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The reference of formulas for converting various 3D rotation formats.

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Rotation3D

The reference of formulas for converting various 3D rotation formats.

Euler angles are right-handed with YXZ axis priority order, where Y (up) is yaw, X (right) is pitch, and Z (back) is roll.

Normalized source

To AxisAngle To EulerAngles To Matrix4x4 To Quaternion
AxisAngle  – ⏳ Updating ✅ Proved ✅ Proved
EulerAngles ❌ Not yet  – ✅ Proved ✅ Proved
Matrix4x4 ❌ Not yet ✅ Proved  – ✅ Proved
Quaternion ✅ Proved ⏳ Updating ✅ Proved  –

Not normalized source

To AxisAngle To EulerAngles To Matrix4x4 To Quaternion
AxisAngle  – ❌ Not yet ❌ Not yet ❌ Not yet
EulerAngles ❌ Not yet  – ❌ Not yet ❌ Not yet
Matrix4x4 ❌ Not yet ⚠️ Draft  – ❌ Not yet
Quaternion ❌ Not yet ✅ Proved ✅ Proved  –

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The reference of formulas for converting various 3D rotation formats.

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