Perfect Shape 1.0.0 was released today, providing the Ruby community with an opensource library of Pure Ruby Geometric Algorithms that are mostly useful for GUI (Graphical User Interface) manipulation like checking viewport rectangle intersection or containment of a mouse click point in popular geometry shapes such as rectangle, square, arc (open, chord, and pie), ellipse, circle, polygon, and paths containing lines, quadratic bézier curves, and cubic bezier curves, potentially with affine transforms applied like translation, scale, rotation, shear/skew, and inversion (including both Ray Casting Algorithm, aka Evenodd Rule, and Winding Number Algorithm, aka Nonzero Rule).
The reason behind creating this library was that before, there were no comprehensive geometric algorithm libraries in Ruby that covered all the geometric shapes mentioned above. Most of them either lacked support for certain shapes like arc or lacked algorithms for checking point containment in every shape, including Cubic Bezier Curves. Thankfully, Perfect Shape addresses that issue completely for the Ruby community.
Another reason why this library was created was to address the need for supporting automated declarative drag and drop features in Glimmer DSL for LibUI coming soon (right now, it supports manually implementing drag and drop with area listeners out of the box).
Below is a summary of the Perfect Shape library directly from its README. Put it to good use!
Perfect Shape 1.0.0
Geometric Algorithms
PerfectShape
is a collection of pure Ruby geometric algorithms that are mostly useful for GUI (Graphical User Interface) manipulation like checking viewport rectangle intersection or containment of a mouse click point in popular geometry shapes such as rectangle, square, arc (open, chord, and pie), ellipse, circle, polygon, and paths containing lines, quadratic bézier curves, and cubic bezier curves, potentially with affine transforms applied like translation, scale, rotation, shear/skew, and inversion (including both Ray Casting Algorithm, aka Evenodd Rule, and Winding Number Algorithm, aka Nonzero Rule).
Additionally, PerfectShape::Math
contains some purely mathematical algorithms, like IEEE 7541985 Remainder.
To ensure high accuracy, this library does all its mathematical operations with BigDecimal
numbers.
Setup
Run:
gem install perfectshape v 1.0.0
Or include in Bundler Gemfile
:
gem 'perfectshape', '~> 1.0.0'
And, run:
bundle
API
PerfectShape::Math
Module

::degrees_to_radians(angle)
: converts degrees to radians 
::radians_to_degrees(angle)
: converts radians to degrees 
::normalize_degrees(angle)
: normalizes the specified angle into the range 180 to 180. 
::ieee_remainder(x, y)
(alias:ieee754_remainder
): IEEE 7541985 Remainder (different from standard%
modulo operator as it operates on floats and could return a negative result)
PerfectShape::Shape
Class
This is a base class for all shapes. It is not meant to be used directly. Subclasses implement/override its methods as needed.

#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width 
#height
: height 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height just as those of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside ifoutline
isfalse
or if point is on the outline ifoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a shape from its outline more successfully
PerfectShape::PointLocation
Module

#initialize(x: 0, y: 0)
: initializes a point location, usually representing the topleft point in a shape 
#x
: topleft x 
#y
: topleft y 
#min_x
: min x (x by default) 
#min_y
: min y (y by default)
PerfectShape::RectangularShape
Module
Includes PerfectShape::PointLocation

#initialize(x: 0, y: 0, width: 1, height: 1)
: initializes a rectangular shape 
#x
: topleft x 
#y
: topleft y 
#width
: width 
#height
: height 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y
PerfectShape::AffineTransform
Class
Affine transforms have the following matrix:
[ xxp xyp xt ]
[ yxp yyp yt ]
The matrix is used to transform (x,y) point coordinates as follows:
[ xxp xyp xt ] * [x] = [ xxp * x + xyp * y + xt ]
[ yxp yyp yt ] * [y] = [ yxp * x + yyp * y + yt ]
xxp
is the x coordinate x product (m11
)
xyp
is the x coordinate y product (m12
)
yxp
is the y coordinate x product (m21
)
yyp
is the y coordinate y product (m22
)
xt
is the x coordinate translation (m13
)
yt
is the y coordinate translation (m23
)
Affine transform mutation operations ending with !
can be chained as they all return self
.

