Class: XRVG::BezierSpline

Inherits:
Object show all
Includes:
ParametricLength
Defined in:
lib/bezierspline.rb

Overview

You may never have to use this class. Prefer the use of Bezier class

Constant Summary

Constants included from ParametricLength

ParametricLength::NSAMPLES

Class Method Summary collapse

Instance Method Summary collapse

Methods included from ParametricLength

#compute_length, #compute_length_interpolator, #length, #length_interpolator, #parameterfromlength

Constructor Details

#initialize(type, v1, v2, v3, v4) ⇒ BezierSpline

Returns a new instance of BezierSpline.



17
18
19
20
21
 
# File 'lib/bezierspline.rb', line 17

def initialize( type, v1, v2, v3, v4 )
  self.checktype( type )
  self.checkvalues( v1, v2, v3, v4 )
  self.initdata( type, v1, v2, v3, v4 )
end

Class Method Details

.[](*args) ⇒ Object

:nodoc:



13
14
15
 
# File 'lib/bezierspline.rb', line 13

def BezierSpline.[](*args)
  return BezierSpline.new( *args )
end

Instance Method Details

#acc(t, result = nil) ⇒ Object

compute the acc of bezier curve at t abscissa



149
150
151
152
153
154
155
156
157
158
159
160
161
162
 
# File 'lib/bezierspline.rb', line 149

def acc( t, result=nil )
  if not result
    result = V2D[0.0,0.0]
  end

  if not @factors
    compute_factors
  end

  result.x = @afactors[1].x  + @afactors[0].x * t
  result.y = @afactors[1].y  + @afactors[0].y * t

  return result
end

#axesym(origin, v) ⇒ Object

simple axe sym operation : sym every point of the piece return a new BezierSpline



207
208
209
210
 
# File 'lib/bezierspline.rb', line 207

def axesym( origin, v )
  newpoints = self.pointlist.map {|point| point.axesym( origin, v )}
  return BezierSpline[ :raw, *newpoints ]
end

#checktype(type) ⇒ Object 



31
32
33
34
35
 
# File 'lib/bezierspline.rb', line 31

def checktype( type )
  if not type == :raw || type == :vector
    Kernel::raise( "BezierSpline : type #{type.inspect} is not :raw or :vector" )
  end
end

#checkvalues(v1, v2, v3, v4) ⇒ Object 



23
24
25
26
27
28
29
 
# File 'lib/bezierspline.rb', line 23

def checkvalues( v1, v2, v3, v4 )
  [v1, v2, v3, v4].each do |v| 
    if not (v.respond_to?(:x) || v.respond_to?(:y))
	Kernel::raise( "BezierSpline : init value #{v.inspect} does not respond to :x or :y" )
    end
  end
end

#compute_factors ⇒ Object 

bezier formula



101
102
103
104
105
106
 
# File 'lib/bezierspline.rb', line 101

def compute_factors
  p1, p2, p3, p4 = self.pointlist
  @factors  = [-(p1 - p2 * 3.0 + p3 * 3.0 - p4), (p1 - p2 * 2.0 + p3) * 3.0, (p2 - p1) * 3.0, p1]
  @tfactors = [@factors[0], @factors[1] * 2.0 / 3.0, @factors[2] / 3.0]
  @afactors = [@tfactors[0] * 2.0, @tfactors[1]]
end

#compute_rawpointlist ⇒ Object 



51
52
53
54
 
# File 'lib/bezierspline.rb', line 51

def compute_rawpointlist
  # Assert{ @vectorpointlist }
  @rawpointlist = [@vectorpointlist[0], @vectorpointlist[0] +  @vectorpointlist[1], @vectorpointlist[2] +  @vectorpointlist[3], @vectorpointlist[2]]
end

#compute_vectorpointlist ⇒ Object 



56
57
58
59
 
# File 'lib/bezierspline.rb', line 56

def compute_vectorpointlist
  # Assert{ @rawpointlist }
  @vectorpointlist = [@rawpointlist[0], @rawpointlist[1] - @rawpointlist[0], @rawpointlist[3], @rawpointlist[2] - @rawpointlist[3]]
end

#data ⇒ Object 



37
38
39
 
# File 'lib/bezierspline.rb', line 37

def data()
  return [:raw] + self.pointlist
end

#firstpoint ⇒ Object

shortcut method to get piece first point



78
79
80
 
# File 'lib/bezierspline.rb', line 78

def firstpoint
  return self.pointlist()[0]
end

#firstvector ⇒ Object

shortcut method to get piece first vector



88
89
90
 
# File 'lib/bezierspline.rb', line 88

def firstvector
  return self.pointlist(:vector)[1]
end

#gdebug(render) ⇒ Object 



212
213
214
215
216
217
218
219
220
221
222
223
224
 
# File 'lib/bezierspline.rb', line 212

def gdebug(render)
  p1, pc1, pc2, p2 = self.pointlist()
  v1 = pc1 - p1
  r1 = v1.r / 30.0
  v2 = pc2 - p2
  r2 = v2.r / 30.0
  render.add( Circle[ :center, p1, :radius, r1  ],  Style[ :fill, "red" ])
  render.add( Circle[ :center, pc1, :radius, r1 ],  Style[ :fill, "red" ])
  render.add( Line[ :points, [p1, pc1]          ],  Style[ :stroke, "red", :strokewidth, (r1 / 10.0) ])
  render.add( Circle[ :center, p2, :radius, r2  ],  Style[ :fill, "red" ])
  render.add( Circle[ :center, pc2, :radius, r1 ],  Style[ :fill, "red" ])
  render.add( Line[ :points, [p2, pc2]          ],  Style[ :stroke, "red", :strokewidth, (r2 / 10.0) ])
end

