line |
stmt |
bran |
cond |
sub |
pod |
time |
code |
1
|
|
|
|
|
|
|
########################################################################### |
2
|
|
|
|
|
|
|
# |
3
|
|
|
|
|
|
|
# Math::CatmullRom |
4
|
|
|
|
|
|
|
# |
5
|
|
|
|
|
|
|
# $Id: CatmullRom.pm,v 1.1.1.1 2003/08/31 16:53:16 wiggly Exp $ |
6
|
|
|
|
|
|
|
# |
7
|
|
|
|
|
|
|
# $Author: wiggly $ |
8
|
|
|
|
|
|
|
# |
9
|
|
|
|
|
|
|
# $Revision: 1.1.1.1 $ |
10
|
|
|
|
|
|
|
# |
11
|
|
|
|
|
|
|
########################################################################### |
12
|
|
|
|
|
|
|
|
13
|
|
|
|
|
|
|
package Math::CatmullRom; |
14
|
|
|
|
|
|
|
|
15
|
1
|
|
|
1
|
|
14222
|
use strict; |
|
1
|
|
|
|
|
2
|
|
|
1
|
|
|
|
|
28
|
|
16
|
|
|
|
|
|
|
|
17
|
1
|
|
|
1
|
|
867
|
use Data::Dumper; |
|
1
|
|
|
|
|
11204
|
|
|
1
|
|
|
|
|
772
|
|
18
|
|
|
|
|
|
|
|
19
|
|
|
|
|
|
|
our $VERSION = '0.00'; |
20
|
|
|
|
|
|
|
|
21
|
|
|
|
|
|
|
|
22
|
|
|
|
|
|
|
########################################################################### |
23
|
|
|
|
|
|
|
# |
24
|
|
|
|
|
|
|
# new |
25
|
|
|
|
|
|
|
# |
26
|
|
|
|
|
|
|
########################################################################### |
27
|
|
|
|
|
|
|
sub new |
28
|
|
|
|
|
|
|
{ |
29
|
3
|
|
|
3
|
0
|
539
|
my $class = shift; |
30
|
|
|
|
|
|
|
|
31
|
|
|
|
|
|
|
# control points |
32
|
3
|
|
|
|
|
6
|
my @p = @_; |
33
|
|
|
|
|
|
|
|
34
|
3
|
|
|
|
|
5
|
my $self = {}; |
35
|
|
|
|
|
|
|
|
36
|
3
|
|
|
|
|
5
|
$self = bless $self, $class; |
37
|
|
|
|
|
|
|
|
38
|
3
|
|
|
|
|
9
|
$self->control_points( @p ); |
39
|
|
|
|
|
|
|
|
40
|
1
|
|
|
|
|
5
|
$self->plot_all( 0 ); |
41
|
|
|
|
|
|
|
|
42
|
1
|
|
|
|
|
5
|
return $self; |
43
|
|
|
|
|
|
|
} |
44
|
|
|
|
|
|
|
|
45
|
|
|
|
|
|
|
|
46
|
|
|
|
|
|
|
########################################################################### |
47
|
|
|
|
|
|
|
# |
48
|
|
|
|
|
|
|
# control_points |
49
|
|
|
|
|
|
|
# |
50
|
|
|
|
|
|
|
########################################################################### |
51
|
|
|
|
|
|
|
sub control_points |
52
|
|
|
|
|
|
|
{ |
53
|
3
|
|
|
3
|
0
|
4
|
my $self = shift; |
54
|
|
|
|
|
|
|
|
55
|
3
|
|
|
|
|
5
|
my @p = @_; |
56
|
|
|
|
|
|
|
|
57
|
|
|
|
|
|
|
# make sure we have enough points |
58
|
3
|
100
|
|
|
|
11
|
if( ( scalar( @p ) / 2 ) < 4 ) |
59
|
|
|
|
|
|
|
{ |
60
|
2
|
|
|
|
|
16
|
die "passed too few control points, minimum is 4 pairs.\n"; |
61
|
|
|
|
|
|
|
} |
62
|
|
|
|
|
|
|
|
63
|
|
|
|
|
|
|
# make sure we have an even amount of points |
64
|
1
|
50
|
|
|
|
5
|
if( scalar( @p ) % 2 ) |
65
|
|
|
|
|
|
|
