parserParametricLine.pl - Implements Formulas that represent parametric lines.
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.
#
# 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.
#