Bend Diagonal Angle Geometry Checker (45°)
Compute actual bend angle from measured orthogonal extents, not force45 degrees for nonsquare shields.
Description
A diagonal's angle follows from its horizontal run and vertical rise in a specified coordinate model.
A diagonal's angle follows from its horizontal run and vertical rise in a specified coordinate model.1
Comparing that angle with a reference does not establish a universal bend convention.
When to use Bend Diagonal Angle Geometry Checker (45°)
Use this tool to calculate or review the supplied observations under the stated rules. Establish the source tradition, viewing frame, coordinate units and independently annotated features.
How to use Bend Diagonal Angle Geometry Checker (45°) and understand its results
- Establish the source tradition, viewing frame, coordinate units and independently annotated features.
- Enter horizontalRun, verticalRise, callerReferenceAngleDegrees, using the field meanings and rules below, then run the tool.
- Read result.observedAngleDegrees, result.signedReferenceDifferenceDegrees, using the output meanings and calculation rules below.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| horizontalRun | Horizontal run | number | Required |
| verticalRise | Vertical rise | number | Required |
| callerReferenceAngleDegrees | Caller reference angle degrees | number | Required |
Use a strictly positive horizontal run, nonnegative vertical rise and finite caller reference angle. Calculate atan2(rise,run) in degrees, then subtract the reference angle, retaining the sign.
angleDegrees=atan2(verticalRise,horizontalRun)×180/π; deviation=angleDegrees−referenceAngle Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or reference | object |
| result.observedAngleDegrees | observed Angle Degrees | number |
| result.signedReferenceDifferenceDegrees | signed Reference Difference Degrees; preserve the subtraction order and sign defined in the mechanics | number |
{
"input": {
"horizontalRun": 100,
"verticalRise": 100,
"callerReferenceAngleDegrees": 45
},
"output": {
"result": {
"observedAngleDegrees": 45,
"signedReferenceDifferenceDegrees": 0
}
}
}Limitations and assumptions
The calculated angle is in [0,90), but the supplied reference is unrestricted. The tool does not infer drawing orientation or a mandatory heraldic angle.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Chevron Apex Height Calculator: A chevron apex can be derived from half-span, arm angle and a baseline. For a complementary comparison, use Per Bend Sinister Diagonal Path Generator: A per-bend-sinister division can be represented as a diagonal across a rectangular envelope.
References
Similar or alternative tools
- Chevron Apex Height Calculator
A chevron apex can be derived from half-span, arm angle and a baseline.
- Per Bend Sinister Diagonal Path Generator
A per-bend-sinister division can be represented as a diagonal across a rectangular envelope.