# CASA Function: paraOffset

Compute the offset curve in parametric representation to a given curve.

### Calling Sequence:

• S := paraOffset(C)
• S := paraOffset(C,d)
• S := paraOffset(C,d,variable)

### Parameters:

C : {algset("impl"),algset("para")}
• Algebraic curve in implicit or parametric representation,
d : {name,rational }
• A variable or a rational number, specifying the distance of the offset curve to the original curve.
variable : name
• A variable name that is used for the resulting parametric representation.

### Result:

S : algset("para")
• The offset curve in parametric representation.

### Description:

• The function computes the offset curve in parametric representation at distance d to a given plane algebraic curve (in implicit or parametric representation).
• If the parameter d is not provided it is assumed that the distance is a parameter.
• If the parameter variable is not provided, the given algebraic curve is in parametric form and d is not its parameter then this parameter is taken.

### Examples:

> a:=mkImplAlgSet([x^2-y],[x,y]);

> paraOffset(a,2);

> a:=mkParaAlgSet([2*t/(t^2+1),(t^2-1)/(t^2+1)],[t]);

> [paraOffset(a)];

> [paraOffset(a,d)];