# 8.9.6.2 IfcBaseAxis

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8.9.6.2.1 Semantic definition

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8.9.6.2.2 Formal representation

```
FUNCTION IfcBaseAxis
(Dim : INTEGER;
Axis1, Axis2, Axis3 : IfcDirection)
: LIST [2:3] OF IfcDirection;
LOCAL
U : LIST [2:3] OF IfcDirection;
Factor : REAL;
D1, D2 : IfcDirection;
END_LOCAL;
IF (Dim = 3) THEN
D1 := NVL(IfcNormalise(Axis3), IfcRepresentationItem() || IfcGeometricRepresentationItem () || IfcDirection([0.0,0.0,1.0]));
D2 := IfcFirstProjAxis(D1, Axis1);
U := [D2, IfcSecondProjAxis(D1, D2, Axis2), D1];
ELSE
IF EXISTS(Axis1) THEN
D1 := IfcNormalise(Axis1);
U := [D1, IfcOrthogonalComplement(D1)];
IF EXISTS(Axis2) THEN
Factor := IfcDotProduct(Axis2, U[2]);
IF (Factor < 0.0) THEN
U[2].DirectionRatios[1] := -U[2].DirectionRatios[1];
U[2].DirectionRatios[2] := -U[2].DirectionRatios[2];
END_IF;
END_IF;
ELSE
IF EXISTS(Axis2) THEN
D1 := IfcNormalise(Axis2);
U := [IfcOrthogonalComplement(D1), D1];
U[1].DirectionRatios[1] := -U[1].DirectionRatios[1];
U[1].DirectionRatios[2] := -U[1].DirectionRatios[2];
ELSE
U := [IfcRepresentationItem() || IfcGeometricRepresentationItem () || IfcDirection([1.0, 0.0]),
IfcRepresentationItem() || IfcGeometricRepresentationItem () || IfcDirection([0.0, 1.0])];
END_IF;
END_IF;
END_IF;
RETURN(U);
END_FUNCTION;
```

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8.9.6.2.3 References