According to the lunar calendar, the 5th of May is the Dragon Boat Festival. The day celebrates the dragon casting out plagues, by blaring gongs and beating drums together.
The noisiest competition is the dragon boat race, with teams of people rowing long flat-bottomed boats, vying to send the Devil of Plague away as quickly as possible.
The result depends on team effort. A dedicated team with a common goal can achieve amazing results.
Last time we have a graphic novel "Logicomix", the marvelous work of a team. Did you find out how such an exquisite book is produced?
A graphic novel tells a story by pictures, frame by frame.
As the story flows, the characters are alive in the frames.
Indeed, if you can insert more frames in between, the graphic novel becomes a cartoon animation!
Have you played with a flipbook? You can make a cat sitting on a branch (shown on the right) vanish with a smile!
Flipbooks are the earliest form of animation【A1】. Flashing before our eyes lots of pictures, each with slight variations, gives the illusion of continuous motion.
Replacing the pictures by photos will make an animated movie. Usually, the camera takes photos from drawings, as in cartoon animation. Sometimes, the camera shoots at static miniature models, as in stop-motion animation【A2】. When the camera is virtual, and the digital photos are generated by a computer, the result is computer animation.
This episode goes from graphic novels to graphic movies: animations.
Would you like to know:
* the first full-length color animation?
* the first full-length computer animation?
* the math and physics behind animation?
* the creation of fantasies in animation?
Welcome to the world of animation!
Surely you love animation, but are you curious about the work behind the scenes?
Perhaps not interested in computer graphics? Please go and enjoy a wonderful 2019 animated movie【M1】.
The story is an epic journey of life, in contrast to the epic journey of math last time. This movie has a theme song, with both English and Chinese versions.
動畫，你一定喜歡，但對幕後工作不感好奇？或對電腦繪圖不感興趣？請去享受一齣精彩的2019年動畫電影【M1】。故事是史詩式的人生旅程，與上次傳奇式的數學之旅，形成鮮明對比。電影的主題曲，有中、英文版本。
Bonus獎勵
Ah, you choose to stay on! Let me entice you with this: at the heart of animation is calculus!
Calculus consists of two parts:
* Differentiation, with symbol $\partial$, is to cut a thing into tiny bits,
* Integration, with symbol $\int$, is to paste back all the tiny bits.
If integration exactly undoes differentiation, we have the original thing.
If integration changes the differentiation bits, we have the **transformed** thing.
Any animated movie starts with a story, broken down into frames:
\[
\text{frames} = \partial\ \text{story}
\]
The frames are combined into a film roll, or a computer file:
\[
\text{movie} = \int\text{frames}
\]
Putting together, we have:
\[
\text{movie} = \int\partial\ \text{story}
\]
That's how a story is transformed into an animated movie!
Walt Disney had a love for drawings. As a kid he would copy cartoons from newspapers. Later he posted his cartoons in school magazines. With a borrowed movie camera he learned the techniques of animation. As an animation artist, he was famous for his invention of the Mickey Mouse, a little fellow that is smart, often outwits the big fellow.
In 1916, when Disney was a teenage boy, he watched the silent movie "Snow White and the Seven Dwarfs" in his hometown. The film made a lasting impression on him.
In 1934, Disney gathered his animators in a room, and informed them about his dream: to produce a full-featured color animation based on this fairy tale. He turned on a spotlight, went on stage, and enacted all the scenes, all the characters, of the Snow White story. Disney was a superb storyteller, and the animators were mesmerized【B1】.
The studio was captivated by Disney's vision, but they knew this would be a huge challenge. It took months to produce a short cartoon, so it would take years to produce a 90-minute movie. There are 24 frames per second for a movie with smooth viewing. Therefore, the total number of frames is:
\[
90\;\text{minutes}\times{60}\;\text{seconds/minute}\times{24}\;\text{frames/second}\\
= 129,600\;\text{frames}
\]
Although animators have various tricks to reduce their workload, there are still a lot of frames to be drawn!