{ |
66
|
0
|
|
|
|
|
0
|
die "passed odd number of control points.\n"; |
67
|
|
|
|
|
|
|
} |
68
|
|
|
|
|
|
|
|
69
|
1
|
|
|
|
|
5
|
$self->{'p'} = \@p; |
70
|
|
|
|
|
|
|
|
71
|
|
|
|
|
|
|
# pre-calculate some useful values |
72
|
1
|
|
|
|
|
5
|
$self->{'np'} = scalar( @p ) / 2; |
73
|
1
|
|
|
|
|
3
|
$self->{'nl'} = $self->{'np'} - 3; |
74
|
|
|
|
|
|
|
|
75
|
|
|
|
|
|
|
#print STDERR "NP : " . $self->{'np'} . "\n"; |
76
|
|
|
|
|
|
|
#print STDERR "NL : " . $self->{'nl'} . "\n"; |
77
|
|
|
|
|
|
|
|
78
|
1
|
|
|
|
|
4
|
return 1; |
79
|
|
|
|
|
|
|
} |
80
|
|
|
|
|
|
|
|
81
|
|
|
|
|
|
|
|
82
|
|
|
|
|
|
|
########################################################################### |
83
|
|
|
|
|
|
|
# |
84
|
|
|
|
|
|
|
# plot_all |
85
|
|
|
|
|
|
|
# |
86
|
|
|
|
|
|
|
########################################################################### |
87
|
|
|
|
|
|
|
sub plot_all |
88
|
|
|
|
|
|
|
{ |
89
|
1
|
|
|
1
|
0
|
2
|
my $self = shift; |
90
|
|
|
|
|
|
|
|
91
|
1
|
50
|
|
|
|
4
|
my $all = shift |
92
|
|
|
|
|
|
|
or 1; |
93
|
|
|
|
|
|
|
|
94
|
1
|
|
|
|
|
3
|
$self->{'plot_all'} = $all; |
95
|
|
|
|
|
|
|
|
96
|
1
|
|
|
|
|
2
|
return 1; |
97
|
|
|
|
|
|
|
} |
98
|
|
|
|
|
|
|
|
99
|
|
|
|
|
|
|
|
100
|
|
|
|
|
|
|
########################################################################### |
101
|
|
|
|
|
|
|
# |
102
|
|
|
|
|
|
|
# point |
103
|
|
|
|
|
|
|
# |
104
|
|
|
|
|
|
|
########################################################################### |
105
|
|
|
|
|
|
|
sub point |
106
|
|
|
|
|
|
|
{ |
107
|
0
|
|
|
0
|
0
|
|
my $self = shift; |
108
|
|
|
|
|
|
|
|
109
|
0
|
|
|
|
|
|
my $theta = shift; |
110
|
|
|
|
|
|
|
|
111
|
0
|
|
|
|
|
|
my @p = (); |
112
|
|
|
|
|
|
|
|
113
|
0
|
|
|
|
|
|
my ( $segment, $ps, $pf ); |
114
|
|
|
|
|
|
|
|
115
|
|
|
|
|
|
|
#print STDERR "TH : $theta\n"; |
116
|
|
|
|
|
|
|
|
117
|
|
|
|
|
|
|
# figure out where along the total curve we are |
118
|
0
|
|
|
|
|
|
$theta = $theta * $self->{'nl'}; |
119
|
|
|
|
|
|
|
|
120
|
|
|
|
|
|
|
#print STDERR "TH : $theta\n"; |
121
|
|
|
|
|
|
|
|
122
|
|
|
|
|
|
|
# figure out which segment we are plotting for |
123
|
0
|
|
|
|
|
|
$segment = int( $theta ); |
124
|
|
|
|
|
|
|
|
125
|
|
|
|
|
|
|
# calculate theta within segment |
126
|
0
|
|
|
|
|
|
$theta = $theta - $segment; |
127
|
|
|
|
|
|
|
|
128
|
|
|
|
|
|
|
#print STDERR "TH : $theta\n"; |
129
|
|
|
|
|
|
|
|
130
|
0
|
|
|
|
|
|
$ps = $segment * 2; |
131
|
|
|
|
|
|
|
|
132
|
0
|
|
|
|
|
|
$pf = ( ( $segment + 3 ) * 2 ) + 1; |
133
|
|
|
|
|
|
|
|
134
|
|
|
|
|
|
|
