Description
Return that offsetRadius and its reciprocal as curvature inside result.
Circle calculations distinguish radius, diameter, chord, sagitta, tangent, and oriented offsets. Branch choices determine signs and which arc or segment is meant; a scalar identity does not always establish an actual geometric construction.
Return that offsetRadius and its reciprocal as curvature inside result.
When to use this tool
Use Geometry: Circle Radial Offset Curvature when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter radius, radialOffset. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require positive radius and radius+radialOffset. Return that offsetRadius and its reciprocal as curvature inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number. |
| radialOffset | Radial Offset | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.offsetRadius | Offset Radius | Calculated result member: number. |
| result.curvature | Curvature | Calculated result member: number. |
{
"input": {
"radius": 4,
"radialOffset": 1
},
"output": {
"result": {
"offsetRadius": 5,
"curvature": 0.2
}
}
}Limitations and assumptions
- Positive offset expands the circle and curvature has inverse-length units; this does not offset an arbitrary curve, infer orientation-signed curvature, or validate an actual part.
- Outputs are nested inside result. 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
Construct the circles, chord, or segment in coordinates when existence or orientation matters. Use the complete geometry and an appropriate tolerance for intersection or tangency decisions.
References
Similar or alternative tools
- Circle Common Chord Midpoint Offset
Return (d²+r1²-r2²)/(2d) along the first-to-second center axis and sqrt(max(0, r1²-offset²)) for halfChord.
- Chord Sagitta Curvature Sensitivity
Return 8 × sagitta/(chord²+4 × sagitta²) and its derivative with respect to sagitta.