::new(xxp_element = nil, xyp_element = nil, yxp_element = nil, yyp_element = nil, xt_element = nil, yt_element = nil, xxp: nil, xyp: nil, yxp: nil, yyp: nil, xt: nil, yt: nil, m11: nil, m12: nil, m21: nil, m22: nil, m13: nil, m23: nil)
: The constructor accepts either the (x,y)operation related argument/kwarg names or traditional matrix element kwarg names. If no arguments are supplied, it constructs an identity matrix (i.e. like calling::new(xxp: 1, xyp: 0, yxp: 0, yyp: 1, xt: 0, yt: 0)
). 
#matrix_3d
: Returns RubyMatrix
object representing affine transform in 3D (used internally for performing multiplication) 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#identity!
(alias:reset!
): Resets to identity matrix (i.e. like calling::new(xxp: 1, xyp: 0, yxp: 0, yyp: 1, xt: 0, yt: 0)
) 
#invertible?
Returnstrue
if matrix is invertible andfalse
otherwise 
#invert!
: Inverts affine transform matrix if invertible or raises an error otherwise 
#multiply!(other)
: Multiplies affine transform with another affine transform, storing resulting changes in matrix elements 
#translate!(x_or_point, y=nil)
: Translates affine transform with (x, y) translation values 
#scale!(x_or_point, y=nil)
: Scales affine transform with (x, y) scale values 
#rotate!(degrees)
: Rotates by angle degrees counterclockwise if angle value is positive or clockwise if angle value is negative. Note that it returns very close approximate results for rotations that are 90/180/270 degrees (good enough for inversetransform GUI point containment checks needed when checking if mouseclickpoint is inside a transformed shape). 
#shear!(x_or_point, y=nil)
: Shears by x and y factors 
#clone
: Returns a new AffineTransform with the same matrix elements 
#transform_point(x_or_point, y=nil)
: returns[xxp * x + xyp * y + xt, yxp * x + yyp * y + yt]
. Note that result is a close approximation, but should be good enough for GUI mouseclickpoint containment checks. 
#transform_points(*xy_coordinates_or_points)
: returnsArray
of (x,y) pairArray
s transformed with#transform_point
method 
#inverse_transform_point(x_or_point, y=nil)
: returns inverse transform of a point (x,y) coordinates (clones self and inverts clone, and then transforms point). Note that result is a close approximation, but should be good enough for GUI mouseclickpoint containment checks. 
#inverse_transform_points(*xy_coordinates_or_points)
: returns inverse transforms of a pointArray
of (x,y) coordinates
Example:
xxp = 2
xyp = 3
yxp = 4
yyp = 5
xt = 6
yt = 7
affine_transform1 = PerfectShape::AffineTransform.new(xxp: xxp, xyp: xyp, yxp: yxp, yyp: yyp, xt: xt, yt: yt) # (x,y)operation kwarg names
affine_transform2 = PerfectShape::AffineTransform.new(m11: xxp, m12: xyp, m21: yxp, m22: yyp, m13: xt, m23: yt) # traditional matrix element kwarg names
affine_transform3 = PerfectShape::AffineTransform.new(xxp, xyp, yxp, yyp, xt, yt) # standard arguments
affine_transform2.matrix_3d == affine_transform1.matrix_3d # => true
affine_transform3.matrix_3d == affine_transform1.matrix_3d # => true
affine_transform = PerfectShape::AffineTransform.new.translate!(30, 20).scale!(2, 3)
affine_transform.transform_point(10, 10) # => approximately [50, 50]
affine_transform.inverse_transform_point(50, 50) # => approximately [10, 10]
PerfectShape::Point
Class
Extends PerfectShape::Shape
Includes PerfectShape::PointLocation
Points are simply represented by an Array
of [x,y]
coordinates when used within other shapes, but when needing pointspecific operations like point_distance
, the PerfectShape::Point
class can come in handy.

::point_distance(x, y, px, py)
: Returns the distance from a point to another point 
::normalize_point(x_or_point, y = nil)
: Normalizes point args whether twonumberpoint
Array
orx
,y
args, returning normalized pointArray
of twoBigDecimal
's 
::new(x_or_point=nil, y_arg=nil, x: nil, y: nil)
: constructs a point with (x,y) pair (default: 0,0) whether specified asArray
of (x,y) pair, flatx,y
args, orx:, y:
kwargs. 
#min_x
: min x (always x) 
#min_y
: min y (always y) 
#max_x
: max x (always x) 
#max_y
: max y (always y) 
#width
: width (always 0) 
#height
: height (always 0) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x (always x) 
#center_y
: center y (always y) 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: true, distance_tolerance: 0)
: checks if point matches self, with a distance tolerance (0 by default). Distance tolerance provides a fuzz factor that for example enables GUI users to mouseclickselect a point shape more successfully.outline
option makes no difference on point 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#point_distance(x_or_point, y=nil)
: Returns the distance from a point to another point
Example:
require 'perfectshape'
shape = PerfectShape::Point.new(x: 200, y: 150)
shape.contain?(200, 150) # => true
shape.contain?([200, 150]) # => true
shape.contain?(200, 151) # => false
shape.contain?([200, 151]) # => false
shape.contain?(200, 151, distance_tolerance: 5) # => true
shape.contain?([200, 151], distance_tolerance: 5) # => true
PerfectShape::Line
Class
Extends PerfectShape::Shape
Includes PerfectShape::MultiPoint