#print STDERR "PS : $ps\n"; |
135
|
|
|
|
|
|
|
#print STDERR "PF : $pf\n"; |
136
|
|
|
|
|
|
|
|
137
|
|
|
|
|
|
|
#print STDERR "POINTS : " . join( ',', ( @{$self->{'p'}}[ $ps .. $pf ] ) ) . "\n"; |
138
|
|
|
|
|
|
|
|
139
|
|
|
|
|
|
|
#print STDERR "DUMP : " . Dumper( ( @{$self->{'p'}}[ $ps .. $pf ] ) ) . "\n"; |
140
|
|
|
|
|
|
|
|
141
|
0
|
|
|
|
|
|
push @p, catmull_rom( $theta, ( @{$self->{'p'}}[ $ps .. $pf ] ) ); |
|
0
|
|
|
|
|
|
|
142
|
|
|
|
|
|
|
|
143
|
0
|
0
|
|
|
|
|
return wantarray ? @p : \@p; |
144
|
|
|
|
|
|
|
} |
145
|
|
|
|
|
|
|
|
146
|
|
|
|
|
|
|
|
147
|
|
|
|
|
|
|
########################################################################### |
148
|
|
|
|
|
|
|
# |
149
|
|
|
|
|
|
|
# curve |
150
|
|
|
|
|
|
|
# |
151
|
|
|
|
|
|
|
########################################################################### |
152
|
|
|
|
|
|
|
sub curve |
153
|
|
|
|
|
|
|
{ |
154
|
0
|
|
|
0
|
0
|
|
my $self = shift; |
155
|
|
|
|
|
|
|
|
156
|
0
|
|
|
|
|
|
my $num = shift; |
157
|
|
|
|
|
|
|
|
158
|
0
|
0
|
|
|
|
|
my $per_segment = shift |
159
|
|
|
|
|
|
|
or 0; |
160
|
|
|
|
|
|
|
|
161
|
|
|
|
|
|
|
# list of points on curve |
162
|
0
|
|
|
|
|
|
my @p = (); |
163
|
|
|
|
|
|
|
|
164
|
|
|
|
|
|
|
# if we want to plot per-segemnt then we multiply our number of required |
165
|
|
|
|
|
|
|
# points by the number of segments in our line |
166
|
0
|
0
|
|
|
|
|
if( $per_segment ) |
167
|
|
|
|
|
|
|
{ |
168
|
0
|
|
|
|
|
|
$num = $num * $self->{'nl'}; |
169
|
|
|
|
|
|
|
} |
170
|
|
|
|
|
|
|
|
171
|
|
|
|
|
|
|
# figure out what our theta increment is |
172
|
0
|
|
|
|
|
|
my $increment = 1 / $num; |
173
|
|
|
|
|
|
|
|
174
|
0
|
|
|
|
|
|
my ( $point, $theta ); |
175
|
|
|
|
|
|
|
|
176
|
0
|
|
|
|
|
|
$theta = 0; |
177
|
|
|
|
|
|
|
|
178
|
|
|
|
|
|
|
# plot every point and push it onto our return array |
179
|
0
|
|
|
|
|
|
for( $point = 0; $point < $num; $point++ ) |
180
|
|
|
|
|
|
|
{ |
181
|
0
|
|
|
|
|
|
$theta = $point * $increment; |
182
|
0
|
|
|
|
|
|
push @p, $self->point( $theta ); |
183
|
|
|
|
|
|
|
} |
184
|
0
|
|
|
|
|
|
push @p, $self->point( 1.0 ); |
185
|
|
|
|
|
|
|
|
186
|
|
|
|
|
|
|
# return as an array or reference depending on context |
187
|
0
|
0
|
|
|
|
|
return wantarray ? @p : \@p; |
188
|
|
|
|
|
|
|
} |
189
|
|
|
|
|
|
|
|
190
|
|
|
|
|
|
|
|
191
|
|
|
|
|
|
|
########################################################################### |
192
|
|
|
|
|
|
|
# |
193
|
|
|
|
|
|
|
# catmull_rom |
194
|
|
|
|
|
|
|
# |
195
|
|
|
|
|
|
|
########################################################################### |
