Calculus is about two concepts: differentiation (微分) and integration (積分).
Differentiation is to chop up a smooth curve into tiny tangent parts.
Integration is the reverse: stitching up the tiny tangent parts back into a smooth curve.
What does movie making have to do with the math of calculus?
Well, a movie works frame by frame. You perceive motion in a movie, but nothing is moving in a frame.
Effectively, you watch a movie by integration, inside your head.
Thus a movie is created by differentiation: shooting each frame.
That is the purpose of a movie camera: actors keep moving, the camera keeps clicking, getting each frame.
Besides live action, there are animations: artists just draw frame by frame.
This was how the Disney cartoons started.
Nowadays, we use computer animations, like the Toy Story from Pixar, or Shrek from Dreamworks.
Other than image animations, there is also stop-motion animation. Instead of drawing Mickey Mouse, you make a Mickey Mouse, say out of clay. Nudge the clay Mickey into various postures, and keep taking photos using your smartphone. If you are patient enough, you can make a video by integrating your Micky photos!
Of course, this is an extremely tedious process. This is especially true if the final result is a full-length movie of 100+ minutes!【A1】【A2】【A3】
However, this method can create a fantasy world: creatures out of this world flying around, the sky in colors you haven't seen, and characters doing impossible things.
On the other hand, the fantasy world must still be credible: creatures exist in proportions, there are sky and water (although not real sky nor real water),
characters look real, and act within imagination.
That's the challenge of making a stop-motion animation. Nowadays, the 3D models for filming are not made from clay for nudging. Instead, they are 3D printed with variations, and catalogued into a vast model library for the animators to pick.
It is breath-holding work to snap frame by frame of 3D models, often small for fast printing. Yet the reward is breathtaking: an animation full of life!
Kubo and the Two Strings (2016)酷寶：魔弦傳說 (Kubo and the Two Strings, 2016)
Click to enlarge (click again to close)
點擊放大(再擊關閉)
Download【M1】
Everyone has two strings, tie to the first two words every baby learns.
Adding his own string, the main character Kubo plays magic with his Japanese three-string instrument, a shamisen (三味線).
Kubo and the Two Strings is a spectacular example of stop-motion animation from Laika【B1】.
You'll see a boat tossing in a wild storm, but in fact there is no wind, no rain, no water, no waves. Nothing moves: the boat, the people, their faces, their hair. Only light, while sound is added afterwards. Everything is static when the animators take each frame -- stops make motion!
Imagine the technical challenges in creating models for the following scenes:
stormy sea against the full moon, no storm,
rain falling on a sandy shore, without rain,
paper folding sheets enacting a story, dream or illustration,
sweeping wind by the wizards, without wind,
spearfishing from a sailboat on a lake, all by origami (摺紙),
big eyes watching from the deep seabed, no ocean.
For answers, marvel at these snapshots【B2】【B3】【B4】【B5】【B6】.
The story is dynamic, but everything is static; that's magic!
This fully illustrated book is fascinating. The creators of "Kubo and the Two Strings" reveal the inventiveness and painstaking work they poured into creating Kubo’s world and his odyssey. With concept art, puppets, props, and set photos on every page, and with insights from the filmmakers and artists themselves, this is a lovingly curated behind-the-scenes look at the making of the film.
This soundtrack is a famous Beatles song, written by George Harrison.
The lyrics start with the following:
I look at you all
See the love there that's sleeping
While my guitar gently weeps.
What follows are random imagery about love -- the kind of "world love" that matters to George Harrison.
This song shows his talent in songwriting, trying to rhyme various words in the style of Bob Dylan.
The result is a rhythmic song with simple lyrics, easy to follow, with fantastic guitar accompaniment.
'Kubo and the Two Strings' takes this song with a twist: putting "love" to refer to a child.
Thus it becomes a song from a mother to a child, replacing the guitar by the shamisen (三味線), a traditional Japanese string instrument.
The soundtrack features Regina Spektor【C1】, a Russian-born American singer-songwriter with classical training on the piano.
Her rendition of this Beatles' classic in the end credit song is majestic【C2】.
本片配樂用上一首披頭四著名歌曲，由 George Harrison（喬治·哈里森）撰寫。歌詞開首是：
I look at you all
See the love there that's sleeping
While my guitar gently weeps.
