Description
Return external and internal circle-tangency residuals.
Radial geometry distinguishes a solid region from its boundary. A point inside a ball has zero distance to the solid, while its signed boundary gap is negative and its absolute boundary distance can be positive.
Return external and internal circle-tangency residuals.
When to use this tool
Use Circle Center Distance Tangency Slack when checking a supplied radial boundary or solid-region convention.
How to use the tool and how it works
- Enter distance, firstRadius, secondRadius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read externalSlack, internalSlack. Use the output convention below.
Return external and internal circle-tangency residuals. Require nonnegative center distance and radii; externalSlack = distance-r1-r2, internalSlack = distance-abs(r1-r2).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| distance | Distance | Required. Finite number; minimum 0. |
| firstRadius | First Radius | Required. Finite number; minimum 0. |
| secondRadius | Second Radius | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| externalSlack | External Slack | Required. Finite number. |
| internalSlack | Internal Slack | Required. Finite number. |
{
"input": {
"distance": 8,
"firstRadius": 3,
"secondRadius": 5
},
"output": {
"externalSlack": 0,
"internalSlack": 6
}
}Limitations and assumptions
- Zeros describe distinct tangency conditions; no tolerance, actual circles or collision classification is inferred.
- 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 full point and shape geometry when a radius or center distance has not already been established.
References
Similar or alternative tools
- Distance: Radial Distance To Circle Boundary
Return signed and absolute distance from a supplied circular boundary.
- Circle Circle Boundary Gap One Axis
Return minimum boundary gap for two coplanar circles with collinear center coordinates.