196
|
|
|
|
|
|
|
sub catmull_rom |
197
|
|
|
|
|
|
|
{ |
198
|
0
|
|
|
0
|
0
|
|
my ( $t, $x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4 ) = @_; |
199
|
|
|
|
|
|
|
|
200
|
0
|
|
|
|
|
|
my $t2 = $t * $t; |
201
|
0
|
|
|
|
|
|
my $t3 = $t2 * $t; |
202
|
|
|
|
|
|
|
|
203
|
|
|
|
|
|
|
return ( |
204
|
0
|
|
|
|
|
|
( 0.5 |
205
|
|
|
|
|
|
|
* ( ( - $x1 + 3 * $x2 -3 * $x3 + $x4 ) * $t3 |
206
|
|
|
|
|
|
|
+ ( 2 * $x1 -5 * $x2 + 4 * $x3 - $x4 ) * $t2 |
207
|
|
|
|
|
|
|
+ ( -$x1 + $x3 ) * $t |
208
|
|
|
|
|
|
|
+ 2 * $x2 ) ) |
209
|
|
|
|
|
|
|
, |
210
|
|
|
|
|
|
|
( 0.5 |
211
|
|
|
|
|
|
|
* ( ( - $y1 + 3 * $y2 -3 * $y3 + $y4 ) * $t3 |
212
|
|
|
|
|
|
|
+ ( 2 * $y1 -5 * $y2 + 4 * $y3 - $y4 ) * $t2 |
213
|
|
|
|
|
|
|
+ ( -$y1 + $y3 ) * $t |
214
|
|
|
|
|
|
|
+ 2 * $y2 ) ) |
215
|
|
|
|
|
|
|
); |
216
|
|
|
|
|
|
|
|
217
|
|
|
|
|
|
|
# return 0.5 |
218
|
|
|
|
|
|
|
# * ( ( - $p1 + 3 * $p2 -3 * $p3 + $p4 ) * $t * $t * $t |
219
|
|
|
|
|
|
|
# + ( 2 * $p1 -5 * $p2 + 4 * $p3 - $p4 ) * $t * $t |
220
|
|
|
|
|
|
|
# + ( -$p1 + $p3 ) * $t |
221
|
|
|
|
|
|
|
# + 2 * $p2 ); |
222
|
|
|
|
|
|
|
} |
223
|
|
|
|
|
|
|
|
224
|
|
|
|
|
|
|
|
225
|
|
|
|
|
|
|
########################################################################### |
226
|
|
|
|
|
|
|
1; |
227
|
|
|
|
|
|
|
|
228
|
|
|
|
|
|
|
=pod |
229
|
|
|
|
|
|
|
|
230
|
|
|
|
|
|
|
=head1 NAME |
231
|
|
|
|
|
|
|
|
232
|
|
|
|
|
|
|
Math::CatmullRom - Calculate Catmull-Rom splines |
233
|
|
|
|
|
|
|
|
234
|
|
|
|
|
|
|
=head1 SYNOPSIS |
235
|
|
|
|
|
|
|
|
236
|
|
|
|
|
|
|
use Math::CatmullRom; |
237
|
|
|
|
|
|
|
|
238
|
|
|
|
|
|
|
# create curve passing through list of control points |
239
|
|
|
|
|
|
|
my $curve = new Math::CatmullRom( $x1, $y1, $x2, $y2, ..., $xn, $yn ); |
240
|
|
|
|
|
|
|
|
241
|
|
|
|
|
|
|
# or pass reference to list of control points |
242
|
|
|
|
|
|
|
my $curve = new Math::CatmullRom( [ $x1, $y1, $x2, $y2, ..., $xn, $yn ] ); |
243
|
|
|
|
|
|
|
|
244
|
|
|
|
|
|
|
# determine (x, y) at point along curve, range 0.0 -> 1.0 |
245
|
|
|
|
|
|
|
my ($x, $y) = $curve->point( 0.5 ); |
246
|
|
|
|
|
|
|
|
247
|
|
|
|
|
|
|
# returns list ref in scalar context |
248
|
|
|
|
|
|
|
my $xy = $curve->point( 0.5 ); |
249
|
|
|
|
|
|
|
|
250
|
|
|
|
|
|
|
# return list of 20 (x, y) points along curve |
251
|
|
|
|
|
|
|
my @curve = $curve->curve( 20 ); |
252
|
|
|
|
|
|
|
|
253
|
|
|
|
|
|
|
# returns list ref in scalar context |
254
|
|
|
|
|
|
|
my $curve = $curve->curve( 20 ); |
255
|
|
|
|
|
|
|
|
256
|
|
|
|
|
|
