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THE FEUTEX TOOLKIT

Implicit Curve Local Geometry

Compute slope and curvature of F(x,y)=0 from first and second partial derivatives.

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01 Your input
02 Your result
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FormulaSlope = -fx/fy; Curvature = abs(fy**2*fxx-2*fx*fy*fxy+fx**2*fyy)/(fx**2+fy**2)**1.5
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Made for real tasks

  • Compute slope and curvature of F(x,y)=0 from first and second partial derivatives.
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Worked example

Inputs

F_x
2 number
F_y
2 number
F_xx
2 number
F_xy
0 number
F_yy
2 number

Expected results

Slope
-1 number
Curvature
0.7071067812 1/length

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter f_x, f_y, f_xx, f_xy, f_yy.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "fx": 2,
  "fy": 2,
  "fxx": 2,
  "fxy": 0,
  "fyy": 2
}

Accuracy and scope

All derivatives must be evaluated at the same regular point on F=0; no symbolic differentiation is performed.

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