::relative_counterclockwise(x1, y1, x2, y2, px, py)
: Returns an indicator of where the specified point (px,py) lies with respect to the line segment from (x1,y1) to (x2,y2). The return value can be either 1, 1, or 0 and indicates in which direction the specified line must pivot around its first end point, (x1,y1), in order to point at the specified point (px,py). A return value of 1 indicates that the line segment must turn in the direction that takes the positive X axis towards the negative Y axis. In the default coordinate system, this direction is counterclockwise. A return value of 1 indicates that the line segment must turn in the direction that takes the positive X axis towards the positive Y axis. In the default coordinate system, this direction is clockwise. A return value of 0 indicates that the point lies exactly on the line segment. Note that an indicator value of 0 is rare and not useful for determining collinearity because of floating point rounding issues. If the point is colinear with the line segment, but not between the end points, then the value will be 1 if the point lies “beyond (x1,y1)” or 1 if the point lies “beyond (x2,y2)”. 
::point_distance_square(x1, y1, x2, y2, px, py)
: Returns the square of distance from a point to a line segment. 
::point_distance(x1, y1, x2, y2, px, py)
: Returns the distance from a point to a line segment. 
::new(points: [])
: constructs a line with twopoints
asArray
ofArray
s of[x,y]
pairs or flattenedArray
of alternating x and y coordinates 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width (from min x to max x) 
#height
: height (from min y to max y) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: true, distance_tolerance: 0)
: checks if point lies on line, with a distance tolerance (0 by default). Distance tolerance provides a fuzz factor that for example enables GUI users to mouseclickselect a line shape more successfully.outline
option makes no difference on line 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#relative_counterclockwise(x_or_point, y=nil)
: Returns an indicator of where the specified point (px,py) lies with respect to the line segment from (x1,y1) to (x2,y2). The return value can be either 1, 1, or 0 and indicates in which direction the specified line must pivot around its first end point, (x1,y1), in order to point at the specified point (px,py). A return value of 1 indicates that the line segment must turn in the direction that takes the positive X axis towards the negative Y axis. In the default coordinate system, this direction is counterclockwise. A return value of 1 indicates that the line segment must turn in the direction that takes the positive X axis towards the positive Y axis. In the default coordinate system, this direction is clockwise. A return value of 0 indicates that the point lies exactly on the line segment. Note that an indicator value of 0 is rare and not useful for determining collinearity because of floating point rounding issues. If the point is colinear with the line segment, but not between the end points, then the value will be 1 if the point lies “beyond (x1,y1)” or 1 if the point lies “beyond (x2,y2)”. 
#point_distance(x_or_point, y=nil)
: Returns the distance from a point to a line segment. 
#rect_crossings(rxmin, rymin, rxmax, rymax, crossings = 0)
: rectangle crossings (adds to crossings arg)
Example:
require 'perfectshape'
shape = PerfectShape::Line.new(points: [[0, 0], [100, 100]]) # start point and end point
shape.contain?(50, 50) # => true
shape.contain?([50, 50]) # => true
shape.contain?(50, 51) # => false
shape.contain?([50, 51]) # => false
shape.contain?(50, 51, distance_tolerance: 5) # => true
shape.contain?([50, 51], distance_tolerance: 5) # => true
PerfectShape::QuadraticBezierCurve
Class
Extends PerfectShape::Shape
Includes PerfectShape::MultiPoint

::tag(coord, low, high)
: Determine where coord lies with respect to the range from low to high. It is assumed that low < high. The return value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE, or ABOVE. 
::eqn(val, c1, cp, c2)
: Fill an array with the coefficients of the parametric equation in t, ready for solving against val with solve_quadratic. We currently have: val = Py(t) = C1*(1t)^2 + 2*CP*t*(1t) + C2*t^2 = C1  2*C1*t + C1*t^2 + 2*CP*t  2*CP*t^2 + C2*t^2 = C1 + (2*CP  2*C1)*t + (C1  2*CP + C2)*t^2; 0 = (C1  val) + (2*CP  2*C1)*t + (C1  2*CP + C2)*t^2; 0 = C + Bt + At^2; C = C1  val; B = 2*CP  2*C1; A = C1  2*CP + C2 
::solve_quadratic(eqn)
: Solves the quadratic whose coefficients are in the eqn array and places the noncomplex roots into the res array, returning the number of roots. The quadratic solved is represented by the equation:eqn = {C, B, A}; ax^2 + bx + c = 0
A return value of1
is used to distinguish a constant equation, which might be always 0 or never 0, from an equation that has no zeroes. 
::eval_quadratic(vals, num, include0, include1, inflect, c1, ctrl, c2)
: Evaluate the t values in the first num slots of the vals[] array and place the evaluated values back into the same array. Only evaluate t values that are within the range <, >, including the 0 and 1 ends of the range iff the include0 or include1 booleans are true. If an "inflection" equation is handed in, then any points which represent a point of inflection for that quadratic equation are also ignored. 
::new(points: [])
: constructs a quadratic bézier curve with threepoints
(start point, control point, and end point) asArray
ofArray
s of[x,y]
pairs or flattenedArray
of alternating x and y coordinates 
#points
: points (start point, control point, and end point) 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width (from min x to max x) 
#height
: height (from min y to max y) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape (bounding box only guarantees that the shape is within it, but it might be bigger than the shape) 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a quadratic bezier curve shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#curve_center_point
: point at the center of the curve outline (not the center of the bounding box area likecenter_x
andcenter_y
) 
#curve_center_x
: point x coordinate at the center of the curve outline (not the center of the bounding box area likecenter_x
andcenter_y
) 
#curve_center_y
: point y coordinate at the center of the curve outline (not the center of the bounding box area likecenter_x
andcenter_y
) 
#subdivisions(level=1)
: subdivides quadratic bezier curve at its center into into 2 quadratic bezier curves by default, or more iflevel
of recursion is specified. The resulting number of subdivisions is2
to the power oflevel
. 
#point_distance(x_or_point, y=nil, minimum_distance_threshold: OUTLINE_MINIMUM_DISTANCE_THRESHOLD)
: calculates distance from point to curve segment. It does so by subdividing curve into smaller curves and checking against the curve center points until the distance is less thanminimum_distance_threshold
, to avoid being an overly costly operation. 
#rect_crossings(rxmin, rymin, rxmax, rymax, level, crossings = 0)
: rectangle crossings (adds to crossings arg)
Example:
require 'perfectshape'
shape = PerfectShape::QuadraticBezierCurve.new(points: [[200, 150], [270, 320], [380, 150]]) # start point, control point, and end point
shape.contain?(270, 220) # => true
shape.contain?([270, 220]) # => true
shape.contain?(270, 220, outline: true) # => false
shape.contain?([270, 220], outline: true) # => false
shape.contain?(280, 235, outline: true) # => true
shape.contain?([280, 235], outline: true) # => true
shape.contain?(281, 235, outline: true) # => false
shape.contain?([281, 235], outline: true) # => false
shape.contain?(281, 235, outline: true, distance_tolerance: 1) # => true
shape.contain?([281, 235], outline: true, distance_tolerance: 1) # => true
PerfectShape::CubicBezierCurve
Class
Extends PerfectShape::Shape
Includes PerfectShape::MultiPoint

