Description
Project supplied heel-to-toe displacement onto an almost-unit forward axis.
Movement geometry depends on coordinate registration, time origins, force signs and reference axes. A moment arm must already represent perpendicular leverage, a stride percentage has an endpoint convention, and a toe-to-heel projection differs from full Euclidean separation. Scalar results do not establish a movement diagnosis or a safe activity.
Project supplied heel-to-toe displacement onto an almost-unit forward axis.
When to use this tool
Use Gait Toe Heel Distance Projection when you already have heelPosition, toePosition, forwardUnitAxis and need to project supplied heel-to-toe displacement onto an almost-unit forward axis.
How to use the tool and how it works
- Enter heelPosition, toePosition, forwardUnitAxis. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read forwardDistance. Use the output convention below.
Require equal-length nonempty coordinate/axis arrays and abs(hypot(axis)-1)<=1e-12; return sum((toe-heel)*axis).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| heelPosition | Heel Position | Required. Array of finite number; maximum items 256. |
| toePosition | Toe Position | Required. Array of finite number; maximum items 256. |
| forwardUnitAxis | Nonempty axis matching both coordinate vectors; norm must be within 1e-12 of one and is not normalized internally. | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| forwardDistance | Dot product of toePosition-heelPosition with the supplied axis; signed projected distance, not full Euclidean distance. | Required. Finite number. |
{
"input": {
"heelPosition": [
0,
0
],
"toePosition": [
3,
4
],
"forwardUnitAxis": [
1,
0
]
},
"output": {
"forwardDistance": 3
}
}Limitations and assumptions
- Output is signed projected distance, not Euclidean separation. Units and frame must match; no normalization is performed, tolerance is fixed, and no gait, anatomy, tracking or clinical conclusion is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use calibrated motion, force and timing records with a complete biomechanical model. Check coordinate frames, axis normalization and sampling limitations before interpreting local distances, moments or phase values as performance or clinical findings.
References
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