Description
Dot their separately normalized components and compare its absolute value inclusively with tolerance 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.
Dot their separately normalized components and compare its absolute value inclusively with tolerance inside result.
When to use this tool
Use Geometry: Circle Tangent Radius Dot Check when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter radiusVector, tangentVector, normalizedTolerance. 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 result. Expand result to inspect the returned fields.
Require nonzero two-dimensional radius and tangent vectors and normalizedTolerance in [0, 1]. Dot their separately normalized components and compare its absolute value inclusively with tolerance inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radiusVector | Radius Vector | Required. Array of finite number. Implementation limit: 128 items. |
| tangentVector | Tangent Vector | Required. Array of finite number. Implementation limit: 128 items. |
| normalizedTolerance | Normalized Tolerance | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.normalizedDot | Normalized Dot | Calculated result member: number. |
| result.tangentConsistent | Tangent Consistent | Calculated result member: boolean. |
{
"input": {
"radiusVector": [
1,
0
],
"tangentVector": [
0,
2
],
"normalizedTolerance": 1e-8
},
"output": {
"result": {
"normalizedDot": 0,
"tangentConsistent": true
}
}
}Limitations and assumptions
- The check measures directional perpendicularity only; it does not locate a tangent point on a circle, infer a geometric tolerance, or verify actual radius and tangent roles.
- 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 External Tangent Length Squared Gap
Return distance²-radius² and exists when that value is nonnegative.
- Circle Tangent Chord Angle
Require centralAngle in [0, 2π] radians and return half that angle.