Description
Require positive radius and distance and return radius squared divided by distance.
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.
Require positive radius and distance and return radius squared divided by distance.
When to use this tool
Use Sphere Inversion Radial Coordinate when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter radius, distance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read invertedDistance. Use the output convention below.
Require positive radius and distance and return radius squared divided by distance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; strictly above 0. |
| distance | Distance in the stated common unit and geometric model. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| invertedDistance | Inverted Distance | Required. Finite number. |
{
"input": {
"radius": 4,
"distance": 8
},
"output": {
"invertedDistance": 2
}
}Limitations and assumptions
- Both are radial distances from the same inversion center in one unit; this gives radial inversion only, without a point direction, full coordinates, or an origin case.
- 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
- Geometry: Circle Radial Offset Curvature
Return that offsetRadius and its reciprocal as curvature inside result.
- Circular Annulus Area Bisecting Radius
Return hypot(inner,outer)/sqrt(2).