::new(points: [])
: constructs a cubic bézier curve with fourpoints
(start point, two control points, and end point) asArray
ofArray
s of[x,y]
pairs or flattenedArray
of alternating x and y coordinates 
#points
: points (start point, two control points, and end point) 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width (from min x to max x) 
#height
: height (from min y to max y) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape (bounding box only guarantees that the shape is within it, but it might be bigger than the shape) 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a cubic bezier curve shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#curve_center_point
: point at the center of the curve outline (not the center of the bounding box area likecenter_x
andcenter_y
) 
#curve_center_x
: point x coordinate at the center of the curve outline (not the center of the bounding box area likecenter_x
andcenter_y
) 
#curve_center_y
: point y coordinate at the center of the curve outline (not the center of the bounding box area likecenter_x
andcenter_y
) 
#subdivisions(level=1)
: subdivides cubic bezier curve at its center into into 2 cubic bezier curves by default, or more iflevel
of recursion is specified. The resulting number of subdivisions is2
to the power oflevel
. 
#point_distance(x_or_point, y=nil, minimum_distance_threshold: OUTLINE_MINIMUM_DISTANCE_THRESHOLD)
: calculates distance from point to curve segment. It does so by subdividing curve into smaller curves and checking against the curve center points until the distance is less thanminimum_distance_threshold
, to avoid being an overly costly operation. 
#rectangle_crossings(rectangle)
: rectangle crossings (used to determine rectangle interior intersection), optimized to check if line represented by cubic bezier curve crosses the rectangle first, and if not then perform expensive check with#rect_crossings

#rect_crossings(rxmin, rymin, rxmax, rymax, level, crossings = 0)
: rectangle crossings (adds to crossings arg)
Example:
require 'perfectshape'
shape = PerfectShape::CubicBezierCurve.new(points: [[200, 150], [235, 235], [270, 320], [380, 150]]) # start point, two control points, and end point
shape.contain?(270, 220) # => true
shape.contain?([270, 220]) # => true
shape.contain?(270, 220, outline: true) # => false
shape.contain?([270, 220], outline: true) # => false
shape.contain?(261.875, 245.625, outline: true) # => true
shape.contain?([261.875, 245.625], outline: true) # => true
shape.contain?(261.875, 246.625, outline: true) # => false
shape.contain?([261.875, 246.625], outline: true) # => false
shape.contain?(261.875, 246.625, outline: true, distance_tolerance: 1) # => true
shape.contain?([261.875, 246.625], outline: true, distance_tolerance: 1) # => true
PerfectShape::Rectangle
Class
Extends PerfectShape::Shape
Includes PerfectShape::RectangularShape

::new(x: 0, y: 0, width: 1, height: 1)
: constructs a rectangle 
#x
: topleft x 
#y
: topleft y 
#width
: width 
#height
: height 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a rectangle shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#edges
: edges of rectangle asPerfectShape::Line
objects 
#out_state(x_or_point, y = nil)
: Returns "out state" of specified point (x,y) (whether it lies to the left, right, top, bottom of rectangle). If point is outside rectangle, it returns a bit mask combination ofRectangle::OUT_LEFT
,Rectangle::OUT_RIGHT
,Rectangle::OUT_TOP
, orRectangle::OUT_BOTTOM
. Otherwise, it returns0
if point is inside the rectangle. 
#empty?
: Returnstrue
if width or height are 0 (or negative) andfalse
otherwise
Example:
require 'perfectshape'
shape = PerfectShape::Rectangle.new(x: 15, y: 30, width: 200, height: 100)
shape.contain?(115, 80) # => true
shape.contain?([115, 80]) # => true
shape.contain?(115, 80, outline: true) # => false
shape.contain?([115, 80], outline: true) # => false
shape.contain?(115, 30, outline: true) # => true
shape.contain?([115, 30], outline: true) # => true
shape.contain?(115, 31, outline: true) # => false
shape.contain?([115, 31], outline: true) # => false
shape.contain?(115, 31, outline: true, distance_tolerance: 1) # => true
shape.contain?([115, 31], outline: true, distance_tolerance: 1) # => true
PerfectShape::Square
Class
Extends PerfectShape::Rectangle

