Finding tangent at Spline Function

[seregag]

Hello.
I have some piecewise polynomial (pp).
And I have to find a point with tangent = 45'.
How can I do it using built function in Spline ToolBox.
Thanks

 

[electricpete]

To define a tangent line you need a point and a slope.

Let's say on the interval of interest the function is quadratic
y(x) = ax^2 + bx + c
y(45) = a*45^2 + b*45 + c
That is a point

dy/dx = 2ax + b
dy/dx(x=45) = 2*a*45 + b
That is a slope


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[electricpete]

I'm sorry, I thought you were looking for tangent at x=45 (easy problem).

Are you looking for a point with slope of 1 (45 degrees from axis)?

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[seregag]

yes, 45 degrees from axis
thanks

 

[electricpete]

You want an angle 45 degrees from axis (assuming x and y axis are 1:1 ratio). That corresponds to slope = +1 or -1.

Again assuming a quadratic fit...

y(x) = ax^2 + bx + c
dy/dx = 2ax + b

For dy/dx = 1
dy/dx = 2ax + b = 1
x = (1-b)/(2a)

For dy/dx = -1
dy/dx = 2ax + b = -1
x = (-1-b)/(2a)

Calculate the x for each of these and see if it falls within the interval that the quadratic is valid for. If it is, then it is a point with 45 degree angle slope. If both solutions (for slope = 1 and slope=-1) are outside of the interval that the quadratic is defined for, then there is no 45-degree slope in that interval.

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