|
# include start and finish points by adding false data points |
257
|
|
|
|
|
|
|
$curve->plot_all; |
258
|
|
|
|
|
|
|
|
259
|
|
|
|
|
|
|
=head1 DESCRIPTION |
260
|
|
|
|
|
|
|
|
261
|
|
|
|
|
|
|
This module provides an algorithm to generate plots for Catmull-Rom splines. |
262
|
|
|
|
|
|
|
|
263
|
|
|
|
|
|
|
A Catmull-Rom spline can be considered a special type of Bezier curve that |
264
|
|
|
|
|
|
|
guarantees that the curve will cross every control point starting at the |
265
|
|
|
|
|
|
|
second point and terminating at the penultimate one. For this reason the |
266
|
|
|
|
|
|
|
minimum number of control points is 4. |
267
|
|
|
|
|
|
|
|
268
|
|
|
|
|
|
|
To plot a curve where you have a set of points but want the curve to be |
269
|
|
|
|
|
|
|
drawn through the start and finish points you can tell the module to plot |
270
|
|
|
|
|
|
|
all of the points. In this case it assumes that there are two extra points, |
271
|
|
|
|
|
|
|
prior to the start point with the same values as the start point and one |
272
|
|
|
|
|
|
|
prior to the finish point with the same values as the finish point. This is |
273
|
|
|
|
|
|
|
really just a convenience function for certain kinds of plot. |
274
|
|
|
|
|
|
|
|
275
|
|
|
|
|
|
|
A new Catmull-Rom spline is created using the new() constructor, passing a |
276
|
|
|
|
|
|
|
list of control points. |
277
|
|
|
|
|
|
|
|
278
|
|
|
|
|
|
|
use Math::CatmullRom; |
279
|
|
|
|
|
|
|
|
280
|
|
|
|
|
|
|
# create curve passing through list of control points |
281
|
|
|
|
|
|
|
my @control = ( $x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4 ); |
282
|
|
|
|
|
|
|
my $spline = new Math::CatmullRom( @control ); |
283
|
|
|
|
|
|
|
|
284
|
|
|
|
|
|
|
Alternatively, a reference to a list of control points may be passed. |
285
|
|
|
|
|
|
|
|
286
|
|
|
|
|
|
|
# or pass reference to list of control points |
287
|
|
|
|
|
|
|
my $spline = new Math::CatmullRom( \@control ); |
288
|
|
|
|
|
|
|
|
289
|
|
|
|
|
|
|
The point( $theta ) method can be called on the object, passing a value in |
290
|
|
|
|
|
|
|
the range 0.0 to 1.0 which represents the distance along the spline. When |
291
|
|
|
|
|
|
|
called in list context, the method returns the x and y coordinates of that |
292
|
|
|
|
|
|
|
point on the curve. |
293
|
|
|
|
|
|
|
|
294
|
|
|
|
|
|
|
my ( $x, $y ) = $curve->plot( 0.75 ); |
295
|
|
|
|
|
|
|
print "X : $x\nY : $y\n"; |
296
|
|
|
|
|
|
|
|
297
|
|
|
|
|
|
|
When called in a scalar context, it returns a reference to a list containing |
298
|
|
|
|
|
|
|