Walt Disney 熱愛繪畫。小時候，從報紙上抄繪漫畫。後來，在學校雜誌上發表漫畫。他借來活動攝影機，學習動畫技術。他是一名動畫藝術家，成名作是米奇老鼠︰小傢伙很聰明，經常勝過大傢伙。
1916年，才十多歲的黃毛小子 Disney，在家鄉觀看默片《白雪公主和七個小矮人》，留下深刻印象。
1934年，Disney 召集動畫師聚首一堂，講述自己的夢想︰根據此童話故事，製作長篇彩色動畫。他打亮射燈，走上舞台，扮演白雪公主故事中所有角色、演繹所有情節。Disney 講故事技巧出色，動畫師們嘆為觀止【B1】。
工作室眾人，著迷于 Disney 的願景。但他們清楚，面臨挑戰頗巨。製作一齣卡通短片，需時多月，推算製作 90分鐘長片，需時幾年。要觀看流暢，電影每秒閃 24幀。因此，總幀數為：
\[
90\;\text{分鐘}\times{60}\;\text{秒每分}\times{24}\;\text{幀每秒} = 129,600\;\text{幀}
\]
雖然動畫師運用各種技巧，減少工作量，但仍要繪製多不勝數的圖幀！
Walt Disney understood the whole process of animation production. Though he was not a math person, he intuitively applied the principle of calculus【B2】:
| movie task | differentitation | integration |
|---------------|-------------------------------------|----------------------------------|
| story | break apart into snippets | make a coherent whole |
| dialogue | break down into words and syllables | draw pictures with lips to match |
| music | break up all the notes | draw movements in sync |
| movement | film how live actors move | view frames to draw actions |
For the first task 'story', Walt Disney knew that story was the soul of a movie. Although he had the whole story in his head, he needed to pin down the story for analysis. He set up a 'story room' for this job, invented the technique of story-boarding.
The Disney Studio had been drawing cartoon characters with cartoon movements, e.g., running with rotating legs. They had trouble drawing human with natural movements. They experimented with a short animation *The Goddess of Spring* featuring a female singing and dancing, but the dance was too simplistic.
This was a problem with the 'movement' task in the table above, and Disney devised a solution. He sent his animators to dancing classes, and invited actors to the studio, filming their dances wearing the same costume as the cartoon characters. He gave hand-held mini-projectors to the animators, so that they could roll the film loop, or examine the loop frame by frame.
The animators did try to trace the actor dancing frame by frame, then fill in the trace with the cartoon human characters. Though this was correct in math, the result looked unnatural. The animators found out that the proportions had to be distorted slightly to give the natural feel. Why? Maybe subconsciously, our fantasy world deviates from the math world!
It was such time-consuming experiments that kept delaying the project, and Walt Disney was a perfectionist. The studio avanced animation technology by trial-and-error. For example, they tried to give depth to the 2D cartoons. Using overlapping glass drawings of background, foreground and characters, they mounted a multilayer camera to make frames with a perception of depth. They prefected this technique near the end of the production of Snow White, but Disney ordered re-drawing parts of the animation to be filmed using the multilayer camera.
In the end, the animators produced over 362,000 celluloids of hand drawn and painted animations for Snow White. The production cost was $1.5 million, nearly four times the original budget. It debuted at Christmas 1937 in USA, then worldwide in 1938. Just the opening scenes wowed every child and every adult【B3】. The box office grossed over $8 million.
Walt Disney was eager to share his enthusiasm in making cartoons and animations. He hosted the TV series "The Wonderful World of Disney"【B4】, revealing his techniques and inviting the audience into his studio. The series was a hit, inspiring the next generation of animators.
