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);