the X and Y coordinates. |
299
|
|
|
|
|
|
|
|
300
|
|
|
|
|
|
|
my $point = $curve->plot( 0.75 ); |
301
|
|
|
|
|
|
|
print "X : $point->[0]\nY : $point->[1]\n"; |
302
|
|
|
|
|
|
|
|
303
|
|
|
|
|
|
|
The curve( $n, $per_segment ) method can be used to return a set of points |
304
|
|
|
|
|
|
|
sampled along the length of the curve (i.e. in the range 0.0 <= $theta <= |
305
|
|
|
|
|
|
|
1.0). |
306
|
|
|
|
|
|
|
|
307
|
|
|
|
|
|
|
The parameter indicates the number of sample points required. The method |
308
|
|
|
|
|
|
|
returns a list of ($x1, $y1, $x2, $y2, ..., $xn, $yn) points when called in |
309
|
|
|
|
|
|
|
list context, or a reference to such an array when called in scalar context. |
310
|
|
|
|
|
|
|
|
311
|
|
|
|
|
|
|
The $per_segment parameter determines whether $n points total will be plotted |
312
|
|
|
|
|
|
|
or $n points between every point, defaulting to $n points total. |
313
|
|
|
|
|
|
|
|
314
|
|
|
|
|
|
|
my @points = $curve->curve( 10, 1 ); |
315
|
|
|
|
|
|
|
|
316
|
|
|
|
|
|
|
while( @points ) |
317
|
|
|
|
|
|
|
{ |
318
|
|
|
|
|
|
|
my ( $x, $y ) = splice( @points, 0, 2 ); |
319
|
|
|
|
|
|
|
print "X : $x\nY : $y\n"; |
320
|
|
|
|
|
|
|
} |
321
|
|
|
|
|
|
|
|
322
|
|
|
|
|
|
|
my $points = $curve->curve( 50 ); |
323
|
|
|
|
|
|
|
|
324
|
|
|
|
|
|
|
while( @$points ) |
325
|
|
|
|
|
|
|
{ |
326
|
|
|
|
|
|
|
my ( $x, $y ) = splice( @$points, 0, 2 ); |
327
|
|
|
|
|
|
|
print "X : $x\nY : $y\n"; |
328
|
|
|
|
|
|
|
} |
329
|
|
|
|
|
|
|
|
330
|
|
|
|
|
|
|
=head1 TODO |
331
|
|
|
|
|
|
|
|
332
|
|
|
|
|
|
|
Test, test, test. |
333
|
|
|
|
|
|
|
|
334
|
|
|
|
|
|
|
=head1 BUGS |
335
|
|
|
|
|
|
|
|
336
|
|
|
|
|
|
|
None known so far. Please report any and all to Nigel Rantor > |
337
|
|
|
|
|
|
|
|
338
|
|
|
|
|
|
|
=head1 SUPPORT / WARRANTY |
339
|
|
|
|
|
|
|
|
340
|
|
|
|
|
|
|
This module is free software. IT COMES WITHOUT WARRANTY OF ANY KIND. |
341
|
|
|
|
|
|
|
|
342
|
|
|
|
|
|
|
=head1 LICENSE |
343
|
|
|
|
|
|
|
|
344
|
|
|
|
|
|
|
The Math::CatmullRom module is Copyright (c) 2003 Nigel Rantor. England. All |
345
|
|
|
|
|
|
|
rights reserved. |
346
|
|
|
|
|
|
|
|
347
|
|
|
|
|
|
|
You may distribute under the terms of either the GNU General Public License |
348
|
|
|
|
|
|
|
or the Artistic License, as specified in the Perl README file. |
349
|
|
|
|
|
|
|
|
350
|
|
|
|
|
|
|
=head1 AUTHORS |
351
|
|
|
|
|
|
|
|
352
|
|
|
|
|
|
|
Nigel Rantor > |
353
|
|
|
|
|
|
|
|
354
|
|
|
|
|
|
|
=head1 SEE ALSO |
355
|
|
|
|
|
|
|
|
356
|
|
|
|
|
|
|
L. |
357
|
|
|
|
|
|
|
|
358
|
|
|
|
|
|
|
=cut |