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1 2 3 =head1 NAME 4 5 PGgraphmacros -- in courseScripts directory 6 7 =head1 SYNPOSIS 8 9 10 # use Fun; 11 # use Label; 12 # use Circle; 13 # use WWPlot; 14 15 =head1 DESCRIPTION 16 17 This collection of macros provides easy access to the facilities provided by the graph 18 module WWPlot and the modules for objects which can be drawn on a graph: functions (Fun.pm) 19 labels (Label.pm) and images. The only image implemented currently are open and closed circles 20 (Circle) which can be used to mark graphs of functions defined on open and closed intervals. 21 22 These macros provide an easy ability to graph simple functions. More complicated projects 23 may require direct access to the underlying modules. If these complicated projects are common 24 then it may be desirable to create additional macros. (See numericalmacros.pl for one example.) 25 26 27 =cut 28 29 =head2 Other constructs 30 31 See F<PGbasicmacros> for definitions of C<image> and C<caption> 32 33 =cut 34 35 36 #my $User = $main::studentLogin; 37 #my $psvn = $main::psvnNumber; #$main::in{'probSetKey'}; #in{'probSetNumber'}; #$main::probSetNumber; 38 #my $setNumber = $main::setNumber; 39 #my $probNum = $main::probNum; 40 41 ######################################################### 42 # this initializes a graph object 43 ######################################################### 44 # graphObject = init_graph(xmin,ymin,xmax,ymax,options) 45 # options include 'grid' =>[8,8] or 46 # 'ticks'=>[8,8] and/or 47 # 'axes' 48 ######################################################### 49 50 my %images_created = (); # this keeps track of the base names of the images created during this session. 51 # We tack on 52 # $imageNum = ++$images_created{$imageName} to keep from overwriting files 53 # when we don't want to. 54 55 56 57 58 =head2 init_graph 59 60 =pod 61 62 $graphObject = init_graph(xmin,ymin,xmax,ymax,'ticks'=>[4,4],'axes'=>[0,0]) 63 options are 64 'grid' =>[8,8] or 65 # there are 8 evenly spaced lines intersecting the horizontal axis 66 'ticks'=>[8,8] and/or 67 # there are 8 ticks on the horizontal axis, 8 on the vertical 68 'axes' => [0,0] 69 # axes pass through the point (0,0) in real coordinates 70 'size' => [200,200] 71 # dimensions of the graph in pixels. 72 'pixels' =>[200,200] # synonym for size 73 74 Creates a graph object with the default size 200 by 200 pixels. 75 If you want axes or grids you need to specify them in options. But the default values can be selected for you. 76 77 78 =cut 79 BEGIN { 80 be_strict(); 81 } 82 sub _PGgraphmacros_init { 83 84 85 } 86 #sub _PGgraphmacros_export { 87 # 88 # my @EXPORT = ( 89 # '&init_graph', '&add_functions', '&plot_functions', '&open_circle', 90 # '&closed_circle', '&my_math_constants', '&string_to_sub', 91 # ); 92 # @EXPORT; 93 #} 94 95 sub init_graph { 96 my ($xmin,$ymin,$xmax,$ymax,%options) = @_; 97 my @size; 98 if ( defined($options{'size'}) ) { 99 @size = @{$options{'size'}}; 100 } elsif ( defined($options{'pixels'}) ) { 101 @size = @{$options{'pixels'}}; 102 } else { 103 @size=(200,200); 104 } 105 my $graphRef = new WWPlot(@size); 106 # select a name for this graph based on the user, the psvn and the problem 107 my $imageName = "$main::studentLogin-$main::psvnNumber-set${main::setNumber}prob${main::probNum}"; 108 # $imageNum counts the number of graphs with this name which have been created since PGgraphmacros.pl was initiated. 109 my $imageNum = ++$main::images_created{$imageName}; 110 # this provides a unique name for the graph -- it does not include an extension. 111 $graphRef->imageName("${imageName}image${imageNum}"); 112 113 $graphRef->xmin($xmin) if defined($xmin); 114 $graphRef->xmax($xmax) if defined($xmax); 115 $graphRef->ymin($ymin) if defined($ymin); 116 $graphRef->ymax($ymax) if defined($ymax); 117 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/8; 118 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/8; 119 if (defined($options{grid})) { # draw grid 120 my $xdiv = ( ${$options{'grid'}}[0]) ? ${$options{'grid'}}[0] : 8; # number of ticks (8 is default) 121 my $ydiv = ( ${$options{'grid'}}[1] ) ? ${$options{'grid'}}[1] : 8; 122 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 123 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 124 my $i; my @x_values=(); my @y_values=(); 125 foreach $i (1..($xdiv-1) ) { 126 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 127 } 128 foreach $i (1..