::new(x: 0, y: 0, length: 1)
(length
alias:size
): constructs a square 
#x
: topleft x 
#y
: topleft y 
#length
: length 
#width
: width (equal to length) 
#height
: height (equal to length) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a square shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#edges
: edges of square asPerfectShape::Line
objects 
#empty?
: Returnstrue
if length is 0 (or negative) andfalse
otherwise
Example:
require 'perfectshape'
shape = PerfectShape::Square.new(x: 15, y: 30, length: 200)
shape.contain?(115, 130) # => true
shape.contain?([115, 130]) # => true
shape.contain?(115, 130, outline: true) # => false
shape.contain?([115, 130], outline: true) # => false
shape.contain?(115, 30, outline: true) # => true
shape.contain?([115, 30], outline: true) # => true
shape.contain?(115, 31, outline: true) # => false
shape.contain?([115, 31], outline: true) # => false
shape.contain?(115, 31, outline: true, distance_tolerance: 1) # => true
shape.contain?([115, 31], outline: true, distance_tolerance: 1) # => true
PerfectShape::Arc
Class
Extends PerfectShape::Shape
Includes PerfectShape::RectangularShape
Arcs can be of type :open
, :chord
, or :pie
Open Arc  Chord Arc  Pie Arc 


::new(type: :open, x: 0, y: 0, width: 1, height: 1, start: 0, extent: 360, center_x: nil, center_y: nil, radius_x: nil, radius_y: nil)
: constructs an arc of type:open
(default),:chord
, or:pie

#type
::open
,:chord
, or:pie

#x
: topleft x 
#y
: topleft y 
#width
: width 
#height
: height 
#start
: start angle in degrees 
#extent
: extent angle in degrees 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#radius_x
: radius along the xaxis 
#radius_y
: radius along the yaxis 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect an arc shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#contain_angle?(angle)
: returnstrue
if the angle is within the angular extents of the arc andfalse
otherwise
Example:
require 'perfectshape'
shape = PerfectShape::Arc.new(type: :open, x: 2, y: 3, width: 50, height: 60, start: 45, extent: 270)
shape2 = PerfectShape::Arc.new(type: :open, center_x: 2 + 25, center_y: 3 + 30, radius_x: 25, radius_y: 30, start: 45, extent: 270)
shape.contain?(39.5, 33.0) # => true
shape.contain?([39.5, 33.0]) # => true
shape2.contain?(39.5, 33.0) # => true
shape2.contain?([39.5, 33.0]) # => true
shape.contain?(39.5, 33.0, outline: true) # => false
shape.contain?([39.5, 33.0], outline: true) # => false
shape2.contain?(39.5, 33.0, outline: true) # => false
shape2.contain?([39.5, 33.0], outline: true) # => false
shape.contain?(2.0, 33.0, outline: true) # => true
shape.contain?([2.0, 33.0], outline: true) # => true
shape2.contain?(2.0, 33.0, outline: true) # => true
shape2.contain?([2.0, 33.0], outline: true) # => true
shape.contain?(3.0, 33.0, outline: true) # => false
shape.contain?([3.0, 33.0], outline: true) # => false
shape2.contain?(3.0, 33.0, outline: true) # => false
shape2.contain?([3.0, 33.0], outline: true) # => false
shape.contain?(3.0, 33.0, outline: true, distance_tolerance: 1.0) # => true
shape.contain?([3.0, 33.0], outline: true, distance_tolerance: 1.0) # => true
shape2.contain?(3.0, 33.0, outline: true, distance_tolerance: 1.0) # => true
shape2.contain?([3.0, 33.0], outline: true, distance_tolerance: 1.0) # => true
shape.contain?(shape.center_x, shape.center_y, outline: true) # => false
shape.contain?([shape.center_x, shape.center_y], outline: true) # => false
shape2.contain?(shape2.center_x, shape2.center_y, outline: true) # => false
shape2.contain?([shape2.center_x, shape2.center_y], outline: true) # => false
shape3 = PerfectShape::Arc.new(type: :chord, x: 2, y: 3, width: 50, height: 60, start: 45, extent: 270)
shape4 = PerfectShape::Arc.new(type: :chord, center_x: 2 + 25, center_y: 3 + 30, radius_x: 25, radius_y: 30, start: 45, extent: 270)
shape3.contain?(39.5, 33.0) # => true
shape3.contain?([39.5, 33.0]) # => true
shape4.contain?(39.5, 33.0) # => true
shape4.contain?([39.5, 33.0]) # => true
shape3.contain?(39.5, 33.0, outline: true) # => false
shape3.contain?([39.5, 33.0], outline: true) # => false
shape4.contain?(39.5, 33.0, outline: true) # => false
shape4.contain?([39.5, 33.0], outline: true) # => false
shape3.contain?(2.0, 33.0, outline: true) # => true
shape3.contain?([2.0, 33.0], outline: true) # => true
shape4.contain?(2.0, 33.0, outline: true) # => true
shape4.contain?([2.0, 33.0], outline: true) # => true
shape3.contain?(3.0, 33.0, outline: true) # => false
shape3.contain?([3.0, 33.0], outline: true) # => false
shape4.contain?(3.0, 33.0, outline: true) # => false
shape4.contain?([3.0, 33.0], outline: true) # => false
shape3.contain?(3.0, 33.0, outline: true, distance_tolerance: 1.0) # => true
shape3.contain?([3.0, 33.0], outline: true, distance_tolerance: 1.0) # => true
shape4.contain?(3.0, 33.0, outline: true, distance_tolerance: 1.0) # => true
shape4.contain?([3.0, 33.0], outline: true, distance_tolerance: 1.0) # => true
shape3.contain?(shape3.center_x, shape3.center_y, outline: true) # => false
shape3.contain?([shape3.center_x, shape3.center_y], outline: true) # => false
shape4.contain?(shape4.center_x, shape4.center_y, outline: true) # => false
shape4.contain?([shape4.center_x, shape4.center_y], outline: true) # => false
shape5 = PerfectShape::Arc.new(type: :pie, x: 2, y: 3, width: 50, height: 60, start: 45, extent: 270)
shape6 = PerfectShape::Arc.new(type: :pie, center_x: 2 + 25, center_y: 3 + 30, radius_x: 25, radius_y: 30, start: 45, extent: 270)
shape5.contain?(39.5, 33.0) # => false
shape5.contain?([39.5, 33.0]) # => false
shape6.contain?(39.5, 33.0) # => false
shape6.contain?([39.5, 33.0]) # => false
shape5.contain?(9.5, 33.0) # => true
shape5.contain?([9.5, 33.0]) # => true
shape6.contain?(9.5, 33.0) # => true
shape6.contain?([9.5, 33.0]) # => true
shape5.contain?(39.5, 33.0, outline: true) # => false
shape5.contain?([39.5, 33.0], outline: true) # => false
shape6.contain?(39.5, 33.0, outline: true) # => false
shape6.contain?([39.5, 33.0], outline: true) # => false
shape5.contain?(2.0, 33.0, outline: true) # => true
shape5.contain?([2.0, 33.0], outline: true) # => true
shape6.contain?(2.0, 33.0, outline: true) # => true
shape6.contain?([2.0, 33.0], outline: true) # => true
shape5.contain?(3.0, 33.0, outline: true) # => false
shape5.contain?([3.0, 33.0], outline: true) # => false
shape6.contain?(3.0, 33.0, outline: true) # => false
shape6.contain?([3.0, 33.0], outline: true) # => false
shape5.contain?(3.0, 33.0, outline: true, distance_tolerance: 1.0) # => true
shape5.contain?([3.0, 33.0], outline: true, distance_tolerance: 1.0) # => true
shape6.contain?(3.0, 33.0, outline: true, distance_tolerance: 1.0) # => true
shape6.contain?([3.0, 33.0], outline: true, distance_tolerance: 1.0) # => true
shape5.contain?(shape5.center_x, shape5.center_y, outline: true) # => true
shape5.contain?([shape5.center_x, shape5.center_y], outline: true) # => true
shape6.contain?(shape6.center_x, shape6.center_y, outline: true) # => true
shape6.contain?([shape6.center_x, shape6.center_y], outline: true) # => true
PerfectShape::Ellipse
Class
Extends PerfectShape::Arc

