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protect @ signs in user_id when naming graphs. add Quiz prefix in MultiAnswer questions replace psvnNumber by psvn
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 images 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 = $main::psvn; #$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 #loadMacros("MathObjects.pl"); # avoid loading the entire package 51 # of MathObjects since that can mess up 52 # problems that don't use MathObjects but use Matrices. 53 54 my %images_created = (); # this keeps track of the base names of the images created during this session. 55 # We tack on 56 # $imageNum = ++$images_created{$imageName} to keep from overwriting files 57 # when we don't want to. 58 59 60 61 62 =head2 init_graph 63 64 =pod 65 66 $graphObject = init_graph(xmin,ymin,xmax,ymax,'ticks'=>[4,4],'axes'=>[0,0]) 67 options are 68 'grid' =>[8,8] or 69 # there are 8 evenly spaced lines intersecting the horizontal axis 70 'ticks'=>[8,8] and/or 71 # there are 8 ticks on the horizontal axis, 8 on the vertical 72 'axes' => [0,0] 73 # axes pass through the point (0,0) in real coordinates 74 'size' => [200,200] 75 # dimensions of the graph in pixels. 76 'pixels' =>[200,200] # synonym for size 77 78 Creates a graph object with the default size 200 by 200 pixels. 79 If you want axes or grids you need to specify them in options. But the default values can be selected for you. 80 81 82 =cut 83 BEGIN { 84 be_strict(); 85 } 86 sub _PGgraphmacros_init { 87 88 89 } 90 #sub _PGgraphmacros_export { 91 # 92 # my @EXPORT = ( 93 # '&init_graph', '&add_functions', '&plot_functions', '&open_circle', 94 # '&closed_circle', '&my_math_constants', '&string_to_sub', 95 # ); 96 # @EXPORT; 97 #} 98 99 sub init_graph { 100 my ($xmin,$ymin,$xmax,$ymax,%options) = @_; 101 my @size; 102 if ( defined($options{'size'}) ) { 103 @size = @{$options{'size'}}; 104 } elsif ( defined($options{'pixels'}) ) { 105 @size = @{$options{'pixels'}}; 106 } else { 107 my $defaultSize = $main::envir{onTheFlyImageSize} || 200; 108 @size=($defaultSize, $defaultSize); 109 } 110 my $graphRef = new WWPlot(@size); 111 # select a name for this graph based on the user, the psvn and the problem 112 my $setName = $main::setNumber; 113 # replace dots, commmas and @ signs in set and user names to keep latex and html happy 114 # this should be abstracted and placed in PGalias.pm or PGcore.pm or perhaps PG.pm 115 #FIXME 116 $setName =~ s/Q/QQ/g; 117 $setName =~ s/\./-Q-/g; 118 my $studentLogin = $main::studentLogin; 119 $studentLogin =~ s/Q/QQ/g; 120 $studentLogin =~ s/\./-Q-/g; 121 $studentLogin =~ s/\,/-Q-/g; 122 $studentLogin =~ s/\@/-Q-/g; 123 my $imageName = "$studentLogin-$main::problemSeed-set${setName}prob${main::probNum}"; 124 # $imageNum counts the number of graphs with this name which have been created since PGgraphmacros.pl was initiated. 125 my $imageNum = ++$main::images_created{$imageName}; 126 # this provides a unique name for the graph -- it does not include an extension. 127 $graphRef->imageName("${imageName}image${imageNum}"); 128 129 $graphRef->xmin($xmin) if defined($xmin); 130 $graphRef->xmax($xmax) if defined($xmax); 131 $graphRef->ymin($ymin) if defined($ymin); 132 $graphRef->ymax($ymax) if defined($ymax); 133 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/8; 134 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/8; 135 if (defined($options{grid})) { # draw grid 136 my $xdiv = ( ${$options{'grid'}}[0]) ? ${$options{'grid'}}[0] : 8; # number of ticks (8 is default) 137 my $ydiv = ( ${$options{'grid'}}[1] ) ? ${$options{'grid'}}[1] : 8; 138 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 139 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 140 my $i; my @x_values=(); my @y_values=(); 141 foreach $i (1..($xdiv-1) ) { 142 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 143 } 144 foreach $i (1..($ydiv-1) ) { 145 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 146 } 147 $graphRef->v_grid('gray',@x_values); 148 $graphRef->h_grid('gray',@y_values); 149 $graphRef->lb(new Label($x_delta,0,sprintf("%1.1f",$x_delta),'black','center','middle')); 150 $graphRef->lb(new Label(0,$y_delta,sprintf("%1.1f",$y_delta),'black','center','middle')); 151 152 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 153 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 154 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top')); 155 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 156 157 } elsif ($options{ticks}) { # draw ticks -- grid over rides ticks 158 my $xdiv = ${$options{ticks}}[0]? ${$options{ticks}}[0] : 8; # number of ticks (8 is default) 159 my $ydiv = ${$options{ticks}}[1]? ${$options{ticks}}[1] : 8; 160 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 161 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 162 my $i; my @x_values=(); my @y_values=(); 163 foreach $i (1..