NAME CAD::Calc - generic cad-related geometry calculations AUTHOR Eric L. Wilhelm ewilhelm at sbcglobal dot net http://pages.sbcglobal.net/mycroft COPYRIGHT This module is copyright (C) 2003 by Eric L. Wilhelm and A. Zahner Co. LICENSE This module is distributed under the same terms as Perl. See the Perl source package for details. You may use this software under one of the following licenses: (1) GNU General Public License (found at http://www.gnu.org/copyleft/gpl.html) (2) Artistic License (found at http://www.perl.com/pub/language/misc/Artistic.html) NO WARRANTY This software is distributed with ABSOLUTELY NO WARRANTY. The author and his employer will in no way be held liable for any loss or damages resulting from its use. Modifications The source code of this module is made freely available and distributable under the GPL or Artistic License. Modifications to and use of this software must adhere to one of these licenses. Changes to the code should be noted as such and this notification (as well as the above copyright information) must remain intact on all copies of the code. Additionally, while the author is actively developing this code, notification of any intended changes or extensions would be most helpful in avoiding repeated work for all parties involved. Please contact the author with any such development plans. CHANGES 0.20 Added sprintf("%0.9f") to seg_seg_intersection() 0.21 Several new functions and features. Configuration Used to set package global values such as precision. import Not called directly. Triggered by the use() function. import(%options, @EXPORT_TAGS); Example: use CAD::Calc ( -precision => 0.125, -angular => 1.0e-6, qw( seg_seg_intersection dist2d print_line ) ); Constants pi Returns the value of CAD::Calc::pi pi; Functions These are all exported as options. distdivide Returns a list of point references resulting from dividing $line into as many parts as possible which are at least $dist apart. @points = distdivide(\@line, $dist); subdivide Returns a list of point references resulting from subdividing $line into $count parts. The list will be $count-1 items long, (does not include $line->[0] and $line->[1]); $line is of the form: [ [x1, y1, z1], [x2, y2, z2] ] where z1 and z2 are optional. @points = subdivide($line, $count); shorten_line Shortens the line by the distances given in $lead and $tail. @line = shorten_line(\@line, $lead, $tail); dist Returns the direct distance from ptA to ptB. dist($ptA, $ptB); dist2d Purposefully ignores a z (2) coordinate. dist2d($ptA, $ptB); line_vec Returns a Math::Vec object representing the vector from $ptA to $ptB (which is actually a segment.) $vec = line_vec($ptA, $ptB); slope Calculates the 2D slope between points @ptA and @ptB. Slope is defined as dy / dx (rise over run.) If dx is 0, will return the string "inf", which Perl so kindly treats as you would expect it to (except it doesn't like to answer the question "what is infinity over infinity?") $slope = slope(\@ptA, \@ptB); segs_as_transform Allows two segments to specify transform data. Returns: (\@translate, $rotate, $scale), where: @translate is a 2D array [$x, $y] basically describing segment @A $rotate is the angular difference between $A[0]->$B[0] and $A[1]->$B[1] $scale is the length of $A[1]->$B[1] divided by the length of $A[0]->$B[0] my ($translate, $rotate, $scale) = segs_as_transform(\@A, \@B); chevron_to_ray Converts a chevron into a directional line by finding the midpoint between the midpoints of each edge and connecting to the middle point. @line = chevron_to_ray(@pts); signdist Returns the signed distance signdist(\@ptA, \@ptB); offset Creates a contour representing the offset of @polygon by $dist. Positive distances are inward when @polygon is ccw. @polygons = offset(\@polygon, $dist); intersection_data Calculates the two numerators and the denominator which are required for various (seg-seg, line-line, ray-ray, seg-ray, line-ray, line-seg) intersection calculations. ($k, $l, $d) = intersection_data(\@line, \@line); line_intersection Returns the intersection point of two lines. @pt = line_intersection(\@line, \@line, $tolerance); @pt or die "no intersection"; If tolerance is defined, it will be used to sprintf the parallel factor. Beware of this, it is clunky and might change if I come up with something better. seg_line_intersection Finds the intersection of @segment and @line. my @pt = seg_line_intersection(\@segment, \@line); @pt or die "no intersection"; unless(defined($pt[1])) { die "lines are parallel"; } seg_seg_intersection my @pt = seg_seg_intersection(\@segmenta, \@segmentb); seg_ray_intersection Intersects @seg with @ray, where $ray[1] is the direction of the infinite ray. seg_ray_intersection(\@seg, \@ray); ray_pgon_int_index Returns the first (lowest) index of @polygon which has a segment intersected by @ray. $index = ray_pgon_int_index(\@ray, \@polygon); ray_pgon_closest_index Returns the closest (according to dist2d) index of @polygon which has a segment intersected by @ray. $index = ray_pgon_closest_index(\@ray, \@polygon); perp_through_point @line = perp_through_point(\@pt, \@line); foot_on_segment Returns the perpendicular foot of @pt on @seg. See seg_ray_intersection. @pt = foot_on_segment(\@pt, \@seg); Determinant Determinant($x1, $y1, $x2, $y2); pgon_as_segs Returns a list of [[@ptA],[@ptB]] segments representing the edges of @pgon, where segment "0" is from $pgon[0] to $pgon[1] @segs = pgon_as_segs(@pgon); pgon_area $area = pgon_area(@polygon); pgon_angles Returns the angle of each edge of polygon in xy plane. These fall between -$pi and +$pi due to the fact that it is basically just a call to the atan2() builtin. Edges are numbered according to the index of the point which starts the edge. @angles = pgon_angles(@points); pgon_deltas Returns the differences between the angles of each edge of @polygon. These will be indexed according to the point at which they occur, and will be positive radians for ccw angles. Summing the @deltas will yield +/-2pi (negative for cw polygons.) @deltas = pgon_deltas(@pgon); ang_deltas Returns the same thing as pgon_deltas, but saves a redundant call to pgon_angles. my @angs = pgon_angles(@pts); my @dels = ang_deltas(@angs); pgon_direction Returns 1 for counterclockwise and 0 for clockwise. Uses the sum of the differences of angles of @polygon. If this sum is less than 0, the polygon is clockwise. $ang_sum = pgon_direction(@polygon); angs_direction Returns the same thing as pgon_direction, but saves a redundant call to pgon_deltas. my @angs = pgon_deltas(@pgon); my $dir = angs_direction(@angs); pgon_bisectors pgon_bisectors(); sort_pgons_lr Sorts polygons by their average points returning a list which reads from left to right. (Rather odd place for this?) @pgons = sort_pgons_lr(@pgons); shift_line Shifts line to right or left by $distance. @line = shift_line(\@line, $distance, right|left); line_to_rectangle Creates a rectangle, centered about @line. my @rec = line_to_rectangle(\@line, $offset, \%options); The direction of the returned points will be counter-clockwise around the original line, with the first point at the 'lower-left' (e.g. if your line points up, $rec[0] will be below and to the left of $line[0].) Available options ends => 1|0, # extend endpoints by $offset (default = 1) isleft Returns positive if @point is left of @line. isleft(\@line, \@point); iswithin Returns true if @pt is within the polygon @bound. $fact = iswithin(\@bound, \@pt); iswithinc Seems to be consistently much faster than the typical winding-number iswithin. iswithinc(); unitleft Returns a unit vector which is perpendicular and to the left of @line. Purposefully ignores any z-coordinates. $vec = unitleft(@line); unitright Negative of unitleft(). $vec = unitright(@line); unit_angle Returns a Math::Vec vector which has a length of one at angle $ang (in the XY plane.) $ang is fed through angle_parse(). $vec = unit_angle($ang); angle_reduce Reduces $ang (in radians) to be between -pi and +pi. $ang = angle_reduce($ang); angle_parse Parses the variable $ang and returns a variable in radians. To convert degrees to radians: $rad = angle_parse($deg . "d") $rad = angle_parse($ang); angle_quadrant Returns the index of the quadrant which contains $angle. $angle is in radians. $q = angle_quadrant($angle); @syms = qw(I II III IV); print "angle is in quadrant: $syms[$q]\n"; collinear $fact = collinear(\@pt1, \@pt2, \@pt3); triangle_angles Calculates the angles of a triangle based on it's lengths. @angles = triangle_angles(@lengths); The order of the returned angle will be "the angle before the edge". stringify Turns point into a string rounded according to $rnd. The optional $count allows you to specify how many coordinates to use. $string = stringify(\@pt, $rnd, $count); pol_to_cart Convert from polar to cartesian coordinates. my ($x, $y, $z) = pol_to_cart($radius, $theta, $z); cart_to_pol Convert from polar to cartesian coordinates. my ($radius, $theta, $z) = cart_to_pol($x, $y, $z); print_line print_line(\@line, $message); point_avg Averages the x and y coordinates of a list of points. my ($x, $y) = point_avg(@points);