- NAME
- AUTHOR
- COPYRIGHT
- LICENSE
- NO WARRANTY
- Modifications
- Configuration
- Constants
- Functions
- distdivide
- subdivide
- shorten_line
- dist
- dist2d
- line_vec
- slope
- segs_as_transform
- chevron_to_ray
- signdist
- offset
- intersection_data
- line_intersection
- seg_line_intersection
- seg_seg_intersection
- line_ray_intersection
- seg_ray_intersection
- ray_pgon_int_index
- ray_pgon_closest_index
- perp_through_point
- foot_on_line
- foot_on_segment
- Determinant
- pgon_as_segs
- pgon_area
- pgon_centroid
- pgon_lengths
- pgon_angles
- pgon_deltas
- ang_deltas
- pgon_direction
- angs_direction
- pgon_bisectors
- sort_pgons_lr
- pgon_start_index
- pgon_start_indexb
- pgon_start_index_z
- re_order_pgon
- order_pgon
- shift_line
- line_to_rectangle
- isleft
- howleft
- iswithin
- iswithinc
- unitleft
- unitright
- unit_angle
- angle_reduce
- angle_parse
- angle_quadrant
- collinear
- triangle_angles
- stringify
- stringify_line
- pol_to_cart
- cart_to_pol
- print_line
- point_avg
- arc_2pt

# NAME

CAD::Calc - generic cad-related geometry calculations

# AUTHOR

Eric Wilhelm @ <ewilhelm at cpan dot org>

http://scratchcomputing.com

# COPYRIGHT

This module is copyright (C) 2004, 2005, 2006, 2008 Eric L. Wilhelm. Portions 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, his former employer, and any other contributors 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.

# 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?") 5.8.? users: sorry, there seems to be some regression here! (now we're using Math::BigFloat to return inf, so rounding has to go through that)

` $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);`

## line_ray_intersection

Intersects @line with @ray, where $ray[1] is the direction of the infinite ray.

` line_ray_intersection(\@line, \@ray);`

## 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_line

` @pt = foot_on_line(\@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

Returns the area of @polygon. Returns a negative number for clockwise polygons.

` $area = pgon_area(@polygon);`

## pgon_centroid

` @centroid = pgon_centroid(@polygon);`

## pgon_lengths

` @lengths = pgon_lengths(@pgon);`

## 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);`

## pgon_start_index

Returns the index of pgon which is at the "lowest left".

` $i = pgon_start_index(@pgon);`

## pgon_start_indexb

Returns the index of pgon which is at the "lowest left".

Different method (is it faster?)

` $i = pgon_start_indexb(@pgon);`

## pgon_start_index_z

Yet another different method (is this even correct?)

` pgon_start_index_z();`

## re_order_pgon

Imposes counter-clockwise from "lower-left" ordering.

` @pgon = re_order_pgon(@pgon);`

## order_pgon

Rewinds the polygon (e.g. list) to the specified $start index. This is not restricted to polygons (just continuous (looped) lists.)

` @pgon = order_pgon($start, \@pgon);`

## 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 true if @point is left of @line.

` $bool = isleft(\@line, \@point);`

## howleft

Returns positive if @point is left of @line.

` $number = howleft(\@line, \@point);`

## iswithin

Returns true if @pt is within the polygon @bound. This will be negative for clockwise input.

` $fact = iswithin(\@bound, \@pt);`

## iswithinc

Seems to be consistently much faster than the typical winding-number iswithin. The true return value is always positive regardless of the polygon's direction.

` $fact = iswithinc(\@bound, \@pt);`

## 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);`

## stringify_line

Turns a line (or polyline) into a string. See stringify().

` stringify_line(\@line, $char, $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);`

## arc_2pt

Given a pair of endpoints and an angle (in radians), returns an arc with center, radius, and start/end angles.

` my %arc = arc_2pt(\@pts, $angle);`