# NAME

parserParametricLine.pl - Implements Formulas that represent parametric lines.

# DESCRIPTION

This is a Parser class that implements parametric lines as a subclass of the Formula class. The standard ->cmp routine will work for this, provided we define the compare() function needed by the overloaded ==. We assign the special precedence so that overloaded operations will be promoted to the ones below.

Use ParametricLine(point,vector) or ParametricLine(formula) to create a ParametricLine object. You can pass an optional additional parameter that indicated the variable to use for the parameter for the line.

Usage examples:

``````        \$L = ParametricLine(Point(3,-1,2),Vector(1,1,3));
\$L = ParametricLine([3,-1,2],[1,1,3]);
\$L = ParametricLine("<t,1-t,2t-3>");

\$p = Point(3,-1,2); \$v = Vector(1,1,3);
\$L = ParametricLine(\$p,\$v);

\$t = Formula('t'); \$p = Point(3,-1,2); \$v = Vector(1,1,3);
\$L = ParametricLine(\$p+\$t*\$v);

Context()->constants->are(a=>1+pi^2); # won't guess this value
\$L = ParametricLine("(a,2a,-1) + t <1,a,a^2>");``````

Then use

``   ANS(\$L->cmp);``

to get the answer checker for \$L.

## \$lhs == \$rhs

`````` #
#  Two parametric lines are equal if they have
#  parallel direction vectors and either the same
#  points or the vector between the points is
#  parallel to the (common) direction vector.
#``````