# IfcPolynomialCurve clarification

Hello Experts,

I am investigating new entities that were introduced in IFC4x3.
And I have noticed that the IfcPolynomialCurve specification is not fully completed yet.

So, the description of this entity in terms of IFC is very unclear to me.
Probably someone has already met this entity in IFC files and can provide some clarification on my questions:

1. Can anyone provide a short definition of a polynomial curve in IFC?
2. In which way polynomial’s degree can be found?
3. I have found some examples in the IFC file. I noticed that in most of the cases, the number of elements in the ‘CoefficientX’ and ‘CoefficientY’ lists does not match.

e.g. #7= IFCPOLYNOMIALCURVE(#4, (0.0,1.0), (0.0,0.0,-1.08943564E-04), \$);

Does this mean that when the number of elements in the lists is different then all lacking coefficients in the lesser list are equal to zero (in my example third element of the 'CoefficientX list)?

I will really appreciate any clarifications.
Thank You!

2 Likes

Seems that documentation was not developed for this concept.
Here’s is my understanding of the concept, let me know if anyone disagrees or can improve it.
A polynomial curve is effectively a curve in x, y, and z parameterized by f(u)
The list of coefficients are u ^ position.
So in the example you have highlighted
x coefficients are (0.0,1.0)
x = 0 * u^0 + 1 * u ^1
x = u

y coefficients are (0.0,0.0,-1.08943564E-04)
y = 0 * u^0 + 0 * u^1 + -1.08943564E-04 * u^2
y = -1.08943564E-04 * u^2

z coefficients are not provided so it’s a curve in the positioning plane.
Because x = u, in this case y is a function of x
y = -1.08943564E-04 * x^2

The count of coefficients for x, y and z are independent as you can see.

Primarily this concept is used for parabolic transitions in an alignment vertical/profile.
Let me know if this makes sense or if further information is needed.

Cheers,

Jon