#initdata(type, v1, v2, v3, v4) ⇒ Object 



41
42
43
44
45
46
47
48
49
 
# File 'lib/bezierspline.rb', line 41

def initdata( type, v1, v2, v3, v4 )
  @rawpointlist      = nil
  @vectorpointlist   = nil
  if type == :raw
    @rawpointlist       = [v1, v2, v3, v4]
  else
    @vectorpointlist    = [v1, v2, v3, v4]
  end
end

#lastpoint ⇒ Object

shortcut method to get piece last point



83
84
85
 
# File 'lib/bezierspline.rb', line 83

def lastpoint
  return self.pointlist()[-1]
end

#lastvector ⇒ Object

shortcut method to get piece last vector



93
94
95
 
# File 'lib/bezierspline.rb', line 93

def lastvector
  return self.pointlist(:vector)[-1]
end

#parameter_range ⇒ Object 



228
229
230
 
# File 'lib/bezierspline.rb', line 228

def parameter_range
  return (0.0..1.0)
end

#point(t, result = nil) ⇒ Object Also known as: pointfromparameter

get point from the bezier curve this method use the definition of the bezier curve



110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
 
# File 'lib/bezierspline.rb', line 110

def point( t, result=nil )
  t2 = t * t
  t3 = t2 * t
  if not result
    result = V2D[0.0,0.0]
  end
  
  if not @factors
    compute_factors
  end

  # decomposed because avoid to build useless V2D
  result.x = @factors[3].x + @factors[2].x * t + @factors[1].x * t2 + @factors[0].x * t3
  result.y = @factors[3].y + @factors[2].y * t + @factors[1].y * t2 + @factors[0].y * t3

  return result
end

#pointlist(type = :raw) ⇒ Object 



62
63
64
65
66
67
68
69
70
71
72
73
74
75
 
# File 'lib/bezierspline.rb', line 62

def pointlist(type=:raw)
  self.checktype( type )
  if type == :raw
    if not @rawpointlist
	self.compute_rawpointlist
    end
    return @rawpointlist
  elsif type == :vector
    if not @vectorpointlist
	self.compute_vectorpointlist
    end
    return @vectorpointlist
  end
end

#reverse ⇒ Object 



179
180
181
 
# File 'lib/bezierspline.rb', line 179

def reverse()
  return BezierSpline[ :raw, *self.pointlist().reverse ]
end

#rotate(angle, center) ⇒ Object

simple rotation operation : rotate every point of the piece return a new BezierSpline



192
193
194
195
 
# File 'lib/bezierspline.rb', line 192

def rotate( angle, center )
  newpoints = self.pointlist.map {|point| center + (point-center).rotate( angle )}
  return BezierSpline[ :raw, *newpoints ]
end

#subpiece(t1, t2) ⇒ Object

compute a subpiece of the current bezier t1 and t2 must correspond to the same atomic bezier



174
175
176
177
 
# File 'lib/bezierspline.rb', line 174

def subpiece (t1, t2)
  tan1, tan2 = self.subtangents( t1, t2 )
  return BezierSpline.new( :vector, self.point( t1 ), tan1, self.point( t2 ), tan2 )
end

#subtangents(t1, t2) ⇒ Object

compute tangent vectors corresponding to the new subbezier very strange method, but effective



166
167
168
169
170
 
# File 'lib/bezierspline.rb', line 166

def subtangents (t1, t2 )
  v1 = self.tangent( t1 ) * (t2 - t1)
  v2 = self.tangent( t2 ) * (t1 - t2)
  return [v1, v2]
end

#sym(center) ⇒ Object

simple sym operation : sym every point of the piece return a new BezierSpline



199
200
201
202
 
# File 'lib/bezierspline.rb', line 199

def sym( center )
  newpoints = self.pointlist.map {|point| center.sym( point )}
  return BezierSpline[ :raw, *newpoints ]
end

#tangent(t, result = nil) ⇒ Object

compute the bezier tangent vector

Beware that what is actually computed here is 1/3 tangent !!



131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
 
# File 'lib/bezierspline.rb', line 131

def tangent( t, result=nil )
  t2 = t * t
  if not result
    result = V2D[0.0,0.0]
  end

  if not @factors
    compute_factors
  end

  # decomposed because avoid to build useless V2D
  result.x = @tfactors[2].x + @tfactors[1].x * t + @tfactors[0].x * t2
  result.y = @tfactors[2].y + @tfactors[1].y * t + @tfactors[0].y * t2

  return result
end

#translate(v) ⇒ Object

simple translation operation : translate every point of the piece return a new BezierSpline



185
186
187
188
 
# File 'lib/bezierspline.rb', line 185

def translate( v )
  newpoints = self.pointlist.map {|point| point + v}
  return BezierSpline[ :raw, *newpoints ]
end