正是如此耗時的實驗，不斷拖延項目，而 Walt Disney 是完美主義者。通過反複試驗，工作室提升動畫製作技術。例如，為賦予2D漫畫深度，他們嘗試重疊背景、前景和人物的玻璃繪圖，並安裝一個多層攝影機，製作有深度感的幀格。完善這項技術時，《白雪公主》的製作已接近尾聲，但 Disney 下令重新繪製部分動畫內容，以便使用多層攝影機重拍。
最終，動畫師為《白雪公主》手繪和塗彩的動畫膠片，超過362,000幀。製作成本為150萬美元，幾乎是初期預算的四倍。1937年聖誕節在美國首映，然後於1938年在世界各地首次發行。僅開場一幕，已讓每個孩子、每個大人，驚嘆不已【B3】。票房累計總收入，超過800萬美元。
Walt Disney 熱衷卡通和動畫製作，樂於分享。他主持電視節目《迪士尼的奇妙世界》【B4】，展示技巧，並邀請觀眾進入工作室。該系列深受歡迎，啟發新一代動畫師。
When Edwin Catmull was a boy, he found inspiration in Disney animation, and wanted to be an animator【C1】.
He had no talent in drawing, but he learned how to draw using a computer. He studied physics and computer science at the University of Utah, and graduated in 1969. At first his PhD work was in designing languages for computer programming. Then he encountered Ivan Sutherland, who had developed the computer drawing program Sketchpad. This turned his interest to digital imaging【C2】.
From 1970 onwards, Catmull's main goal and ambition was to make digitally realistic films. He understood the principles involved, but the computer technology at that time was primitive. Being a scientist, he estimated how long it would take to produce a 10-minute animation with his computer. The answer: running the machine non-stop for 30 years!
This looked hopeless! However, he knew about "Moore's law". This was not a law in math or physics, but an observation by Gordon Moore, the CEO of Intel. He found that computer power seemed to double every two years.
Doubling computing power means halving the computing time. Assuming this trend of hardware improvement, Catmull reasoned that:
| to make a 10-minute computer animation ... | requires running a computer non-stop for ... |
|--------------------------------------------|----------------------------------------------|
| in 1970 (primitive hardware) | about 30 years |
| in 1972 (with better hardware) | about 15 or 16 years |
| in 1974 (ditto) | about 8 years |
| in 1976 (ditto) | about 4 years |
| in 1978 (ditto) | about 2 years |
| in 1980 (ditto) | about 1 year |
It would still be impractical to run a computer non-stop for a whole year, but that would make the project feasible, hopefully to be completed in a few years. With confidence in the Moore's law, Catmull decided to wait a decade before really starting on his vision.
Of course, Catmull would not sit idle waiting a decade to pass by. Moore's law was all about computer hardware evolution. In the meantime, he developed the necessary software for computer animation.
A movie is a sequence of picture frames. Like a flipbook, the more frames flashing each second, the more natural and smooth the characters act. Movie makers have determined from experience that 24 is the minimum number of frames per second (fps). Thus, the standard frame rate for movies is 24 fps.
An animation portrays an idealized world, populated with cartoon characters. That world can be simple (only a few houses and trees) or complex (like a whole city or community), even imaginary (like heaven or hell). These worlds exist in the minds of animators. They draw pictures from mental images, according to a story.
A **computer animation** combines these two aspects, using computer technology (see process diagram above):
* build the virtual world, put in virtual characters,
* use a virtual camera to take digital frames,
* have scripts to move the virtual camera, and command the virtual characters into action.
* render the details of digital frames to produce a digital movie file.
If you are interested in animation technology, you can find details on the web 【D1】. There are many videos on computer graphics, and the making of various animated movies. Here, we can only take a look at the basics.
How does a computer make a frame?
A frame captures an image of a scene. A computer image is made up of pixels. A pixel is a little bit of the 3D scene to be captured.
This can be described by differentiation:
\[
\text{pixels} = \partial\ \text{scene}
\]
The pixels form the 2D image, which can be represented by integration:
\[
\text{image} = \int\text{pixels}
\]
Combining them, we have:
\[
\text{image} = \int\partial\ \text{scene}
\]
That's how a 3D scene is transformed into a 2D image!
