Examples
Examples
Try the starting example
- Distance km, elevation m, one measured point per line
- 0,0 1,1 2,0 3,2 4,0
- Maximum permitted vertical interpolation error (m)
- 1
- Retained distance/elevation points
- 0, 0; 2, 0; 3, 2; 4, 0
- Retained point count
- 4
- Original point count
- 5
- Point-count reduction (%)
- 20
- Largest vertical error at an original point (m)
- 1
Try another scenario
- Distance km, elevation m, one measured point per line
- 0,0 1,1 2,0 3,2 4,0
- Maximum permitted vertical interpolation error (m)
- 2
- Retained distance/elevation points
- 0, 0; 4, 0
- Retained point count
- 2
- Original point count
- 5
- Point-count reduction (%)
- 60
- Largest vertical error at an original point (m)
- 2
Calculation method
Calculation method
Retained distance/elevation points
Recursively retain the interior point with the largest vertical deviation from the endpoint line whenever that deviation exceeds the entered tolerance.
Retained point count
Count retained endpoints and selected interior points.
Original point count
Count original measurements.
Point-count reduction (%)
100×(1−retained/original).
Largest vertical error at an original point (m)
Reconstruct every original distance from the compressed linear profile and report the maximum vertical deviation.
Symbols and units
- a
- Distance km, elevation m, one measured point per line
- b
- Maximum permitted vertical interpolation error (m)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- An endpoint-preserving vertical-error simplifier for at most 200 measured points. Error is checked at original sample distances; this is not a guarantee about unmeasured terrain, horizontal position or navigation accuracy.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: Euclidean geometry and trigonometric identities ↗
Background reading; this does not imply endorsement or independent review of SumFizz.