Perfect Shape 0.3.0

Geometric Algorithms

PerfectShape is a collection of pure Ruby geometric algorithms that are mostly useful for GUI (Graphical User Interface) manipulation like checking 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 (including both Ray Casting Algorithm, aka Even-odd Rule, and Winding Number Algorithm, aka Nonzero Rule).

Additionally, PerfectShape::Math contains some purely mathematical algorithms, like IEEE 754-1985 Remainder.

To ensure high accuracy, this library does all its mathematical operations with BigDecimal numbers.

Setup

Run:

gem install perfect-shape -v 0.3.0

Or include in Bundler Gemfile:

gem 'perfect-shape', '~> 0.3.0'

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 754-1985 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_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
#normalize_point(x_or_point, y = nil): normalizes point into an Array of [x,y] coordinates
#contain?(x_or_point, y=nil): checks if point is inside
#==(other): Returns true if equal to other or false otherwise

`PerfectShape::PointLocation`

Module

#initialize(x: 0, y: 0): initializes a point location, usually representing the top-left point in a shape
#x: top-left x
#y: top-left 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: top-left x
#y: top-left y
#width: width
#height: height
#min_x: min x
#min_y: min y
#max_x: max x
#max_y: max y
#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

`PerfectShape::Point`

Class

Extends PerfectShape::Shape

Includes PerfectShape::PointLocation

point

Points are simply represented by an Array of [x,y] coordinates when used within other shapes, but when needing point-specific 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
::new(x_or_point=nil, y_arg=nil, x: nil, y: nil): constructs a point with (x,y) pair (default: 0,0) whether specified as Array of (x,y) pair, flat x,y args, or x:, 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_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
#contain?(x_or_point, y=nil, 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 mouse-click-select a point shape in a GUI more successfully.
#point_distance(x_or_point, y=nil): Returns the distance from a point to another point
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

line

::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 used by Java 2D, 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_segment_distance_square(x1, y1, x2, y2, px, py): Returns the square of distance from a point to a line segment.
::point_segment_distance(x1, y1, x2, y2, px, py): Returns the distance from a point to a line segment.
::new(points: []): constructs a line with two points as Array of Arrays of [x,y] pairs or flattened Array 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_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
#contain?(x_or_point, y=nil, 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 mouse-click-select a line shape in a GUI more successfully.
#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 used by Java 2D, 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_segment_distance(x_or_point, y=nil): Returns the distance from a point to a line segment.
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

quadratic_bezier_curve

::new(points: []): constructs a quadratic bézier curve with three points (start point, control point, and end point) as Array of Arrays of [x,y] pairs or flattened Array 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_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)
#contain?(x_or_point, y=nil): checks if point is inside
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

`PerfectShape::CubicBezierCurve`

Class

Extends PerfectShape::Shape

Includes PerfectShape::MultiPoint

cubic_bezier_curve

::new(points: []): constructs a cubic bézier curve with four points (start point, two control points, and end point) as Array of Arrays of [x,y] pairs or flattened Array 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_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)
#contain?(x_or_point, y=nil): checks if point is inside
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

`PerfectShape::Rectangle`

Class

Extends PerfectShape::Shape

Includes PerfectShape::RectangularShape

rectangle

::new(x: 0, y: 0, width: 1, height: 1): constructs a rectangle
#x: top-left x
#y: top-left y
#width: width
#height: height
#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
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0): checks if point is inside when outline is false or if point is on the outline when outline is true. distance_tolerance can be used as a fuzz factor when outline is true, for example, to help users mouse-click-select a rectangle shape from its edges in a GUI more successfully
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

square

::new(x: 0, y: 0, length: 1): constructs a square
#x: top-left x
#y: top-left y
#length: length
#width: width (equal to length)
#height: height (equal to length)
#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
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0): checks if point is inside when outline is false or if point is on the outline when outline is true. distance_tolerance can be used as a fuzz factor when outline is true, for example, to help users mouse-click-select a square shape from its edges in a GUI more successfully
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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: top-left x
#y: top-left y
#width: width
#height: height
#start: start angle in degrees
#extent: extent angle in degrees
#center_x: center x
#center_y: center y
#radius_x: radius along the x-axis
#radius_y: radius along the y-axis
#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
#contain?(x_or_point, y=nil): checks if point is inside
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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: 30, extent: 90)

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

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: 30, extent: 90)

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

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: 30, extent: 90)

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

`PerfectShape::Ellipse`

Class

Extends PerfectShape::Arc

ellipse

::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: top-left x
#y: top-left y
#width: width
#height: height
#center_x: center x
#center_y: center y
#radius_x: radius along the x-axis
#radius_y: radius along the y-axis
#type: always :open
#start: always 0
#extent: always 360
#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
#contain?(x_or_point, y=nil): checks if point is inside
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

`PerfectShape::Circle`

Class

Extends PerfectShape::Ellipse

circle

::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: top-left x
#y: top-left y
#diameter: diameter
#width: width (equal to diameter)
#height: height (equal to diameter)
#center_x: center x
#center_y: center y
#radius: radius
#radius_x: radius along the x-axis (equal to radius)
#radius_y: radius along the y-axis (equal to radius)
#type: always :open
#start: always 0
#extent: always 360
#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
#contain?(x_or_point, y=nil): checks if point is inside
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

`PerfectShape::Polygon`

Class

Extends PerfectShape::Shape

Includes PerfectShape::MultiPoint

A polygon can be thought of as a special case of path that is closed, has the Even-Odd winding rule, and consists of lines only.

polygon

::new(points: []): constructs a polygon with points as Array of Arrays of [x,y] pairs or flattened Array 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_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
#contain?(x_or_point, y=nil, outline: false, distance_tolerance: 0): When outline is false, it checks if point is inside using the Ray Casting Algorithm (aka Even-Odd Rule). Otherwise, when outline is true, it checks if point is on the outline. distance_tolerance can be used as a fuzz factor when outline is true, for example, to help users mouse-click-select a polygon shape from its edges in a GUI more successfully
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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

path

::new(shapes: [], closed: false, winding_rule: :wind_non_zero): constructs a path with shapes as Array of shape objects, which can be PerfectShape::Point (or Array of [x, y] coordinates), PerfectShape::Line, PerfectShape::QuadraticBezierCurve, or PerfectShape::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 with PerfectShape::Point or Array of [x,y] coordinates representing start point)
#closed?: returns true if closed and false 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_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)
#contain?(x_or_point, y=nil): checks if point is inside path utilizing the configured winding rule, which can be the Nonzero-Rule (aka Winding Number Algorithm) or the Even-Odd Rule (aka Ray Casting Algorithm)
#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)
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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?(225, 160) # => true
shape.contain?([225, 160]) # => true

`PerfectShape::CompositeShape`

Class

Extends PerfectShape::Shape

A composite shape is simply an aggregate of multiple shapes (e.g. square and polygon)

composite shape

::new(shapes: []): constructs a composite shape with shapes as Array of PerfectShape::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_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)
#contain?(x_or_point, y=nil): checks if point is inside any of the shapes owned by the composite shape
#==(other): Returns true if equal to other or false otherwise

Example:

require 'perfect-shape'

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
shape.contain?([170, 265]) # => true
shape.contain?(170, 190) # => true
shape.contain?([170, 190]) # => true

Process

Glimmer Process

Resources

Rubydoc: https://www.rubydoc.info/gems/perfect-shape
AWT Geom JavaDoc (inspiration): https://docs.oracle.com/javase/8/docs/api/java/awt/geom/package-summary.html

TODO

TODO.md

Change Log

CHANGELOG.md

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 cherry-pick around it.

Copyright

MIT