Sphinxで作成したドキュメントをherokuでホスティング、Continuous Documentationなススメ(Basic認証付き) ref: http://qiita.com/sawanoboly/items/be1dbc9f19e93e4b62cf

config.ru

require 'sinatra'
set :public_folder, File.dirname(__FILE__) + '/build/html'

get '/' do
  redirect "/index.html", 301
end

run Sinatra::Application

config.ru(basic_auth)

require 'sinatra'
set :public_folder, File.dirname(__FILE__) + '/build/html'


## >>>追記部分
use Rack::Auth::Basic do |username, password|
  username == 'hogehoge' && password == 'mogemoge'
end

before '*' do
  # authenticate!
end
## <<<<追記部分

get '/' do
  redirect "/index.html", 301
end

get '/:dir' do  ## 修正２,3
  unless request.path_info.end_with?('.ico')
    redirect "#{request.path_info}.html", 301
  end
end

run Sinatra::Application

execute-rackup

$ git push heroku
Counting objects: 38, done.
Delta compression using up to 4 threads.
Compressing objects: 100% (37/37), done.
Writing objects: 100% (37/37), 148.40 KiB, done.
Total 37 (delta 4), reused 0 (delta 0)

-----> Ruby/Rack app detected
-----> Using Ruby version: ruby-2.0.0

-- snip --

-----> Compiled slug size: 26.2MB
-----> Launching... done, v4

file2.txt

web: bundle exec rackup -p $PORT

Gemfile

source "https://rubygems.org"

gem "sinatra"
gem "rake"
gem "thin"