78 lines
2.9 KiB
Ruby
78 lines
2.9 KiB
Ruby
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require 'pp'
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def estimate_acceleration_distance(initial_rate, target_rate, acceleration)
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(target_rate*target_rate-initial_rate*initial_rate)/(2*acceleration)
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end
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def intersection_distance(initial_rate, final_rate, acceleration, distance)
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(2*acceleration*distance-initial_rate*initial_rate+final_rate*final_rate)/(4*acceleration)
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end
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ACCELERATION_TICKS_PER_SECOND = 20
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def trapezoid_params(step_event_count, nominal_rate, rate_delta, entry_factor, exit_factor)
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initial_rate = (nominal_rate * entry_factor).round
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final_rate = (nominal_rate * exit_factor).round
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acceleration_per_minute = rate_delta*ACCELERATION_TICKS_PER_SECOND*60
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accelerate_steps =
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estimate_acceleration_distance(initial_rate, nominal_rate, acceleration_per_minute).round;
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decelerate_steps =
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estimate_acceleration_distance(nominal_rate, final_rate, -acceleration_per_minute).round;
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# Calculate the size of Plateau of Nominal Rate.
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plateau_steps = step_event_count-accelerate_steps-decelerate_steps;
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# Is the Plateau of Nominal Rate smaller than nothing? That means no cruising, and we will
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# have to use intersection_distance() to calculate when to abort acceleration and start braking
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# in order to reach the final_rate exactly at the end of this block.
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if (plateau_steps < 0)
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accelerate_steps =
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intersection_distance(initial_rate, final_rate, acceleration_per_minute, step_event_count).round
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plateau_steps = 0;
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end
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accelerate_until = accelerate_steps;
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decelerate_after = accelerate_steps+plateau_steps;
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{:step_event_count => step_event_count,
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:initial_rate => initial_rate,
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:final_rate => final_rate,
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:nominal_rate => nominal_rate,
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:rate_delta => rate_delta,
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:accelerate_until => accelerate_until,
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:decelerate_after => decelerate_after}
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end
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def simulate_trapezoid(params)
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result = {}
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rate = params[:initial_rate]
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step_event = 0.0
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max_rate = 0
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while(step_event < params[:step_event_count]) do
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step_events_in_frame = rate/60.0/ACCELERATION_TICKS_PER_SECOND
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step_event += step_events_in_frame
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max_rate = rate if rate > max_rate
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if (step_event < params[:accelerate_until])
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rate += params[:rate_delta]
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elsif (step_event > params[:decelerate_after])
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if rate > params[:final_rate]
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rate -= params[:rate_delta]
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else
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return :underflow_at => step_event, :final_rate => rate, :max_rate => max_rate
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end
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end
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# puts "#{step_event} #{rate}"
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end
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{:final_rate => rate, :max_rate => max_rate}
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end
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(10..100).each do |rate|
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(1..5).each do |steps|
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params = trapezoid_params(steps*1000, rate*100, 10, 0.1, 0.1)
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result = simulate_trapezoid(params)
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# puts params.inspect
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line = "#{steps*10} final: #{result[:final_rate]} == #{params[:final_rate]} peak: #{result[:max_rate]} == #{params[:nominal_rate]} d#{params[:nominal_rate]-result[:max_rate]} "
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line << " (underflow at #{result[:underflow_at]})" if result[:underflow_at]
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puts line
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end
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end
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