# 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 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
y = SELF\IfcConic.Position.P
z = SELF\IfcConic.Position.P
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

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

## 8.9.3.32.4 Examples

Curve Parameters In Degrees

## 8.9.3.32.5 Formal representation

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