How to form a pixel? A pixel is the intersection of a ray of light with a plane representing the 2D image. The light rays from a source, illuminating a scene, are collected by the observer: the eye, or the camera【D2】.
Thus the math can be turned into an algorithm, a procedure for a machine:
!!! note
for **each** ray to the observer: form **a pixel** of the image.
Click to enlarge (click again to close)
Before the invention of cameras, this was how early artists painted a portrait (shown on the right). Note that this is doing pixel by pixel, one at a time, called *serial*. An artist may draw the pixels for outlines first, then fill in other pixels like the face, then the clothes. A computer will store the scene in a buffer, then just form the pixels: usually from left to right, top to bottom.
Nature provides the light rays all at once, in *parallel*. The algorithm can be modified, like so:
!!! note
For **all** rays to the observer: form **pixels** of the image.
Working in parallel is much more efficient. Indeed, this is how our eyes or cameras work!
How does a computer move the characters?
With real actors, the director just say, "Jump!"
For cartoons, the animator just imagines the character jump, and draws the poses.
For computer animation, we want to do the same: somehow, tell the virtual character to jump.
This is where math and programming come in.
The virtual character is a model inside a computer. The model gives the shape of the character, say the head, the body, arms and legs, etc. The shape is defined by *control points*. By moving the control points, the shape changes, and the virtual character acts.
Obviously, the more control points to define the shape, the more delicate the actions can be expressed:
\[
\text{controls} = \partial\ \text{model}
\]
The control points decide the actions of the character:
\[
\text{character} = \int\text{controls}
\]
Combining them, we have:
\[
\text{character} = \int\partial\ \text{model}
\]
That's how an internal model is transformed into an animated character!
Joining the control points by straight lines gives a **wireframe** for the character. This is a triangular mesh giving the shape of the character (see example on the right). The more points, the denser the mesh, the more realistic is the shape【D3】.
The wireframe allows choosing just a few key points to control, as the wires will shift other points appropriately. This simplifies the commands to control the actions of the character. Each command translates into a series of point movements:
\[
\text{movments} = \partial\ \text{command}
\]
The point movements of each part make up the action for a character:
\[
\text{action} = \int\text{movments}
\]
Combining them, we have:
\[
\text{action} = \int\partial\ \text{command}
\]
That's how each command is transformed into an animated action!
Therefore, the design of computer animation has two tasks:
| task ... | to .... |
|-------------|-------------------------------------------------------------------------------------|
| math | build the model, construct wireframe, select key controls to match various actions. |
| programming | devise commands to move key controls, script commands for an action sequence. |
For example, a script to animate 'jump' can be: raise the legs, lower the head, push body forward, etc.
The scripting of commands becomes a special programming language for computer animations.
Things inside a computer, including the character models and the scenes, are digital: they are virtual. How to make them look real?
Well, we look at them as 2D images on the screen, frame by frame. We briefly looked at how to make a frame: determine each pixel by collecting light rays at that point. Now we come to the nitty-gritties.
The virtual things inside a computer are 3D: models shape the characters, light rays fly around, scenes have foreground and background. Transforming all these 3D information into a 2D photorealistic frame is a process called **rendering**.
In English, the word 'render' comes from Latin *red* (back) and *dare* (come), then in old French as *rendre*, and in old English as *rendere*. Thus, 'render' originally means to give back, retrun or restore. Now this extends to mean redoing in a different way. For example, the scholar renders the Latin text in English, the pianist renders the song artistically. In painting, a line drawing is rendered into a vivid piece.
For computer graphics to be photorealistic, rendering takes care of three aspects, which affect each other:
| to render ... | depends on ... |
|----------------|-----------------------------------------------------------------|
| color | color of objects, and the illuminating light rays from sources, |
| shades | placement of objects, and the diffuse rays from surrounding. |
| texture | surface structures, and details of surface material properties. |
The last aspect 'texture' directly affects realism: smooth ones reflect light, but most natural surfaces scatter light, giving a unique look and feel. This is also the most complex. That's why early computer animations avoid human characters, just using toys or animals.