::new(x: 0, y: 0, width: 1, height: 1, center_x: nil, center_y: nil, radius_x: nil, radius_y: nil)
: constructs an ellipse 
#x
: topleft x 
#y
: topleft y 
#width
: width 
#height
: height 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#radius_x
: radius along the xaxis 
#radius_y
: radius along the yaxis 
#type
: always:open

#start
: always0

#extent
: always360

#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect an ellipse shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing
Example:
require 'perfectshape'
shape = PerfectShape::Ellipse.new(x: 2, y: 3, width: 50, height: 60)
shape2 = PerfectShape::Ellipse.new(center_x: 27, center_y: 33, radius_x: 25, radius_y: 30)
shape.contain?(27, 33) # => true
shape.contain?([27, 33]) # => true
shape2.contain?(27, 33) # => true
shape2.contain?([27, 33]) # => true
shape.contain?(27, 33, outline: true) # => false
shape.contain?([27, 33], outline: true) # => false
shape2.contain?(27, 33, outline: true) # => false
shape2.contain?([27, 33], outline: true) # => false
shape.contain?(2, 33, outline: true) # => true
shape.contain?([2, 33], outline: true) # => true
shape2.contain?(2, 33, outline: true) # => true
shape2.contain?([2, 33], outline: true) # => true
shape.contain?(1, 33, outline: true) # => false
shape.contain?([1, 33], outline: true) # => false
shape2.contain?(1, 33, outline: true) # => false
shape2.contain?([1, 33], outline: true) # => false
shape.contain?(1, 33, outline: true, distance_tolerance: 1) # => true
shape.contain?([1, 33], outline: true, distance_tolerance: 1) # => true
shape2.contain?(1, 33, outline: true, distance_tolerance: 1) # => true
shape2.contain?([1, 33], outline: true, distance_tolerance: 1) # => true
PerfectShape::Circle
Class
Extends PerfectShape::Ellipse

::new(x: 0, y: 0, diameter: 1, width: 1, height: 1, center_x: nil, center_y: nil, radius: nil, radius_x: nil, radius_y: nil)
: constructs a circle 
#x
: topleft x 
#y
: topleft y 
#diameter
: diameter 
#width
: width (equal to diameter) 
#height
: height (equal to diameter) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#radius
: radius 
#radius_x
: radius along the xaxis (equal to radius) 
#radius_y
: radius along the yaxis (equal to radius) 
#type
: always:open

