EasyGeometry::D2::Point

A point in a 2-dimensional Euclidean space.

.project(point1, point2)

Description

Project the point1 onto the line between the origin and point2 along the normal direction.

Signature

Parameters:
    point1 - EasyGeometry::D2::Point
    point2 - EasyGeometry::D2::Point

Returns:
    EasyGeometry::D2::Point
    
Errors:
    raise TypeError if point1 or point2 is not Point
    raise ArgumentError if point2 is zero point (Point(0, 0))

Example

p1 = EasyGeometry::D2::Point.new(1, 1)
p2 = EasyGeometry::D2::Point.new(3, 0)

EasyGeometry::D2::Point.project(p2, p2) # p2
EasyGeometry::D2::Point.project(p2, p3) # Point(1, 0)

.is_collinear?(*points)

Description

Returns True if there exists a line that contains self and points. Returns False otherwise. A trivially True value is returned if no points are given.

Signature

Parameters:
    points - sequence of EasyGeometry::D2::Point

Returns:
    boolean (true or false)
    
Errors:
    raise TypeError if points dont contain Point

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)
p3 = EasyGeometry::D2::Point.new(3, 0)

EasyGeometry::D2::Point.is_collinear?()           # true
EasyGeometry::D2::Point.is_collinear?(p1)         # true
EasyGeometry::D2::Point.is_collinear?(p1, p2)     # true
EasyGeometry::D2::Point.is_collinear?(p1, p2, p3) # false

.affine_rank(*points)

Description

The affine rank of a set of points is the dimension of the smallest affine space containing all the points.

For example, if the points lie on a line (and are not all the same) their affine rank is 1. If the points lie on a plane but not a line, their affine rank is 2.

By convention, the empty set has affine rank -1.

Signature

Parameters:
    points - sequence of EasyGeometry::D2::Point

Returns:
    Numeric
    
Errors:
    raise TypeError if points dont contain Point

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)
p3 = EasyGeometry::D2::Point.new(3, 0)

EasyGeometry::D2::Point.is_collinear?()           # true
EasyGeometry::D2::Point.is_collinear?(p1)         # true
EasyGeometry::D2::Point.is_collinear?(p1, p2)     # true
EasyGeometry::D2::Point.is_collinear?(p1, p2, p3) # false

#dot(point)

Description

Dot product, also known as inner product or scalar product.

Signature

Parameters:
    point - EasyGeometry::D2::Point

Returns:
    Numeric
    
Errors:
    raise TypeError if point is not a Point

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)
p3 = EasyGeometry::D2::Point.new(2, 2)

p1.dot(p2)  # 0
p2.dot(p4)  # 4

#zero?

Description

True if every coordinate is zero, False if any coordinate is not zero.

Signature

Parameters:

Returns:
   boolean (true or false)
    
Errors:

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1.zero?  # true
p2.zero?  # false

#==(point)

Description

Compare self and other Point. Return False unless point is a EasyGeometry::D2::Point

Signature

Parameters:
    point - EasyGeometry::D2::Point

Returns:
    boolean
    
Errors:

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1 == p1  # true
p2 == p1  # false

#-(point)

Description

Subtraction of two points.

Signature

Parameters:
    point - EasyGeometry::D2::Point

Returns:
    EasyGeometry::D2::Point
    
Errors:
    raise TypeError if point is not a Point

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1 - p2  # Point(-1, -1)

#+(point)

Description

Addition of two points.

Signature

Parameters:
    point - EasyGeometry::D2::Point

Returns:
    EasyGeometry::D2::Point
    
Errors:
    raise TypeError if point is not a Point

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1 + p2  # Point(1, 1)

#*(scalar)

Description

Multiplication of point and number.

Signature

Parameters:
    scalar - Numeric

Returns:
    EasyGeometry::D2::Point
    
Errors:
    raise TypeError if scalar is not a Numeric

Example

p2 = EasyGeometry::D2::Point.new(1, 1)

p2 * 10  # Point(10, 10)

#/(scalar)

Description

Dividing of point and number.

Signature

Parameters:
    scalar - Numeric

Returns:
    EasyGeometry::D2::Point
    
Errors:
    raise TypeError if scalar is not a Numeric

Example

p2 = EasyGeometry::D2::Point.new(1, 1)

p2 / 10  # Point(0.1, 0.1)

#abs

Description

Returns the distance between this point and the origin.

Signature

Parameters:

Returns:
    Numeric
    
Errors:
    see #distance

Example

p1 = EasyGeometry::D2::Point.new(1, 0)

p1.abs  # 1

#distance(entity)

Description

Distance between self and another geometry entity.

Signature

Parameters:
    entity - GeometryEntity(Point, Line etc.)
    
Returns:
    Numeric
    
Errors:
    raise TypeError if distance method is not defined for entity

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1.distance(p2)  # Math.sqrt(2)

#intersection(entity)

Description

Intersection between point and another geometry entity.

Signature

Parameters:
    entity - GeometryEntity(Point, Line etc.)
    
Returns:
    Array of EasyGeometry::D2::Point
    
Errors:
    raise TypeError if intersection method is not defined for entity 

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1.distance(p2)  # Math.sqrt(2)

#midpoint(point)

Description

The midpoint between self and another point.

Signature

Parameters:
    point - EasyGeometry::D2::Point
    
Returns:
    EasyGeometry::D2::Point
    
Errors:
    raise TypeError if point is not a Point

Example

p1 = EasyGeometry::D2::Point.new(0, 0)
p2 = EasyGeometry::D2::Point.new(1, 1)

p1.midpoint(p1)  # p1
p1.midpoint(p2)  # Point(0.5, 0.5)