# CASA Function: implOffset

Computes the offset curve in implicit representation to a given curve.

### Calling Sequence:

• S := implOffset(C)
• S := implOffset(C,d)
• S := implOffset(C,d,variables)

### 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.
variables : list(name)
• A list of two names for the representation of the resulting curve.

### Result:

S : algset("impl")
• The offset curve in implicit representation.

### Description:

• The function computes the offset curve in implicit 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 variables is not provided and the curve is given in implicit form and the parameter d does not belong to the variable list of C then this variable list is taken as default.

### Examples:

> a:=mkImplAlgSet([x^2-y],[x,y]); > implOffset(a,2);   > a:=mkParaAlgSet([2*t/(t^2+1),(t^2-1)/(t^2+1)],[t]); > [implOffset(a)];  > [implOffset(a,d)];  