跟著便是關於「愛」的隨機描繪 -- 這是「世界的愛」，也是 George Harrison 的信念。這首歌展示了他在歌曲創作方面的才華，嘗試用 Bob Dylan 的風格作歌詞押韻。結果是一首旋律簡單、歌詞易於上口的佳作，兼具美妙的結他伴奏。
電影歌曲原聲帶，由 Regina Spektor 演唱【C1】。她是來自俄羅斯的美國創作歌手，曾接受古典鋼琴訓練。作為片尾曲，這首披頭四的經典，她演繹得相當壯麗【C2】。
Links連結
Kubo And The Two Strings (Full Movie)【1:41:36】(deleted)（已刪除） "If you must blink, do it now." Everything about this movie is fascinating, perfectly detailed, brilliant! The sceneries and the storytelling is great. Full movie in English, without subtitle. See next item for subtitles.「若想眨眼，就趁此刻。」這齣電影，一切都令人著迷，細節完美，精彩絕倫！風景和故事都非常棒。全高清電影，英語無字幕。若要字幕，請參閱下一項。
【M1】
Click Google Drive for Kubo and the Two Strings download.
The files are:
After downloading to your laptop or smartphone,
try open and play (or simply by double clicking).
Most video player can handle mp4 files, and
figure out how to configure your video player to read the subtitle file.
If there are problems, install VLC, a free video player, from App Store or Google Play or Microsoft Store.
【A2】Go behind the scenes at Laika Studios with an exclusive look at the stop-motion process (Tasha Robinson, 9 April 2019)
A 2019 report of how the studio does everything from Coraline to the new Missing Link, with a behind-the-scenes featurette, Inside the Magic of Laika.
動畫工作室 2019 年另一份報告，訴說歷史：從第一部動畫 Coraline 到最近的 Missing Link。其中包括視頻「萊卡的魔術」，介紹內部的幕後特色。
【A3】How Laika Studios Animates Their Movies (Jason Hellerman, 25 April 2019)
Recounts how Laika build everything, to slowly emerge as one of the most beautiful and inventive animations studios.
追溯 Laika 如何從開始創立，慢慢發展，成為最標致而具創造性的動畫工作室之一。
‘Kubo and the Two Strings’ Blends Animation and Origamis (Mekado Murphy, 10 August 2016)
“Kubo and the Two Strings” may be the most ambitious film the stop-motion animation company Laika has made. It is a sweeping tale of a young Japanese boy’s adventures, featuring fierce samurai warriors battling evil spirits and journeys across oceans and harsh winter landscapes. But the adventures begin with a little origami. The paper-folding art form is the centerpiece of a storytelling show that Kubo performs for his village.
《酷寶：魔弦傳說》可能是定格動畫公司 Laika 芸芸製作中，最雄心勃勃的電影。主題是關於一個日本小男孩 Kubo 的冒險故事，講述兇猛的武士與惡靈的戰鬥，以及穿越浩瀚海洋和嚴寒霜雪的旅程。冒險旅程從摺紙開始，而摺紙藝術形式，正是 Kubo 在村莊廣場中，表演傳奇故事的核心。
If You Must Blink Do It Now | Kubo And The Two Strings【4:16】cc The paper-folding art form is the centerpiece of a storytelling show that Kubo performs for his village.Kubo 來到他的村莊廣場，講故事並作表演。摺紙藝術形式，是表演故事的核心。
【B1】Laika Studios
The current CEO of Laika, Travis Knight, recalled, "When we started Laika 10 years ago, we could see the writing on the wall. Stop-motion animation was basically taking its last, dying breath. We had to come up with a way, if we wanted to continue to make a living in this medium that we loved, to bring it into a new era, to invigorate it."
He is proud of his achievements, "The ethos of this whole place is that we are artists first and foremost. There are easier ways, but we challenge ourselves to take ultra-detailed, time-intensive routes instead."
