# 8.9.3.32 IfcEllipse

## 8.9.3.32.1 Semantic definition

An IfcEllipse is a curve consisting of a set of points whose distances to two fixed points add to the same constant.

The inherited SELF\IfcConic.Position.Location is the center of the IfcEllipse, and the inherited SELF\IfcConic.Position.P[1] is the direction of the SemiAxis1.

Definition of the IfcEllipse within the a three-dimensional position coordinate system is shown in Figure 8.9.3.32.A.

It is placed within the object coordinate system of an element of which it is a representation.

An ellipse is a conic section defined by the lengths of the semi-major and semi-minor diameters and the position (center or mid point of the line joining the foci) and orientation of the curve. Interpretation of the data shall be as follows:

C = SELF\IfcConic.Position.Location
x = SELF\IfcConic.Position.P[1]
y = SELF\IfcConic.Position.P[2]
z = SELF\IfcConic.Position.P[3]
R1 = SemiAxis1
R2 = SemiAxis2


The ellipse is parameterized as:

$$\lambda(u) = C + (R_1\cos(u))x + (R_2\sin(u))y$$

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

$$C(x,y,z) = \frac{x^2}{R_1^2} + \frac{y^2}{R_2^2} - 1$$

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

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

## 8.9.3.32.5 Formal representation

ENTITY IfcEllipse
SUBTYPE OF (IfcConic);
SemiAxis1 : IfcPositiveLengthMeasure;
SemiAxis2 : IfcPositiveLengthMeasure;
END_ENTITY;