($ydiv-1) ) { 129 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 130 } 131 $graphRef->v_grid('gray',@x_values); 132 $graphRef->h_grid('gray',@y_values); 133 $graphRef->lb(new Label($x_delta,0,sprintf("%1.1f",$x_delta),'black','center','middle')); 134 $graphRef->lb(new Label(0,$y_delta,sprintf("%1.1f",$y_delta),'black','center','middle')); 135 136 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 137 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 138 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top')); 139 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 140 141 } elsif ($options{ticks}) { # draw ticks -- grid over rides ticks 142 my $xdiv = ${$options{ticks}}[0]? ${$options{ticks}}[0] : 8; # number of ticks (8 is default) 143 my $ydiv = ${$options{ticks}}[1]? ${$options{ticks}}[1] : 8; 144 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 145 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 146 my $i; my @x_values=(); my @y_values=(); 147 foreach $i (1..($xdiv-1) ) { 148 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 149 } 150 foreach $i (1..($ydiv-1) ) { 151 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 152 } 153 $graphRef->v_ticks(0,'black',@x_values); 154 $graphRef->h_ticks(0,'black',@y_values); 155 $graphRef->lb(new Label($x_delta,0,$x_delta,'black','right')); 156 $graphRef->lb(new Label(0,$y_delta,$y_delta,'black','top')); 157 158 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 159 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 160 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top')); 161 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 162 } 163 164 if ($options{axes}) { # draw axis 165 my $ra_axes = $options{axes}; 166 $graphRef->h_axis($ra_axes->[1],'black'); 167 $graphRef->v_axis($ra_axes->[0],'black'); 168 } 169 170 171 $graphRef; 172 } 173 174 sub init_graph_no_labels { 175 my ($xmin,$ymin,$xmax,$ymax,%options) = @_; 176 my @size; 177 if ( defined($options{'size'}) ) { 178 @size = @{$options{'size'}}; 179 } elsif ( defined($options{'pixels'}) ) { 180 @size = @{$options{'pixels'}}; 181 } else { 182 @size=(200,200); 183 } 184 my $graphRef = new WWPlot(@size); 185 # select a name for this graph based on the user, the psvn and the problem 186 my $imageName = "$main::studentLogin-$main::psvnNumber-set${main::setNumber}prob${main::probNum}"; 187 # $imageNum counts the number of graphs with this name which have been created since PGgraphmacros.pl was initiated. 188 my $imageNum = ++$main::images_created{$imageName}; 189 # this provides a unique name for the graph -- it does not include an extension. 190 $graphRef->imageName("${imageName}image${imageNum}"); 191 192 $graphRef->xmin($xmin) if defined($xmin); 193 $graphRef->xmax($xmax) if defined($xmax); 194 $graphRef->ymin($ymin) if defined($ymin); 195 $graphRef->ymax($ymax) if defined($ymax); 196 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/8; 197 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/8; 198 if (defined($options{grid})) { # draw grid 199 my $xdiv = ( ${$options{'grid'}}[0]) ? ${$options{'grid'}}[0] : 8; # number of ticks (8 is default) 200 my $ydiv = ( ${$options{'grid'}}[1] ) ? ${$options{'grid'}}[1] : 8; 201 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 202 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 203 my $i; my @x_values=(); my @y_values=(); 204 foreach $i (1..($xdiv-1) ) { 205 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 206 } 207 foreach $i (1..($ydiv-1) ) { 208 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 209 } 210 $graphRef->v_grid('gray',@x_values); 211 $graphRef->h_grid('gray',@y_values); 212 #$graphRef->lb(new Label($x_delta,0,sprintf("%1.1f",$x_delta),'black','center','top')); 213 #$graphRef->lb(new Label($x_delta,0,"|",'black','center','middle')); 214 #$graphRef->lb(new Label(0,$y_delta,sprintf("%1.1f ",$y_delta),'black','right','middle')); 215 #$graphRef->lb(new Label(0,$y_delta,"-",'black','center','middle')); 216 217 218 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 219 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 220 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top','right')); 221 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 222 223 } elsif ($options{ticks}) { # draw ticks -- grid over rides ticks 224 my $xdiv = ${$options{ticks}}[0]? ${$options{ticks}}[0] : 8; # number of ticks (8 is default) 225 my $ydiv = ${$options{ticks}}[1]? ${$options{ticks}}[1] : 8; 226 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 227 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 228 my $i; my @x_values=(); my @y_values=(); 229 foreach $i (1..