Laika 現任首席執行總裁 Travis Knight 憶述：「十年前我們開創動畫工作室時，已看到這寫在牆上：定格動畫基本上是苟延殘喘。如果想在我們所喜愛的媒體中繼續謀生，必須提出一種方式，將它帶入一個嶄新的時代，全面振興。」他為自己的成就感到自豪：「我們是徹頭徹尾的藝術家，這也是整個地方的精神之首。當然，有更簡便的方法。但我們挑戰自己，採取極度詳細、時間密集的方向進行。」
【B2】Behind the scenes of Kubo and the Two Strings - BBC Click【7:01】cc
Travis Knight talks about making the film, and how it merged traditional stop-motion animated techniques with cutting edge technology.Travis Knight 談及這部電影的製作，如何結合傳統的定格動畫技術與尖端技術。
【B3】Go Behind the Scenes of Kubo and the Two Strings【16:59】cc
This one shows the processes in the production of a stop-motion animation.視頻展示定格動畫的製作過程。
【B4】Laika Animation: Kubo and the Two Strings【1:14:09】
A conversation with Kubo and the two String, VFX Oscar nominees.一班視覺特效奧斯卡獎的被提名者，暢談《酷寶：魔弦傳說》的製作。
【B5】Insight into LAIKA’s puppet fabrication!【15:57】
An extended look at Puppet Fabrication at Laika Studios.深入探討 Laika 工作室的木偶製作部門。
【B6】3D Printing Enables Stop Motion Facial Animation for Laika Studios【3:36】cc
The fascinating work of Rapid Prototyping and the amazing work with 3D Printers at Laika Studios.Laika 工作室的快速原型設計與3D打印機，引人入勝。
Pixar vs. Dreamworks vs. Laika (Peter Orrestad, 24 June 2014)
Pixar, Dreamworks, and Laika are three animation studios that each have their own distinct style when it comes to children's entertainment.
三個動畫工作室：皮克斯（Pixar）、夢工廠（Dreamworks）、萊卡（Laika），都是提供娛樂給孩子們，各有自己獨特的風格。
Animating Life: The Art, Science, and Wonder of Laika【1:08:04】cc
Get a peek behind the scenes with key members of the Laika creative team, from Portland Art Museum.由波特蘭藝術博物館製作，窺看了解 Laika Creative 團隊關鍵成員的幕後工作。
《酷寶：魔弦傳說 Kubo and the Two Strings》 （鍾豪, 30 August 2016）
For a full one hundred minutes, the perfect combination of shamisen and origami.
整整一百分鐘，是三味線與摺紙藝術的完美結合。
烙印在心中的記憶身影 ──『酷寶：魔弦傳說』 （黑情, 8 March 2017）
In this adventure, the audience will follow the shamisen in the hands of Kubo to listen to the story.
觀眾們在這場冒險的經歷裡，將隨著酷寶手中的三味線，一同聆聽關於整個故事的點點滴滴。
Credited As: Stop Motion Animator【7:10】cc
Daniel Alderson takes viewers behind the scenes to show what he does as a stop motion animator.Daniel Alderson 帶領觀眾往幕後，展示定格動畫師所做的工作。
Stop-motion animation goes high tech at Laika【9:10】cc
Laika studios blended handcrafted puppets, CGI, and 3D printing to create their latest epic, Kubo and the Two Strings.Laika 工作室將手工木偶、CGI和3D打印互相結合，創造他們最新的史詩《酷寶：魔弦傳說》。
The Magic of Laika Tour 2016【10:50】cc
An up-close look at the artistic detail and imagination behind Laika's groundbreaking ten-year filmmaking history.近距離觀察： Laika 開創性的十年動畫製作歷史，及背後的藝術細節和想像力。
From Coraline to Kubo: A Magical Laika Experience【12:54】
A virtual tour at Universal Studios Hollywood.好萊塢環球影城的虛擬之旅。
Behind The Scenes of Laika Animation Studios【5:19】cc
Jeff McCobb walks us through an exclusive behind the scenes look their filmmaking processes.Jeff McCobb 帶我們了解動畫製作過程，及獨家幕後花絮。
The Art and Science of Laika【46:50】
About rapid prototyping in Laika. In Kubo, how wind and waves in the opening scene are modelled, at 31:20, and opening scene stop-motion photography and animation comparison at 38:20.關於 Laika 的快速原型製作。《酷寶》中如何模擬電影開首的風浪（31:20），有開首場景定格攝影與動畫比較（38:20）。
【C1】myStory: Regina Spektor【13:15】cc
Regina Spektor tells her own story.Regina Spektor 講述自己的故事。
【C2】Kubo end credits song【3:24】
This famous classic of George Harrison is played by oriental instruments.由東方樂器演奏，一首 George Harrison 的著名經典作品。
Click to enlarge (click again to close)
Click to enlarge (click again to close)