#start
: always0

#extent
: always360

#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: checks if point is inside whenoutline
isfalse
or if point is on the outline whenoutline
istrue
.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a circle shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing
Example:
require 'perfectshape'
shape = PerfectShape::Circle.new(x: 2, y: 3, diameter: 60)
shape2 = PerfectShape::Circle.new(center_x: 2 + 30, center_y: 3 + 30, radius: 30)
shape.contain?(32, 33) # => true
shape.contain?([32, 33]) # => true
shape2.contain?(32, 33) # => true
shape2.contain?([32, 33]) # => true
shape.contain?(32, 33, outline: true) # => false
shape.contain?([32, 33], outline: true) # => false
shape2.contain?(32, 33, outline: true) # => false
shape2.contain?([32, 33], outline: true) # => false
shape.contain?(2, 33, outline: true) # => true
shape.contain?([2, 33], outline: true) # => true
shape2.contain?(2, 33, outline: true) # => true
shape2.contain?([2, 33], outline: true) # => true
shape.contain?(1, 33, outline: true) # => false
shape.contain?([1, 33], outline: true) # => false
shape2.contain?(1, 33, outline: true) # => false
shape2.contain?([1, 33], outline: true) # => false
shape.contain?(1, 33, outline: true, distance_tolerance: 1) # => true
shape.contain?([1, 33], outline: true, distance_tolerance: 1) # => true
shape2.contain?(1, 33, outline: true, distance_tolerance: 1) # => true
shape2.contain?([1, 33], outline: true, distance_tolerance: 1) # => true
PerfectShape::Polygon
Class
Extends PerfectShape::Shape
Includes PerfectShape::MultiPoint
A polygon can be thought of as a special case of path, consisting of lines only, is closed, and has the EvenOdd winding rule by default.

::new(points: [], winding_rule: :wind_even_odd)
: constructs a polygon withpoints
asArray
ofArray
s of[x,y]
pairs or flattenedArray
of alternating x and y coordinates and specified winding rule (:wind_even_odd
or:wind_non_zero
) 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width (from min x to max x) 
#height
: height (from min y to max y) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: Whenoutline
isfalse
, it checks if point is inside using either the Ray Casting Algorithm (aka EvenOdd Rule) or Winding Number Algorithm (aka NonzeroRule). Otherwise, whenoutline
istrue
, it checks if point is on the outline.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a polygon shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#edges
: edges of polygon asPerfectShape::Line
objects
Example:
require 'perfectshape'
shape = PerfectShape::Polygon.new(points: [[200, 150], [270, 170], [250, 220], [220, 190], [200, 200], [180, 170]])
shape.contain?(225, 185) # => true
shape.contain?([225, 185]) # => true
shape.contain?(225, 185, outline: true) # => false
shape.contain?([225, 185], outline: true) # => false
shape.contain?(200, 150, outline: true) # => true
shape.contain?([200, 150], outline: true) # => true
shape.contain?(200, 151, outline: true) # => false
shape.contain?([200, 151], outline: true) # => false
shape.contain?(200, 151, outline: true, distance_tolerance: 1) # => true
shape.contain?([200, 151], outline: true, distance_tolerance: 1) # => true
PerfectShape::Path
Class
Extends PerfectShape::Shape
Includes PerfectShape::MultiPoint

::new(shapes: [], closed: false, winding_rule: :wind_non_zero)
: constructs a path withshapes
asArray
of shape objects, which can bePerfectShape::Point
(orArray
of[x, y]
coordinates),PerfectShape::Line
,PerfectShape::QuadraticBezierCurve
, orPerfectShape::CubicBezierCurve
. If a path is closed, its last point is automatically connected to its first point with a line segment. The winding rule can be:wind_non_zero
(default) or:wind_even_odd
. 
#shapes
: the shapes that the path is composed of (must always start withPerfectShape::Point
or Array of [x,y] coordinates representing start point) 
#closed?
: returnstrue
if closed andfalse
otherwise 
#winding_rule
: returns winding rule (:wind_non_zero
or:wind_even_odd
) 
#points
: path points calculated (derived) from shapes 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width (from min x to max x) 
#height
: height (from min y to max y) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape (bounding box only guarantees that the shape is within it, but it might be bigger than the shape) 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: Whenoutline
isfalse
, it checks if point is inside path utilizing the configured winding rule, which can be the NonzeroRule (aka Winding Number Algorithm) or the EvenOdd Rule (aka Ray Casting Algorithm). Otherwise, whenoutline
istrue
, it checks if point is on the outline.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a path shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing 
#point_crossings(x_or_point, y=nil)
: calculates the number of times the given path crosses the ray extending to the right from (x,y) 
#disconnected_shapes
: Disconnected shapes have their start point filled in so that each shape does not depend on the previous shape to determine its start point. Also, if a point is followed by a nonpoint shape, it is removed since it is augmented to the following shape as its start point. Lastly, if the path is closed, an extra shape is added to represent the line connecting the last point to the first
Example:
require 'perfectshape'
path_shapes = []
path_shapes << PerfectShape::Point.new(x: 200, y: 150)
path_shapes << PerfectShape::Line.new(points: [250, 170]) # no need for start point, just end point
path_shapes << PerfectShape::QuadraticBezierCurve.new(points: [[300, 185], [350, 150]]) # no need for start point, just control point and end point
path_shapes << PerfectShape::CubicBezierCurve.new(points: [[370, 50], [430, 220], [480, 170]]) # no need for start point, just two control points and end point
shape = PerfectShape::Path.new(shapes: path_shapes, closed: false, winding_rule: :wind_even_odd)
shape.contain?(275, 165) # => true
shape.contain?([275, 165]) # => true
shape.contain?(275, 165, outline: true) # => false
shape.contain?([275, 165], outline: true) # => false
shape.contain?(shape.disconnected_shapes[1].curve_center_x, shape.disconnected_shapes[1].curve_center_y, outline: true) # => true
shape.contain?([shape.disconnected_shapes[1].curve_center_x, shape.disconnected_shapes[1].curve_center_y], outline: true) # => true
shape.contain?(shape.disconnected_shapes[1].curve_center_x + 1, shape.disconnected_shapes[1].curve_center_y, outline: true) # => false
shape.contain?([shape.disconnected_shapes[1].curve_center_x + 1, shape.disconnected_shapes[1].curve_center_y], outline: true) # => false
shape.contain?(shape.disconnected_shapes[1].curve_center_x + 1, shape.disconnected_shapes[1].curve_center_y, outline: true, distance_tolerance: 1) # => true
shape.contain?([shape.disconnected_shapes[1].curve_center_x + 1, shape.disconnected_shapes[1].curve_center_y], outline: true, distance_tolerance: 1) # => true
PerfectShape::CompositeShape
Class
Extends PerfectShape::Shape
A composite shape is simply an aggregate of multiple shapes (e.g. square and polygon)

