Math::NumSeq::PlanePathTurn(3pm)

1Math::NumSeq::PlanePathUTsuerrn(C3o)ntributed Perl DocumMeanttha:t:iNounmSeq::PlanePathTurn(3)
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NAME

6       Math::NumSeq::PlanePathTurn -- turn sequence from PlanePath module
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SYNOPSIS

9        use Math::NumSeq::PlanePathTurn;
10        my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'DragonCurve',
11                                                    turn_type => 'Left');
12        my ($i, $value) = $seq->next;
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DESCRIPTION

15       This is a tie-in to present turns from a "Math::PlanePath" module in
16       the form of a NumSeq sequence.
17
18       The "turn_type" choices are
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20           "Left"         1=left,  0=right or straight
21           "Right"        1=right, 0=left or straight
22           "Straight"     1=straight, 0=left or right
23           "NotStraight"  0=straight, 1=left or right
24           "LSR"          1=left,  0=straight, -1=right
25           "SLR"          0=straight, 1=left,  2=right
26           "SRL"          0=straight, 1=right, 2=left
27
28       In each case the value at sequence index i is the turn at N=i,
29
30                   i+1
31                    ^
32                    |
33                    |
34           i-1 ---> i     turn at i
35                          first turn at i = n_start + 1
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37       For multiple "arms", the turn follows that particular arm so it's
38       i-arms, i, i+arms.  i values start "n_start()+arms_count()" so that
39       i-arms is "n_start()", the first N on the path.  A single arm path
40       beginning N=0 has its first turn at i=1.
41
42       For "Straight", "LSR", "SLR", and "SRL", straight means either straight
43       ahead or 180-degree reversal, ie. the direction N to N+1 is along the
44       same line as N-1 to N was.
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46       "Left" means to the left side of the N-1 to N line, so not straight or
47       right.  Similarly "Right" means to the right side of the N-1 to N line,
48       so not straight or left.
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FUNCTIONS

51       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
52       classes.
53
54       "$seq = Math::NumSeq::PlanePathTurn->new (key=>value,...)"
55           Create and return a new sequence object.  The options are
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57               planepath          string, name of a PlanePath module
58               planepath_object   PlanePath object
59               turn_type          string, as described above
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61           "planepath" can be either the module part such as "SquareSpiral" or
62           a full class name "Math::PlanePath::SquareSpiral".
63
64       "$value = $seq->ith($i)"
65           Return the turn at N=$i in the PlanePath.
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67       "$bool = $seq->pred($value)"
68           Return true if $value occurs as a turn.  Often this is merely the
69           possible turn values 1,0,-1, etc, but some spiral paths for example
70           only go left or straight in which case only 1 and 0 occur and
71           "pred()" reflects that.
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73       "$i = $seq->i_start()"
74           Return the first index $i in the sequence.  This is the position
75           "rewind()" returns to.
76
77           This is "$path->n_start() - $path->arms_count()" from the PlanePath
78           object.
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FORMULAS

81   Turn Left or Right
82       A turn left or right is identified by considering the dX,dY at N-1 and
83       at N.
84
85           N+1      *
86                    |
87                    |
88                    |   dx2,dy2
89                    |
90           N        *
91                   /
92                  /
93                 /  dx1,dy1
94           N-1  *
95
96       With the two vectors dx1,dy1 and dx2,dy2 at a common origin, if the
97       dx2,dy2 is "above" the dx1,dy1 line then it's a turn to the left, or
98       below is a turn to the right
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100           dx2,dy2
101              *
102              ^   * dx1,dy1
103              |  ^
104              | /
105              |/
106              o
107
108       At dx2, the Y value of the dx1,dy1 vector is
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110           cmpY = dx2 * dy1/dx1           if dx1 != 0
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112           left if dy2 > cmpY
113                   dy2 > dx2 * dy1/dx1
114              so   dy2 * dx1 > dx2 * dy1
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116       This cross-product comparison dy2*dx1 > dx2*dy1 works when dx1=0 too,
117       ie. when dx1,dy1 is vertical
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119           left if dy2 * 0 > dx2 * dy1
120                         0 > dx2*dy1
121           good, left if dx2 and dy1 opposite signs
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123       So
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125           dy2*dx1 > dx2*dy1      left
126           dy2*dx1 < dx2*dy1      right
127           dy2*dx1 = dx2*dy1      straight, including 180 degree reverse
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HOME PAGE

136       <http://user42.tuxfamily.org/math-planepath/index.html>
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LICENSE

139       Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 Kevin
140       Ryde
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142       This file is part of Math-PlanePath.
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144       Math-PlanePath is free software; you can redistribute it and/or modify
145       it under the terms of the GNU General Public License as published by
146       the Free Software Foundation; either version 3, or (at your option) any
147       later version.
148
149       Math-PlanePath is distributed in the hope that it will be useful, but
150       WITHOUT ANY WARRANTY; without even the implied warranty of
151       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
152       General Public License for more details.
153
154       You should have received a copy of the GNU General Public License along
155       with Math-PlanePath.  If not, see <http://www.gnu.org/licenses/>.
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159perl v5.32.0                      2020-07-28    Math::NumSeq::PlanePathTurn(3)