Root Model Path Chord Ratio Tool

Description

pathLength is the sum; tortuosity = pathLength/chord; excess = pathLength-chord.

Dental specimen and bench-model measurements need an explicit image scale, coordinate origin and geometric convention. A linear taper, chord ratio or calibrated length describes a supplied model and does not establish anatomy or guide clinical treatment.

pathLength is the sum; tortuosity = pathLength/chord; excess = pathLength-chord.

When to use this tool

Use Root Model Path Chord Ratio when checking a supplied research or bench-model dimension.

How to use the tool and how it works

Enter pathSegments, chord. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read pathLength, tortuosity, excess. Use the output convention below.

Require positive chord and nonnegative pathSegments whose sum is at least chord. pathLength is the sum; tortuosity = pathLength/chord; excess = pathLength-chord.^[1]

Input field	Meaning and units	Accepted input
pathSegments	Path Segments	Required. Array of finite number; maximum items 256.
chord	Chord	Required. Finite number; strictly above 0.

Output field	Interpretation	Returned shape
pathLength	Path Length	Required. Finite number.
tortuosity	Tortuosity	Required. Finite number.
excess	Excess	Required. Finite number.

json

{
  "input": {
    "pathSegments": [
      3,
      4,
      5
    ],
    "chord": 10
  },
  "output": {
    "pathLength": 12,
    "tortuosity": 1.2,
    "excess": 2
  }
}

Limitations and assumptions

This is a sampled path-to-chord ratio with compatible lengths. It does not recover an unsampled three-dimensional canal or validate clinical instrumentation decisions.
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 verified specimen and instrument methods, full geometry and professional clinical assessment when the question extends beyond bench arithmetic.

References

Calculation and input contract: endodontics/root-model-path-chord-ratio — tool.io

Similar or alternative tools

Root Model Section Thickness Offset
nominalDepth = originDepth+index*thickness; correctedDepth adds missingBefore*thickness; lostDepth = missingBefore*thickness.
Root Section Reference Gap
positionGaps[i] = (sectionPosition-referencePosition)*sourceScale; maximumAbsoluteGap is their largest absolute magnitude, or zero for empty arrays.