Class: Geometry::Bezier

Inherits:
Object
  • Object
show all
Defined in:
lib/geometry/bezier.rb

Overview

Bézier curves are like lines, but curvier.

en.wikipedia.org/wiki/Bézier_curve

Constructors

Bezier.new [0,0], [1,1], [2,2]  # From control points

Usage

To get a point on the curve for a particular value of t, you can use the subscript operator

bezier[0.5]	# => [1,1]

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*points) ⇒ Bezier

Returns a new instance of Bezier.



28
29
30
 
# File 'lib/geometry/bezier.rb', line 28

def initialize(*points)
    @points = points.map {|v| Point[v]}
end

Instance Attribute Details

#degree ⇒ Object 



20
21
22
 
# File 'lib/geometry/bezier.rb', line 20

def degree
    points.length - 1
end

#points ⇒ Object

Returns the value of attribute points.



26
27
28
 
# File 'lib/geometry/bezier.rb', line 26

def points
  @points
end

Instance Method Details

#[](t) ⇒ Object

Parameters:

  • t (Float) —

    the input parameter



39
40
41
42
43
44
45
46
 
# File 'lib/geometry/bezier.rb', line 39

def [](t)
    return nil unless (0..1).include?(t)
    result = Point.zero(points.first.size)
    points.each_with_index do |v, i|
	result += v * binomial_coefficient(i) * ((1 - t) ** (degree - i)) * (t ** i)
    end
    result
end

#binomial_coefficient(k) ⇒ Object

en.wikipedia.org/wiki/Binomial_coefficient rosettacode.org/wiki/Evaluate_binomial_coefficients#Ruby



34
35
36
 
# File 'lib/geometry/bezier.rb', line 34

def binomial_coefficient(k)
    (0...k).inject(1) {|m,i| (m * (degree - i)) / (i + 1) }
end