# 8.9.3.66 IfcSphericalSurface

## 8.9.3.66.1 Semantic definition

The IfcSphericalSurface is a bounded elementary surface. The inherited Position attribute defines the IfcAxisPlacement3D and provides:

• SELF\IfcElementarySurface.Position: The location and orientation of the axis system for the primitive.
• SELF\IfcElementarySurface.Position.Location: The center of the spherical surface.
• SELF\IfcElementarySurface.Position.Position[3]: The z axis points at its positive direction towards the north pole, and by its negative directions towards the south pole.

The data is to be interpreted as follows:

C = Position.Location x = Position.P[1] y = Position.P[2] z = Position.P[3] (axis of spherical surface) R = Radius and the surface is parametrised as

σ(u,v) = C + R cos v ((cos u) x + (sin u) y) + R(sin v) z where the parametrisation range is 0 ≤ u ≤ 360 degrees and -90 ≤ v ≤ 90 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^ - 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,

## 8.9.3.66.4 Formal representation

ENTITY IfcSphericalSurface
SUBTYPE OF (IfcElementarySurface);
END_ENTITY;