($xdiv-1) ) { 164 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 165 } 166 foreach $i (1..($ydiv-1) ) { 167 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 168 } 169 $graphRef->h_ticks(0,'black',@x_values); 170 $graphRef->v_ticks(0,'black',@y_values); 171 $graphRef->lb(new Label($x_delta,0,$x_delta,'black','right')); 172 $graphRef->lb(new Label(0,$y_delta,$y_delta,'black','top')); 173 174 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 175 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 176 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top')); 177 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 178 } 179 180 if ($options{axes}) { # draw axis 181 my $ra_axes = $options{axes}; 182 $graphRef->h_axis($ra_axes->[1],'black'); 183 $graphRef->v_axis($ra_axes->[0],'black'); 184 } 185 186 187 $graphRef; 188 } 189 190 sub init_graph_no_labels { 191 my ($xmin,$ymin,$xmax,$ymax,%options) = @_; 192 my @size; 193 if ( defined($options{'size'}) ) { 194 @size = @{$options{'size'}}; 195 } elsif ( defined($options{'pixels'}) ) { 196 @size = @{$options{'pixels'}}; 197 } else { 198 my $defaultSize = $main::envir{onTheFlyImageSize} || 200; 199 @size=($defaultSize, $defaultSize); 200 } 201 my $graphRef = new WWPlot(@size); 202 # select a name for this graph based on the user, the psvn and the problem 203 my $imageName = "$main::studentLogin-$main::psvn-set${main::setNumber}prob${main::probNum}"; 204 # $imageNum counts the number of graphs with this name which have been created since PGgraphmacros.pl was initiated. 205 my $imageNum = ++$main::images_created{$imageName}; 206 # this provides a unique name for the graph -- it does not include an extension. 207 $graphRef->imageName("${imageName}image${imageNum}"); 208 209 $graphRef->xmin($xmin) if defined($xmin); 210 $graphRef->xmax($xmax) if defined($xmax); 211 $graphRef->ymin($ymin) if defined($ymin); 212 $graphRef->ymax($ymax) if defined($ymax); 213 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/8; 214 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/8; 215 if (defined($options{grid})) { # draw grid 216 my $xdiv = ( ${$options{'grid'}}[0]) ? ${$options{'grid'}}[0] : 8; # number of ticks (8 is default) 217 my $ydiv = ( ${$options{'grid'}}[1] ) ? ${$options{'grid'}}[1] : 8; 218 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 219 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 220 my $i; my @x_values=(); my @y_values=(); 221 foreach $i (1..($xdiv-1) ) { 222 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 223 } 224 foreach $i (1..($ydiv-1) ) { 225 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 226 } 227 $graphRef->v_grid('gray',@x_values); 228 $graphRef->h_grid('gray',@y_values); 229 #$graphRef->lb(new Label($x_delta,0,sprintf("%1.1f",$x_delta),'black','center','top')); 230 #$graphRef->lb(new Label($x_delta,0,"|",'black','center','middle')); 231 #$graphRef->lb(new Label(0,$y_delta,sprintf("%1.1f ",$y_delta),'black','right','middle')); 232 #$graphRef->lb(new Label(0,$y_delta,"-",'black','center','middle')); 233 234 235 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 236 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 237 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top','right')); 238 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 239 240 } elsif ($options{ticks}) { # draw ticks -- grid over rides ticks 241 my $xdiv = ${$options{ticks}}[0]? ${$options{ticks}}[0] : 8; # number of ticks (8 is default) 242 my $ydiv = ${$options{ticks}}[1]? ${$options{ticks}}[1] : 8; 243 my $x_delta = ($graphRef->xmax - $graphRef->xmin)/$xdiv; 244 my $y_delta = ($graphRef->ymax - $graphRef->ymin)/$ydiv; 245 my $i; my @x_values=(); my @y_values=(); 246 foreach $i (1..($xdiv-1) ) { 247 push( @x_values, $i*$x_delta+$graphRef->{xmin}); 248 } 249 foreach $i (1..