($xdiv-1) ) { 230 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 231 } 232 foreach $i (1..($ydiv-1) ) { 233 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 234 } 235 $graphRef->v_ticks(0,'black',@x_values); 236 $graphRef->h_ticks(0,'black',@y_values); 237 $graphRef->lb(new Label($x_delta,0,$x_delta,'black','right')); 238 $graphRef->lb(new Label(0,$y_delta,$y_delta,'black','top')); 239 240 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 241 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 242 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top')); 243 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 244 } 245 246 if ($options{axes}) { # draw axis 247 my $ra_axes = $options{axes}; 248 $graphRef->h_axis($ra_axes->[1],'black'); 249 $graphRef->v_axis($ra_axes->[0],'black'); 250 } 251 252 253 $graphRef; 254 } 255 256 257 258 =head2 plot_functions 259 260 =pod 261 262 Usage: ($f1, $f2, $f3) = plot_functions($graph, $f1, $f2, $f3); 263 Synonym: add_functions($graph,$f1,$f2,$f3); 264 265 Where $f1 is a string of the form 266 267 $f1 = qq! x^2 - 3*x + 45 for x in [0, 45) using color:red and weight:2! 268 269 The phrase translates as: formula B<for> variable B<in> interval B<using> option-list. 270 The option-list contains pairs of the form attribute:value. 271 The default for color is "default_color" which is usually black. 272 The default for the weight (pixel width) of the pen is 2 pixels. 273 274 The string_to_sub subroutine is used to translate the formula into a subroutine. 275 276 The functions in the list are installed in the graph object $graph and will appear when the graph object is next drawn. 277 278 =cut 279 280 sub add_functions { 281 &plot_functions; 282 } 283 284 sub plot_functions { 285 my $graph = shift; 286 my @function_list = @_; 287 my $error = ""; 288 $error .= "The first argument to plot_functions must be a graph object" unless ref($graph) =~/WWPlot/; 289 my $fn; 290 my @functions=(); 291 foreach $fn (@function_list) { 292 293 # model: "2.5-x^2 for x in <-1,0> using color:red and weight:2" 294 if ($fn =~ /^(.+)for\s*(\w+)\s*in\s*([\(\[\<])\s*([\d\.\-]+)\s*,\s*([\d\.\-]+)\s*([\)\]\>])\s*using\s*(.*)$/ ) { 295 my ($rule,$var, $left_br, $left_end, $right_end, $right_br, $options)= ($1, $2, $3, $4, $5, $6, $7); 296 297 my %options = split( /\s*and\s*|\s*:\s*|\s*,\s*|\s*=\s*|\s+/,$options); 298 my ($color, $weight); 299 if ( defined($options{'color'}) ){ 300 $color = $options{'color'}; #set pen color 301 } else { 302 $color = 'default_color'; 303 } 304 if ( defined($options{'weight'}) ) { 305 $weight = $options{'weight'}; # set pen weight (width in pixels) 306 } else { 307 $weight =2; 308 } 309 310 my $subRef = string_to_sub($rule,$var); 311 my $funRef = new Fun($subRef,$graph); 312 $funRef->color($color); 313 $funRef->weight($weight); 314 $funRef->domain($left_end , $right_end); 315 push(@functions,$funRef); 316 # place open (1,3) or closed (1,3) circle at the endpoints or do nothing <1,3> 317 if ($left_br eq '[' ) { 318 $graph->stamps(closed_circle($left_end,&$subRef($left_end),$color) ); 319 } elsif ($left_br eq '(' ) { 320 $graph->stamps(open_circle($left_end, &$subRef($left_end), $color) ); 321 } 322 if ($right_br eq ']' ) { 323 $graph->stamps(closed_circle($right_end,&$subRef($right_end),$color) ); 324 } elsif ($right_br eq ')' ) { 325 $graph->stamps(open_circle($right_end, &$subRef($right_end), $color) ); 326 } 327 328 } else { 329 $error .= "Error in parsing: $fn $main::BR"; 330 } 331 332 } 333 die ("Error in plot_functions: \n\t $error ") if $error; 334 @functions; # return function references unless there is an error. 335 } 336 337 =head2 insertGraph 338 339 $filePath = insertGraph(graphObject); 340 returns a path to the file containing the graph image. 341 342 B<Note:> Because insertGraph involves writing to the disk, it is actually defined in dangerousMacros.pl. 343 344 insertGraph(graphObject) writes a image file to the C<html/tmp/gif> directory of the current course. 345 The file name is obtained from the graphObject. Warnings are issued if errors occur while writing to 346 the file. 347 348 The permissions and ownership of the file are controlled by C<$main::tmp_file_permission> 349 and C<$main::numericalGroupID>. 