Row Column 1 Column 2 Column 3 Column 4
1 cos(ψ)·cos(θ)·sx [cos(ψ)·sin(θ)·sin(φ) − sin(ψ)·cos(φ)]·sy [cos(ψ)·sin(θ)·cos(φ) + sin(ψ)·sin(φ)]·sz tx
2 sin(ψ)·cos(θ)·sx [sin(ψ)·sin(θ)·sin(φ) + cos(ψ)·cos(φ)]·sy [sin(ψ)·sin(θ)·cos(φ) − cos(ψ)·sin(φ)]·sz ty
3 −sin(θ)·sx cos(θ)·sin(φ)·sy cos(θ)·cos(φ)·sz tz
4 0 0 0 1
Affine Transformation (Combined Formula)
General
Geodesy
Spatial Analysis

This formula can be used with the ordinary affine transformers like the one in FME (3DAffiner).

+ yaw ψ around Z, pitch θ around Y, roll φ around X

Description :

Example :

2026 Jun