Description
Compute point power for each circle and return left power minus right power.
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.
Compute point power for each circle and return left power minus right power.
When to use this tool
Use Circle Radical Axis Signed Residual when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter point, leftCenter, rightCenter, leftRadius, rightRadius. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Require two-dimensional point and circle centers and nonnegative radii. Compute point power for each circle and return left power minus right power.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| point | Point | Required. Array of finite number; maximum items 256. |
| leftCenter | Left Center | Required. Array of finite number; maximum items 256. |
| rightCenter | Right Center | Required. Array of finite number; maximum items 256. |
| leftRadius | Left Radius | Required. Finite number. |
| rightRadius | Right Radius | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Residual | Required. Finite number. |
{
"input": {
"point": [
1,
0
],
"leftCenter": [
0,
0
],
"rightCenter": [
2,
0
],
"leftRadius": 1,
"rightRadius": 1
},
"output": {
"residual": 0
}
}Limitations and assumptions
- Residual has squared-length units; zero denotes equal power under exact arithmetic, not a tolerance-based line fit. Identical circles and degenerate radii are accepted without a unique radical-axis guarantee.
- 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
- Chord Sagitta Residual
Compute the minor sagitta using its rationalized expression and return measuredSagitta minus expectedSagitta.
- 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.