350 351 B<Returns:> A string containing the full path to the temporary file containing the image. 352 353 354 355 InsertGraph draws the object $graph, stores it in "${tempDirectory}gif/$imageName.gif (or .png)" where 356 the $imageName is obtained from the graph object. ConvertPath and surePathToTmpFile are used to insure 357 that the correct directory separators are used for the platform and that the necessary directories 358 are created if they are not already present. The directory address to the file is the result. 359 360 The most common use of C,insertGraph> is 361 362 TEXT(image(insertGraph($graph)) ); 363 364 where C<image> takes care of creating the proper URL for accessing the graph and for creating the HTML code to display the image. 365 366 Another common usage is: 367 368 TEXT(htmlLink( alias(insertGraph($graph), "picture" ) ) ); 369 370 which inserts the URL pointing to the picture. 371 alias converts the directory address to a URL when serving HTML pages and insures that 372 an eps file is generated when creating TeX code for downloading. (Image, automatically applies alias to its input 373 in order to obtain the URL.) 374 375 See the documentation in F<dangerousMacros.pl> for the latest details. 376 377 =cut 378 379 =head2 'Circle' lables 380 381 Usage: $circle_object = open_circle( $x_position, $y_position, $color ); 382 $circle_object2 = closed_circle( $x_position, $y_position, $color ); 383 384 Creates a small open (resp. filled in or closed) circle for use as a stamp in marking graphs. 385 For example 386 387 $graph -> stamps($circle_object2); # puts a filled dot at $x_position, $y_position 388 389 =cut 390 391 ######################################################### 392 sub open_circle { 393 my ($cx,$cy,$color) = @_; 394 new Circle ($cx, $cy, 4,$color,'nearwhite'); 395 } 396 397 sub closed_circle { 398 my ($cx,$cy, $color) = @_; 399 $color = 'black' unless defined $color; 400 new Circle ($cx, $cy, 4,$color, $color); 401 } 402 403 404 =head2 Auxiliary macros 405 406 =head3 string_to_sub and my_math_constants 407 408 409 These are internal macros which govern the interpretation of equations. 410 411 412 Usage: $string = my_math_constants($string) 413 $subroutine_reference = my_string_to_sub($string) 414 415 C<my_math_constants> 416 interprets pi, e as mathematical constants 3.1415926... and 2.71828... respectively. (Case is important). 417 The power operator ^ is replaced by ** to conform with perl constructs 418 419 C<string_to_sub> 420 converts a string defining a single perl arithmetic expression with independent variable $XVAR into a subroutine. 421 The string is first filtered through C<my_math_macros>. The resulting subroutine 422 takes a single real number as input and produces a single output value. 423 424 =cut 425 426 sub my_math_constants { 427 my($in) = @_; 428 $in =~s/\bpi\b/(4*atan2(1,1))/g; 429 $in =~s/\be\b/(exp(1))/g; 430 $in =~s/\^/**/g; 431 $in; 432 } 433 434 sub string_to_sub { 435 my $str_in = shift; 436 my $var = shift; 437 my $out = undef; 438 if ( defined(&check_syntax) ) { 439 #prepare the correct answer and check it's syntax 440 my $rh_correct_ans = new AnswerHash; 441 $rh_correct_ans->input($str_in); 442 $rh_correct_ans = check_syntax($rh_correct_ans); 443 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 444 $rh_correct_ans->clear_error(); 445 $rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => ['x'], store_in =>'rf_correct_ans'); 446 my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans}; 447 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 448 $out = sub{ scalar( &$correct_eqn_sub(@_) ) }; #ignore the error messages from the function. 449 450 } else { 451 my $in =$str_in; 452 453 $in =~ s/\b$var\b/\$XVAR/g; 454 $in = &my_math_constants($in); 455 my ($subRef, $PG_eval_errors,$PG_full_error_report) = PG_restricted_eval( " sub { my \$XVAR = shift; my \$out = $in; \$out; } "); 456 if ($PG_eval_errors) { 457 die " ERROR while defining a function from the string:\n\n$main::BR $main::BR $str_in $main::BR $main::BR\n\n $PG_eval_errors" 458 } else { 459 $out = $subRef; 460 } 461 462 } 463 $out; 464 } 465 466 467 468 469 470 471 472 473 474 ######################################################### 475 476 1;
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