Each rendering aspect relies on the math and physics of light rays. All these visual effects are computed, using lots of computing power. Software systems called **rendering engines** have been developed to perform this job. Nowadays, there are hardware accelerators called **graphic processing units** (GPU) designed specifically for this task【D4】.
Back in 1974, Ed Catmull was a PhD student with his dream of making computer animations. His supervisor had developed the first computer drawing app: just green line drawings. To demonstrate that computer animation can be done, even with primitive computers of limited power, he made a short animation of a hand, with moving and bending fingers (see next section).
Fantasy worlds are portrayed by stories. Let us return to the story of computer animation.
Ed Catmull studied computer graphics, and his PhD thesis in 1974 was a ground-breaking math treatment of calculating how 3D computer objects will appear on 2D computer screen. He devised and improved several algorithms for the process.
One of his coursework projects was a short movie, "A Computer Animated Hand" (1972)【E1】. This enabled him to join the Computer Graphics Lab in 1974, led by a visionary who also had the ambition to make computer movies.
George Lucas was making the Star Wars series, starting from 1977. In 1979, he would like to add special effects using computers. He approached the Compouter Graphics Lab, and soon Ed Catmull was leading the Lucasfilm Computer Graphics Group【E2】.
For Ed Catmull, almost a decade had passed since 1970, but his dream of a full-length computer animation was still in the air!
As fate would have it, in 1979, a young John Lasseter was recruited by Disney, for his short cartoon "Lady and the Lamp" (1979). This was his dream job, as he had been studying arts and character animations, and longed to be a Disney animator. He would like to improve the production of animations by using computers to draw the background for cartoons, but his ideas were knocked down. He kept pushing, resulting in being fired in 1983.
That November, Ed Catmull met the frustrated John Lasseter in a graphics conference. Since Catmull lacked the artistic skills of an animator, and Lasseter was keen to learn computer technologies, they soon became friends.
In 1984, John Lasseter joined Lucasfilm, teaching the group about film making. Meanwhile, Ed Catmull assembled the hardware and developed the software for the production of computer animation.
幻想世界，由故事譜成。讓我們重拾電腦動畫的故事。
Ed Catmull 攻讀電腦繪圖。1974年，他完成博士論文，對如何把3D電腦對象呈現在2D電腦屏幕上，進行突破性的數學探討。他為該項過程，設計並改良幾種算法。
其中一個課程作品，是短片《電腦動畫之手》（1972年）【E1】。這引致他在1974年加入電腦圖形實驗室。該實驗室的領導人，也有製作電腦電影的理想。
從1977年開始，George Lucas 製作《星球大戰》系列。1979年，他希望引入電腦特效， 接洽電腦圖形實驗室。很快，Ed Catmull 就領導 Lucasfilm 電腦圖形組【E2】。
對 Ed Catmull 來說，自 1970年起，將近十年已逝，但他的長篇電腦動畫夢，仍是空想！
冥冥中命運安排，1979年，年輕的 John Lasseter 因創作卡通短片《女士與燈》（1979年），獲 Disney 募用。這是他夢寐以求的職業，因他一直學習藝術和角色動畫，並渴望成為一名 Disney 動畫師。他想以電腦繪製卡通背景，來改進動畫製作，但他的想法，不被接納。他不斷硬銷，導致在1983年遭解僱。
同年11月，Ed Catmull 在一次圖像交流會議中，遇上沮喪的 John Lasseter。 由於 Catmull 缺乏動畫師的藝術技巧，而 Lasseter 熱衷於學習電腦技術，兩人很快成為知己。
1984年，John Lasseter 加入 Lucasfilm，教授團隊電影製作知識。Ed Catmull 則開始組裝硬件，並開發製作電腦動畫的軟件。
In 1986, Steve Jobs bought Lucas’ computer division and named it Pixar,
As a showcase for the skills of Pixar, Lasseter and Catmull produced a short computer animation Luxo Jr. (1986), a story about a mother lamp and a kid lamp【E3】. This was shown in SIGGRAPH '86 (Special Interest Group on Computer Graphics and Interactive Techniques), and won an award.
