8.9.3.73 IfcToroidalSurface

8.9.3.73.1 Semantic definition

The IfcToroidalSurface is a bounded elementary surface. It is constructed by completely revolving a circle around an axis line. The inherited Position attribute defines the IfcAxis2Placement3D and provides:

SELF\IfcElementarySurface.Position: The location and orientation of the axis system for the primitive.
SELF\IfcElementarySurface.Position.Location: The center of the toroidal surface.
SELF\IfcElementarySurface.Position.Position[3]: The axis of revolution of the toroidal surface

C = Position.Location x = Position.P[1] y = Position.P[2] z = Position.P[3] (axis of toroidal_surface) R = MajorRadius r = MinorRadius

σ(u,v) = C + (R + r_cos _v)((cos_u_)x + (sin u))y) + r(sin_v_))z

where the parametrisation range is 0 ≤ u, v ≤ 360 degrees. u and v are angular parameters and when numerical values are specified they shall use the current units for plane angle measure.

In the placement coordinate system defined above, the surface is represented by the equation S = 0, where

S(x, y, z) = x^2^ + y^2^ + z^2^ -2R√(x^2^+y^2^) - r^2^ + R^2^.

The positive direction of the normal to the surface at any point on the surface is given by

( S~x~, S~y~, S~z~ ).

The unit normal is given by

N(u,v) = cos_v_((cos u)x + (sin u)y) + (sin v)z.

The sense of this normal is away from the nearest point on the circle of radius R with centre C. A manifold surface will be produced if the major radius is greater than the minor radius. If this condition is not fulfilled, the resulting surface will be self-intersecting.

8.9.3.73.2 Entity inheritance

8.9.3.73.3 Attributes

#	Attribute	Type	Description
IfcRepresentationItem (2)
	LayerAssignment	SET [0:1] OF IfcPresentationLayerAssignment FOR AssignedItems	Assignment of the representation item to a single or multiple layer(s). The LayerAssignments can override a LayerAssignments of the IfcRepresentation it is used within the list of Items. IFC2x3-CHANGE The inverse attribute LayerAssignments has been added. IFC4-CHANGE The inverse attribute LayerAssignment has been restricted to max 1. Upward compatibility for file based exchange is guaranteed.
	StyledByItem	SET [0:1] OF IfcStyledItem FOR Item	Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve. IFC2x3-CHANGE The inverse attribute StyledByItem has been added.
IfcSurface (1)
*	Dim	IfcDimensionCount	This attribute is formally derived. `3` The space dimensionality of IfcSurface. It is always a three-dimensional geometric representation item. IFC4-CHANGE Derived attribute promoted from subtypes.
IfcElementarySurface (1)
1	Position	IfcAxis2Placement3D	The position and orientation of the surface. This attribute is used in the definition of the parameterization of the surface.
Click to show 4 hidden inherited attributes
IfcToroidalSurface (2)
2	MajorRadius	IfcPositiveLengthMeasure	The major radius of the torus.
3	MinorRadius	IfcPositiveLengthMeasure	The minor radius of the torus.

Table 8.9.3.73.A

8.9.3.73.4 Formal propositions

Name	Description
MajorLargerMinor	The attribute value of the MinorRadius shall be smaller then the value of the MajorRadius
`MinorRadius < MajorRadius`

Table 8.9.3.73.B

8.9.3.73.5 Formal representation

 ENTITY IfcToroidalSurface
 SUBTYPE OF (IfcElementarySurface);
	MajorRadius : IfcPositiveLengthMeasure;
	MinorRadius : IfcPositiveLengthMeasure;
 WHERE
	MajorLargerMinor : MinorRadius < MajorRadius;
END_ENTITY;

8.9.3.73.6 References

IfcElementarySurface