Class: BezierCurve

Inherits:
Object
  • Object
show all
Defined in:
lib/bezier_curve.rb,
lib/bezier_curve/version.rb

Overview

bezier_curve/version.rb Just the version information for this library

Defined Under Namespace

Classes: DifferingDimensionError, InsufficientPointsError, ZeroDimensionError

Constant Summary collapse

VERSION = 
"0.9.2"
RELEASE_DATE = 
"2015-06-22"

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*controls) ⇒ BezierCurve

create a new curve, from a list of points.



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# File 'lib/bezier_curve.rb', line 19

def initialize(*controls)
  # check for argument errors
  ZeroDimensionError.check! controls
  DifferingDimensionError.check! controls
  InsufficientPointsError.check! controls

  @controls = controls.map(&:to_np)
end

Instance Attribute Details

#controls ⇒ Object (readonly)

Returns the value of attribute controls.



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# File 'lib/bezier_curve.rb', line 28

def controls
  @controls
end

Instance Method Details

#degree ⇒ Object Also known as: order

the degree of the curve



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# File 'lib/bezier_curve.rb', line 38

def degree
  controls.size - 1
end

#dimensions ⇒ Object

the number of dimensions given



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# File 'lib/bezier_curve.rb', line 43

def dimensions
  controls[0].size
end

#divergence ⇒ Object

How much this curve diverges from straight, measuring from ‘t=0.5`



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# File 'lib/bezier_curve.rb', line 127

def divergence
  first.angle_to(self[0.5],last)
end

#first ⇒ Object Also known as: start

the first control point



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# File 'lib/bezier_curve.rb', line 31

def first() controls.first; end

#index(t) ⇒ Object Also known as: []

find the point for a given value of ‘t`.



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# File 'lib/bezier_curve.rb', line 48

def index(t)
  pts = controls
  while pts.size > 1
    pts = (0..pts.size-2).map do |i|
      pts[i].zip(pts[i+1]).map{|a,b| t*(b-a)+a}
    end
  end
  pts[0].to_np
end

#is_straight?(tolerance) ⇒ Boolean

test this curve to see of it can be considered straight, optionally within the given angular tolerance, in radians

Returns:

  • (Boolean) 


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# File 'lib/bezier_curve.rb', line 111

def is_straight?(tolerance)
  # normal check for tolerance 
  if divergence <= tolerance
    # maximum wavyness is `degree` - 1; split at `degree` points
    pts = points(count:degree)
    # size-3, because we ignore the last 2 points as starting points;
    # check all angles against `tolerance`
    (0..pts.size-3).all? do |i|
      pts[i].angle_to(pts[i+1], pts[i+2]) < tolerance
    end
  else
    false
  end
end

#last ⇒ Object Also known as: end

the last control point



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# File 'lib/bezier_curve.rb', line 34

def last()  controls.last;  end

#points(count: nil, tolerance: Math::PI/64) ⇒ Object

Returns a list of points on this curve. If you specify ‘count`, returns that many points, evenly spread over values of `t`. If you specify `tolerance`, no adjoining line segments will deviate from 180 by an angle of more than the value given (in radians). If unspecified, defaults to `tolerance: 1/64pi` (~3 deg)



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# File 'lib/bezier_curve.rb', line 79

def points(count:nil, tolerance:Math::PI/64)
  if count
    (0...count).map{|i| index i/(count-1.0)}
  else
    lines = subdivide(tolerance)
    lines.map{|seg|seg.first} + [lines.last.last]
  end
end

#split_at(t) ⇒ Object

divide this bezier curve into two curves, at the given ‘t`



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# File 'lib/bezier_curve.rb', line 60

def split_at(t)
  pts = controls
  a,b = [pts.first],[pts.last]
  while pts.size > 1
    pts = (0..pts.size-2).map do |i|
      pts[i].zip(pts[i+1]).map{|a,b| t*(b-a)+a}
    end
    a<<pts.first
    b<<pts.last
  end
  [BezierCurve.new(*a), BezierCurve.new(*b.reverse)]
end

#subdivide(tolerance) ⇒ Object

recursively subdivides the curve until each is straight within the given tolerance value, in radians. Then, subdivides further as needed to remove remaining corners.



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# File 'lib/bezier_curve.rb', line 91

def subdivide(tolerance)
  if is_straight? tolerance
    [self]
  else
    a,b = split_at(0.5).map{|c| c.subdivide(tolerance)}
    # now make sure the angle from a to b is good
    while a.last.first.angle_to(a.last.last,b.first.last) > tolerance
      if a.last.divergence > b.first.divergence
        a[-1,1] = a[-1].split_at(0.5)
      else
        b[0,1]  = b[0].split_at(0.5)
      end
    end
    a+b
  end
end