WCS CD Matrix Determinant Orientation Sign Checker

Supplied tangent-plane WCS CD determinant parity, singular zero retained explicitly; no celestial orientation from determinant alone. Caller independently establishes frames, units, epoch, covariance and instrument context; not an identity, association or astrometric quality certification.

Description

A WCS CD matrix maps image-axis increments to declared coordinate increments.

A WCS CD matrix maps image-axis increments to declared coordinate increments.^[1]

Its determinant indicates local parity and degeneracy rather than identifying a physical north-up orientation alone. Use WCS CD Matrix Determinant Orientation Sign Checker to evaluate the supplied inputs under the model explained below.

When to use WCS CD Matrix Determinant Orientation Sign Checker

Use WCS CD Matrix Determinant Orientation Sign Checker to evaluate the supplied inputs under the model explained below. Establish the units, measurement scope and model assumptions before entering values.

How to use WCS CD Matrix Determinant Orientation Sign Checker and understand its results

Establish the units, measurement scope and model assumptions before entering values.
Enter Caller wcs cd degrees per pixel using the field table and validation rules below, then run the tool.
Read Determinant degrees squared per pixel squared, Orientation parity; interpret the units, signs, ordering and unknown-value placeholders described below.
Correct reported input errors and rerun. Apply successful results according to their specific meanings and check the assumptions before using them in a decision.

Input field	Meaning	Value type	Requirement
callerWcsCdDegreesPerPixel	Caller wcs cd degrees per pixel	array of array	Required; constraints below

Enter an exact 2×2 finite CD matrix in degrees/pixel. For rows [a,b] and [c,d], return a×d−b×c in degrees²/pixel² and its sign −1, 0 or 1. A singular matrix succeeds with parity 0; no invertibility requirement or image orientation angle is inferred.

determinant=a×d−b×c; parity=sign(determinant)

Use the field order, units and branch conditions described above.

Output field	Meaning	Value type
determinantDegreesSquaredPerPixelSquared	Determinant degrees squared per pixel squared	number
orientationParity	Orientation parity	number

json

{
  "input": {
    "callerWcsCdDegreesPerPixel": [
      [
        1,
        0
      ],
      [
        0,
        -1
      ]
    ]
  },
  "output": {
    "determinantDegreesSquaredPerPixelSquared": -1,
    "orientationParity": -1
  }
}

Limitations and assumptions

Its determinant indicates local parity and degeneracy rather than identifying a physical north-up orientation alone. Apply the exact scope and assumptions explained above.

All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are explained above; extremely large inputs or outputs can also be rejected. Input errors differ from successful false results, empty match lists and unknown-evidence placeholders.

Alternative or Complementary methods

Use Pixel Scale from CD Matrix Elements Derivation Calculator for a related task: CD-matrix column norms describe local image-axis scales.

Use Astrometric Residual RMS Scatter Quality Grade Rater for a related task: Radial residual RMS combines paired east and north residuals.

References

WCS CD Matrix Determinant Orientation Sign Checker — tool.io

Similar or alternative tools

Pixel Scale from CD Matrix Elements Derivation Calculator
CD-matrix column norms describe local image-axis scales.
Astrometric Residual RMS Scatter Quality Grade Rater
Radial residual RMS combines paired east and north residuals.