- Implements Formulas that represent parametric lines.

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NAME - 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


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.