Class: Kamelopard::Functions::SplineFunction

Inherits:
FunctionMultiDim show all
Defined in:
lib/kamelopard/spline.rb

Instance Attribute Summary collapse

Attributes inherited from FunctionMultiDim

#ndims

Attributes inherited from Function

#append, #compose, #end, #max, #min, #start, #verbose

Instance Method Summary collapse

Methods inherited from FunctionMultiDim

#compose=

Methods inherited from Function

#get_value, interpolate

Constructor Details

#initialize(ndims, tension = 0.5) ⇒ SplineFunction

Returns a new instance of SplineFunction.



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# File 'lib/kamelopard/spline.rb', line 11

def initialize(ndims, tension = 0.5)
    @ndims = ndims
    @control_points = []
    @total_dur = 0
    @tension = tension
    super()
end

Instance Attribute Details

#control_points ⇒ Object (readonly)

Returns the value of attribute control_points.



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# File 'lib/kamelopard/spline.rb', line 9

def control_points
  @control_points
end

#tension ⇒ Object (readonly)

Returns the value of attribute tension.



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# File 'lib/kamelopard/spline.rb', line 9

def tension
  @tension
end

#total_dur ⇒ Object (readonly)

Returns the value of attribute total_dur.



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# File 'lib/kamelopard/spline.rb', line 9

def total_dur
  @total_dur
end

Instance Method Details

#add_control_point(point, dur) ⇒ Object

Adds a new control point. :dur is a way of indicating the duration of the journey from the last point to this one, and is ignored for the first control point in the spline. Values for :dur are in whatever units the user wants; a spline with three control points with durations of 0, 10, and 20 will be identical to one with durations of 0, 1, and 2.



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# File 'lib/kamelopard/spline.rb', line 25

def add_control_point(point, dur)
    @total_dur = @total_dur + dur if @control_points.size > 0
    @control_points << [ point, dur ]
end

#run_function(x) ⇒ Object 



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# File 'lib/kamelopard/spline.rb', line 30

def run_function(x)
    # X will be between 0 and 1
    # Find which control points I should am using for the point in
    # question

    dur = 0
    last_dur = 0
    cur_i = 0
    u = 0
    @control_points.each_index do |i|
        next if i == 0
        cur_i = i
        last_dur = dur
        if 1.0 * (dur + @control_points[i][1]) / @total_dur >= x then
            # I've found the correct two control points: cp[i-1] and cp[i]
            # u is the point on the interval between the two control points
            # that we're interested in. 0 would be the first control point,
            # and 1 the second
            u = (x * @total_dur - dur) / @control_points[i][1]
            break
        end
        dur = dur + @control_points[i][1]
    end

    # http://www.cs.cmu.edu/~462/projects/assn2/assn2/catmullRom.pdf

    # cp = control points. cur_i will be at least 1
    # I need two control points on either side of this part of the
    # spline. If they don't exist, duplicate the endpoints of the
    # control points.
    cp1 = @control_points[cur_i-1][0]
    cp2 = @control_points[cur_i][0]
    if cur_i == 1 then
        cpt1 = cp1
    else
        cpt1 = @control_points[cur_i-2][0]
    end
    if cur_i >= @control_points.size - 1 then
        cpt2 = cp2
    else
        cpt2 = @control_points[cur_i+1][0]
    end

    # Can't just say Matrix[cp], because that adds an extra
    # dimension to the matrix, somehow.
    cps = Matrix[cpt1, cp1, cp2, cpt2]

    t = @tension
    h = Matrix[
        [ 0, 1, 0, 0 ],
        [ -t, 0, t, 0 ],
        [ 2*t, t-3, 3-2*t, -t ],
        [ -t, 2-t, t-2, t]
    ]

    p = Matrix[[1, u, u**2, u**3]] * h * cps
    return p.row(0)
end