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1 : dpvc 2728 loadMacros('Parser.pl');
2 :    
3 :     sub _parserParametricLine_init {}; # don't reload this file
4 :    
5 :     ######################################################################
6 :     #
7 :     # This is a Parser class that implements parametric lines as
8 :     # a subclass of the Formula class. The standard ->cmp routine
9 :     # will work for this, provided we define the compare() function
10 :     # needed by the overloaded ==. We assign the special precedence
11 :     # so that overloaded operations will be promoted to the ones below.
12 :     #
13 :     # Use ParametricLine(point,vector) or ParametricLine(formula)
14 :     # to create a ParametricLine object. You can pass an optional
15 :     # additional parameter that indicated the variable to use for the
16 :     # parameter for the line.
17 :     #
18 :     # Usage examples:
19 :     #
20 :     # $L = ParametricLine(Point(3,-1,2),Vector(1,1,3));
21 :     # $L = ParametricLine([3,-1,2],[1,1,3]);
22 :     # $L = ParametricLine("<t,1-t,2t-3>");
23 :     #
24 :     # $p = Point(3,-1,2); $v = Vector(1,1,3);
25 :     # $L = ParametricLine($p,$v);
26 :     #
27 :     # $t = Formula('t'); $p = Point(3,-1,2); $v = Vector(1,1,3);
28 :     # $L = ParametricLine($p+$t*$v);
29 :     #
30 :     # Context()->constants->are(a=>1+pi^2); # won't guess this value
31 :     # $L = ParametricLine("(a,2a,-1) + t <1,a,a^2>");
32 :     #
33 :     # Then use
34 :     #
35 :     # ANS($L->cmp);
36 :     #
37 :     # to get the answer checker for $L.
38 :     #
39 :    
40 :     #
41 :     # Define a new context for lines
42 :     #
43 :     $context{ParametricLine} = Context("Vector")->copy();
44 :     $context{ParametricLine}->variables->are(t=>'Real');
45 :     $context{ParametricLine}->{precedence}{ParametricLine} =
46 :     $context{ParametricLine}->{precedence}{special};
47 : dpvc 2934 $context{ParametricLine}->reduction->set('(-x)-y'=>0);
48 : dpvc 2728 #
49 :     # Make it active
50 :     #
51 :     Context("ParametricLine");
52 :    
53 :     #
54 :     # Syntactic sugar
55 :     #
56 :     sub ParametricLine {ParametricLine->new(@_)}
57 :    
58 :     #
59 :     # Define the subclass of Formula
60 :     #
61 :     package ParametricLine;
62 :     our @ISA = qw(Value::Formula);
63 :    
64 :     sub new {
65 :     my $self = shift; my $class = ref($self) || $self;
66 :     my ($p,$v,$line,$t);
67 :     return shift if scalar(@_) == 1 && ref($_[0]) eq $class;
68 :     $_[0] = Value::Point->new($_[0]) if ref($_[0]) eq 'ARRAY';
69 :     $_[1] = Value::Vector->new($_[1]) if ref($_[1]) eq 'ARRAY';
70 :     if (scalar(@_) >= 2 && Value::class($_[0]) eq 'Point' &&
71 :     Value::class($_[1]) eq 'Vector') {
72 :     $p = shift; $v = shift;
73 :     $t = shift || Value::Formula->new('t');
74 :     $line = $p + $t*$v;
75 :     } else {
76 :     $line = Value::Formula->new(shift);
77 :     Value::Error("Your formula doesn't look like a parametric line")
78 :     unless $line->type eq 'Vector';
79 :     $t = shift || (keys %{$line->{variables}})[0];
80 : dpvc 2934 Value::Error("A line can't be just a constant vector") unless $t;
81 : dpvc 2728 $p = Value::Point->new($line->eval($t=>0));
82 : dpvc 2934 $v = Value::Vector->new($line->eval($t=>1) - $p);
83 : dpvc 3371 Value::Error("Your formula isn't linear in the variable %s",$t)
84 : dpvc 2728 unless $line == $p + Value::Formula->new($t) * $v;
85 :     }
86 :     Value::Error("The direction vector for a parametric line can't be the zero vector")
87 :     if ($v->norm == 0);
88 :     $line->{p} = $p; $line->{v} = $v;
89 :     $line->{isValue} = $line->{isFormula} = 1;
90 :     return bless $line, $class;
91 :     }
92 :    
93 :     #
94 :     # Two parametric lines are equal if they have
95 :     # parallel direction vectors and either the same
96 :     # points or the vector between the points is
97 :     # parallel to the (common) direction vector.
98 :     #
99 :     sub compare {
100 :     my ($l,$r,$flag) = @_;
101 : dpvc 3195 if ($l->promotePrecedence($r)) {return $r->compare($l,!$flag)}
102 : dpvc 2728 $r = ParametricLine->new($r);
103 :     if ($flag) {my $tmp = $l; $l = $r; $r = $tmp}
104 :     my ($lp,$lv) = ($l->{p},$l->{v});
105 :     my ($rp,$rv) = ($r->{p},$r->{v});
106 :     return $lv <=> $rv unless ($lv->isParallel($rv));
107 :     return 0 if $lp == $rp || $lv->isParallel($rp-$lp);
108 :     return $lp <=> $rp;
109 :     }
110 :    
111 :     sub cmp_class {'a Parametric Line'};
112 :    
113 :     sub cmp_defaults {(
114 :     shift->SUPER::cmp_defaults,
115 :     showEqualErrors => 0, # don't show problems evaluating student answer
116 :     ignoreInfinity => 0, # report infinity as an error
117 :     )}
118 :    
119 :     #
120 :     # Report some errors that were stopped by the showEqualErrors=>0 above.
121 :     #
122 :     sub cmp_postprocess {
123 :     my $self = shift; my $ans = shift;
124 : dpvc 2934 my $error = $$Value::context->{error}{message};
125 : dpvc 2728 $self->cmp_error($ans)
126 : dpvc 2934 if $error =~ m/^(Your formula (isn't linear|doesn't look)|A line can't|The direction vector)/;
127 : dpvc 2728 }
128 :    
129 :     1;

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