($ydiv-1) ) { 250 push( @y_values, $i*$y_delta+$graphRef->{ymin}); 251 } 252 $graphRef->v_ticks(0,'black',@x_values); 253 $graphRef->h_ticks(0,'black',@y_values); 254 $graphRef->lb(new Label($x_delta,0,$x_delta,'black','right')); 255 $graphRef->lb(new Label(0,$y_delta,$y_delta,'black','top')); 256 257 $graphRef->lb(new Label($xmax,0,$xmax,'black','right')); 258 $graphRef->lb(new Label($xmin,0,$xmin,'black','left')); 259 $graphRef->lb(new Label(0,$ymax,$ymax,'black','top')); 260 $graphRef->lb(new Label(0,$ymin,$ymin,'black','bottom','right')); 261 } 262 263 if ($options{axes}) { # draw axis 264 my $ra_axes = $options{axes}; 265 $graphRef->h_axis($ra_axes->[1],'black'); 266 $graphRef->v_axis($ra_axes->[0],'black'); 267 } 268 269 270 $graphRef; 271 } 272 273 274 275 =head2 plot_functions 276 277 =pod 278 279 Usage: ($f1, $f2, $f3) = plot_functions($graph, $f1, $f2, $f3); 280 Synonym: add_functions($graph,$f1,$f2,$f3); 281 282 Where $f1 is a string of the form 283 284 $f1 = qq! x^2 - 3*x + 45 for x in [0, 45) using color:red and weight:2! 285 286 The phrase translates as: formula B<for> variable B<in> interval B<using> option-list. 287 The option-list contains pairs of the form attribute:value. 288 The default for color is "default_color" which is usually black. 289 The default for the weight (pixel width) of the pen is 2 pixels. 290 291 The string_to_sub subroutine is used to translate the formula into a subroutine. 292 293 The functions in the list are installed in the graph object $graph and will appear when the graph object is next drawn. 294 295 =cut 296 297 sub add_functions { 298 &plot_functions; 299 } 300 301 sub plot_functions { 302 my $graph = shift; 303 my @function_list = @_; 304 my $error = ""; 305 $error .= "The first argument to plot_functions must be a graph object" unless ref($graph) =~/WWPlot/; 306 my $fn; 307 my @functions=(); 308 foreach $fn (@function_list) { 309 310 # model: "2.5-x^2 for x in <-1,0> using color:red and weight:2" 311 if ($fn =~ /^(.+)for\s*(\w+)\s*in\s*([\(\[\<])\s*([\d\.\-]+)\s*,\s*([\d\.\-]+)\s*([\)\]\>])\s*using\s*(.*)$/ ) { 312 my ($rule,$var, $left_br, $left_end, $right_end, $right_br, $options)= ($1, $2, $3, $4, $5, $6, $7); 313 314 my %options = split( /\s*and\s*|\s*:\s*|\s*,\s*|\s*=\s*|\s+/,$options); 315 my ($color, $weight); 316 if ( defined($options{'color'}) ){ 317 $color = $options{'color'}; #set pen color 318 } else { 319 $color = 'default_color'; 320 } 321 if ( defined($options{'weight'}) ) { 322 $weight = $options{'weight'}; # set pen weight (width in pixels) 323 } else { 324 $weight =2; 325 } 326 # a workaround to call Parser code without loading MathObjects. 327 my $localContext= Parser::Context->current(\%main::context)->copy; 328 $localContext->variables->add($var=>'Real') unless $localContext->variables->get($var); 329 my $formula = Value->Package("Formula()")->new($localContext,$rule)->perlFunction(undef,[$var]); 330 my $subRef = sub { 331 my $x = shift; 332 my $y = Parser::Eval($formula,$x); # traps errors, e.g. graph domain is larger than 333 # the function's domain. 334 $y = $y->value if defined $y; 335 return $y; 336 }; 337 #my $subRef = string_to_sub($rule,$var); 338 my $funRef = new Fun($subRef,$graph); 339 $funRef->color($color); 340 $funRef->weight($weight); 341 $funRef->domain($left_end , $right_end); 342 push(@functions,$funRef); 343 # place open (1,3) or closed (1,3) circle at the endpoints or do nothing <1,3> 344 if ($left_br eq '[' ) { 345 $graph->stamps(closed_circle($left_end,&$subRef($left_end),$color) ); 346 } elsif ($left_br eq '(' ) { 347 $graph->stamps(open_circle($left_end, &$subRef($left_end), $color) ); 348 } 349 if ($right_br eq ']' ) { 350 $graph->stamps(closed_circle($right_end,&$subRef($right_end),$color) ); 351 } elsif ($right_br eq ')' ) { 352 $graph->stamps(open_circle($right_end, &$subRef($right_end), $color) ); 353 } 354 355 } else { 356 $error .= "Error in parsing: $fn $main::BR"; 357 } 358 359 } 360 die ("Error in plot_functions: \n\t $error ") if $error; 361 @functions; # return function references unless there is an error. 362 } 363 364 365 366 367 =head2 insertGraph 368 369 $filePath = insertGraph(graphObject); 370 returns a path to the file containing the graph image. 371 372 B<Note:> Because insertGraph involves writing to the disk, it is actually defined in dangerousMacros.pl. 373 374 insertGraph(graphObject) writes a image file to the C<html/tmp/gif> directory of the current course. 