IFC 4.3.0.1 (IFC4X3_TC1)

# 8.9.3.18 IfcCircle

## 8.9.3.18.1 Semantic definition

An IfcCircle is a curve consisting of a set of points having equal distance from the center.

Figure 8.9.3.18.A illustrates the definition of IfcCircle within a three-dimensional position coordinate system placed within the object coordinate system of an element.

A circle is defined by a radius and the location and orientation of the circle. Interpretation of data should be as follows:

C = SELF\IfcConic.Position.Location
x = SELF\IfcConic.Position.P
y = SELF\IfcConic.Position.P
z = SELF\IfcConic.Position.P


The circle is parameterized as

$$\lambda(u) = C + R(\cos(u)x + \sin(u)y)$$

The parameterization range is 0 ≤ u ≤ 2π (0 ≤ u ≤ 360 degree). In the placement coordinate system defined above, the circle is the equation C = 0, where

$$C(x,y,z) = x^2 + y^2 - R^2$$

The positive sense of the circle at any point is in the tangent direction, T, to the curve at the point, where

$$T = (-C_y,C_x,0)$$

## 8.9.3.18.4 Formal representation

ENTITY IfcCircle
SUBTYPE OF (IfcConic);
END_ENTITY;