::new(shapes: [])
: constructs a composite shape withshapes
asArray
ofPerfectShape::Shape
objects 
#shapes
: the shapes that the composite shape is composed of 
#min_x
: min x 
#min_y
: min y 
#max_x
: max x 
#max_y
: max y 
#width
: width (from min x to max x) 
#height
: height (from min y to max y) 
#center_point
: center point asArray
of[center_x, center_y]
coordinates 
#center_x
: center x 
#center_y
: center y 
#bounding_box
: bounding box is a rectangle with x = min x, y = min y, and width/height of shape (bounding box only guarantees that the shape is within it, but it might be bigger than the shape) 
#==(other)
: Returnstrue
if equal toother
orfalse
otherwise 
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0)
: Whenoutline
isfalse
, it checks if point is inside any of the shapes owned by the composite shape. Otherwise, whenoutline
istrue
, it checks if point is on the outline of any of the shapes owned by the composite shape.distance_tolerance
can be used as a fuzz factor whenoutline
istrue
, for example, to help GUI users mouseclickselect a composite shape from its outline more successfully 
#intersect?(rectangle)
: Returnstrue
if intersecting with interior of rectangle orfalse
otherwise. This is useful for GUI optimization checks of whether a shape appears in a GUI viewport rectangle and needs redrawing
Example:
require 'perfectshape'
shapes = []
shapes << PerfectShape::Square.new(x: 120, y: 215, length: 100)
shapes << PerfectShape::Polygon.new(points: [[120, 215], [170, 165], [220, 215]])
shape = PerfectShape::CompositeShape.new(shapes: shapes)
shape.contain?(170, 265) # => true inside square
shape.contain?([170, 265]) # => true inside square
shape.contain?(170, 265, outline: true) # => false
shape.contain?([170, 265], outline: true) # => false
shape.contain?(170, 315, outline: true) # => true
shape.contain?([170, 315], outline: true) # => true
shape.contain?(170, 316, outline: true) # => false
shape.contain?([170, 316], outline: true) # => false
shape.contain?(170, 316, outline: true, distance_tolerance: 1) # => true
shape.contain?([170, 316], outline: true, distance_tolerance: 1) # => true
shape.contain?(170, 190) # => true inside polygon
shape.contain?([170, 190]) # => true inside polygon
shape.contain?(170, 190, outline: true) # => false
shape.contain?([170, 190], outline: true) # => false
shape.contain?(145, 190, outline: true) # => true
shape.contain?([145, 190], outline: true) # => true
shape.contain?(145, 189, outline: true) # => false
shape.contain?([145, 189], outline: true) # => false
shape.contain?(145, 189, outline: true, distance_tolerance: 1) # => true
shape.contain?([145, 189], outline: true, distance_tolerance: 1) # => true
Process
Resources
 Rubydoc: https://www.rubydoc.info/gems/perfectshape
 Point in Polygon: https://en.wikipedia.org/wiki/Point_in_polygon
 EvenOdd Rule: https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule
 Nonzero Rule: https://en.wikipedia.org/wiki/Nonzerorule
 IEEE 7541985 Remainder: https://en.wikipedia.org/wiki/IEEE_7541985
TODO
Change Log
Contributing
 Check out the latest master to make sure the feature hasn't been implemented or the bug hasn't been fixed yet.
 Check out the issue tracker to make sure someone already hasn't requested it and/or contributed it.
 Fork the project.
 Start a feature/bugfix branch.
 Commit and push until you are happy with your contribution.
 Make sure to add tests for it. This is important so I don't break it in a future version unintentionally.
 Please try not to mess with the Rakefile, version, or history. If you want to have your own version, or is otherwise necessary, that is fine, but please isolate to its own commit so I can cherrypick around it.
Copyright
Copyright (c) 20212022 Andy Maleh. See
LICENSE.txt for further details.
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