375 The file name is obtained from the graphObject. Warnings are issued if errors occur while writing to 376 the file. 377 378 The permissions and ownership of the file are controlled by C<$main::tmp_file_permission> 379 and C<$main::numericalGroupID>. 380 381 B<Returns:> A string containing the full path to the temporary file containing the image. 382 383 384 385 InsertGraph draws the object $graph, stores it in "${tempDirectory}gif/$imageName.gif (or .png)" where 386 the $imageName is obtained from the graph object. ConvertPath and surePathToTmpFile are used to insure 387 that the correct directory separators are used for the platform and that the necessary directories 388 are created if they are not already present. The directory address to the file is the result. 389 390 The most common use of C,insertGraph> is 391 392 TEXT(image(insertGraph($graph)) ); 393 394 where C<image> takes care of creating the proper URL for accessing the graph and for creating the HTML code to display the image. 395 396 Another common usage is: 397 398 TEXT(htmlLink( alias(insertGraph($graph), "picture" ) ) ); 399 400 which inserts the URL pointing to the picture. 401 alias converts the directory address to a URL when serving HTML pages and insures that 402 an eps file is generated when creating TeX code for downloading. (Image, automatically applies alias to its input 403 in order to obtain the URL.) 404 405 See the documentation in F<dangerousMacros.pl> for the latest details. 406 407 =cut 408 409 =head2 'Circle' lables 410 411 Usage: $circle_object = open_circle( $x_position, $y_position, $color ); 412 $circle_object2 = closed_circle( $x_position, $y_position, $color ); 413 414 Creates a small open (resp. filled in or closed) circle for use as a stamp in marking graphs. 415 For example 416 417 $graph -> stamps($circle_object2); # puts a filled dot at $x_position, $y_position 418 419 =cut 420 421 ######################################################### 422 sub open_circle { 423 my ($cx,$cy,$color) = @_; 424 new Circle ($cx, $cy, 4,$color,'nearwhite'); 425 } 426 427 sub closed_circle { 428 my ($cx,$cy, $color) = @_; 429 $color = 'black' unless defined $color; 430 new Circle ($cx, $cy, 4,$color, $color); 431 } 432 433 434 =head2 Auxiliary macros 435 436 =head3 string_to_sub and my_math_constants 437 438 439 These are internal macros which govern the interpretation of equations. 440 441 442 Usage: $string = my_math_constants($string) 443 $subroutine_reference = my_string_to_sub($string) 444 445 C<my_math_constants> 446 interprets pi, e as mathematical constants 3.1415926... and 2.71828... respectively. (Case is important). 447 The power operator ^ is replaced by ** to conform with perl constructs 448 449 C<string_to_sub> 450 converts a string defining a single perl arithmetic expression with independent variable $XVAR into a subroutine. 451 The string is first filtered through C<my_math_macros>. The resulting subroutine 452 takes a single real number as input and produces a single output value. 453 454 =cut 455 456 sub my_math_constants { 457 my($in) = @_; 458 $in =~s/\bpi\b/(4*atan2(1,1))/g; 459 $in =~s/\be\b/(exp(1))/g; 460 $in =~s/\^/**/g; 461 $in; 462 } 463 464 sub string_to_sub { 465 my $str_in = shift; 466 my $var = shift; 467 my $out = undef; 468 if ( defined(&check_syntax) ) { 469 #prepare the correct answer and check it's syntax 470 my $rh_correct_ans = new AnswerHash; 471 $rh_correct_ans->input($str_in); 472 $rh_correct_ans = check_syntax($rh_correct_ans); 473 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 474 $rh_correct_ans->clear_error(); 475 $rh_correct_ans = function_from_string2($rh_correct_ans, ra_vars => ['x'], store_in =>'rf_correct_ans'); 476 my $correct_eqn_sub = $rh_correct_ans->{rf_correct_ans}; 477 warn $rh_correct_ans->{error_message} if $rh_correct_ans->{error_flag}; 478 $out = sub{ scalar( &$correct_eqn_sub(@_) ) }; #ignore the error messages from the function. 479 480 } else { 481 my $in =$str_in; 482 483 $in =~ s/\b$var\b/\$XVAR/g; 484 $in = &my_math_constants($in); 485 my ($subRef, $PG_eval_errors,$PG_full_error_report) = PG_restricted_eval( " sub { my \$XVAR = shift; my \$out = $in; \$out; } "); 486 if ($PG_eval_errors) { 487 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" 488 } else { 489 $out = $subRef; 490 } 491 492 } 493 $out; 494 } 495 496 ######################################################### 497 498 1;
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