Conformal:

minimum of 2 tiepoints required;

Col = aX + bY + c₁

Row = bX - aY + c₂

Affine:

recommended for satellite images and for most vector maps with a coordinate system tiepoints; minimum of 3 tiepoints required;

Col = a₁₁X + a₁₂Y + b₁

Row = a₁₂X + a₂₂Y + b₂

Second order bilinear:

minimum of 4 tiepoints required;

Col = a₁ + b₁X + c₁Y + d₁XY

Row = a₂ + b₂X + c₂Y + d₂XY

Full second order:

minimum of 6 tiepoints required;

Col = a₁ + b₁X + c₁Y + d₁XY + e₁X² + f₁Y²

Row = a₂ + b₂X + c₂Y + d₂XY + e₂X² + f₂Y²

Third order:

minimum of 10 tiepoints required;

Col = a₁ + b₁X + c₁Y + d₁XY + e₁X² + f₁Y² + g₁ X³ + h₁ X²Y + i₁XY² + j₁ Y³

Row = a₂ + b₂X + c₂Y + d₂XY + e₂X² + f₂Y² + g₂ X³ + h₂ X²Y + i₂XY² + j₂ Y³

Projective:

recommended for scanned photographs when a DTM is not available; minimum of 4 tiepoints required;

Col = (aX + bY + c) / (gX + hY +1)

Row = (dX + eY + f) / (gX + hY + 1)