire is proportional and fixed: Vplastic = Ratio * Vwire.
In addition to that there is a point I need the curve to pass by at a certain time as well as the end point at the end of the movement should be on the X axis.
I need to model how the ending point of the plastic tube will evolve through time.
So here is the starting schema:
Here is an example (fake curve… it is what I need to find):
These are the conditions I have:
- Vplastic = Ratio * Vwire
- Vplastic = Length of arc at the end divided by time
- Vwire = Max length divided by time, note that is possible that the PassBy point has a length superior to the final length. In this case the Vwire = Length at PassBy + abs value of (length PassBy – End Length)
- T0 plastic = Point (0, 2) or parametric
- T0 wire = Point (0, 0) or parametric
- Tangent of curve at T0 plastic is vertical
- For any T the length of the arc is proportional to the length of the wire. Is related to point 1)
- Tangent of curve at and point can with any inclination (in the diagram is vertical by chance)
- Tend = Point (0, 26) or parametric.