By 1990, Pixar was ready to produce the first full-length 3D computer animated movie. Lasseter, who stuffed his office with toys, suggested a story about inaimate toys being alive. Catmull supported this idea as rendering was only possible for smooth surfaces, due to computer hardware limitations at that time.
In 1991, Pixar made a deal with Disney Animation about "Toy Story"【E4】. Just before its release, Steve Jobs gave a keynote speech at SIGGRAPH '95, highlighting the significance of Toy Story【E5】.
1986年，Steve Jobs 收購 Lucas 旗下的電腦部門，並命名為 Pixar（皮克斯）。
為展示 Pixar 的科技藝術水平，Lasseter 和 Catmull 製作電腦動畫短片《Luxo Jr.》 （1986年），講述一對母燈、子燈的故事【E3】。這一齣片，在1986年的圖像特別興趣組 (SIGGRAPH '86， Special Interest Group on Computer Graphics and Interactive Techniques) 中展出並獲獎。
到1990年，Pixar 準備就緒，製作第一部長篇3D電腦動畫電影。辦公室塞滿玩具的 Lasseter，提出故事︰讓無生命的玩具變得活躍。Catmull 贊成此想法，因為基於當時電腦硬件的限制，只有光滑的表面才能作渲染。
1991年，Pixar 與 Disney 動畫達成協議，籌備製作《反斗奇兵》【E4】。公映前夕，Steve Jobs 在 SIGGRAPH '95 發表主題演講，強調《反斗奇兵》的重大意義【E5】。
Click to enlarge (click again to close)點擊放大(再擊關閉)
Here are some examples of fantasy worlds in computer animations from Pixar (see posters above):
| year | animated movie | fantasy world | animation technology |
|------|-----------------|-----------------|------------------------|
| 1995 | Toy Story | Toys are alive when no one is looking | Characters have plastic faces (ok for toys) |
| 2003 | Finding Nemo | A fish in an aquarium can escape back to home | Underwater worlds, coral reef, deep ocean and harbour |
| 2004 | The Incredibles | A family of superheroes and superheroines | Strong muscles and half-covering long hair |
| 2012 | Brave | An enchanted forest with spells and curses | Bouncy and curly red hair swinging with body |
| 2015 | Inside Out | Emotions are characters inside your head | Bodies glowing with energy, to depict a mind world |
John Lasseter was not the only person dissatisfied with the Disney enterprise. Jeffrey Katzenberg, who was credited with reviving Disney's traditional animation in the 1990s, was bitterly disappointed when he was not promoted to a top job. He left in 1994, and with others formed DreamWorks.
In 1995, DreamWorks signed a co-production deal with Pacific Data Images, and started working on a new full-length computer animation: Shrek.
Shrek was initially a low-budget experimental project, as Katzenberg stubbornly adhered to traditional 2D hand-drawn animation. He persuaded animators from Disney to join DreamWorks to work on his planned 2D animated movie. Those animators not up to his standard were assigned to work on Shrek.
Katzenberg also wanted to change the story of Shrek as the original was too kid-oriented. He believed that both adults and children should enjoy a fairy tale. The final story was completely opposite to a typical Disney's fairy tale【E6】.
John Lasseter 並不是唯一對 Disney 企業不滿的人。 Jeffrey Katzenberg 曾是功臣，在1990年代復興 Disney 傳統動畫。但他對未能晉升為高層，感到非常失望。1994年離職後，與其他人一起成立 DreamWorks（夢工廠）。
1995年，DreamWorks 與 Pacific Data Images 簽約合作，開始製作全新長篇電腦動畫︰《史力加》。
《史力加》最初是個低成本的實驗項目，因為 Katzenberg 固執地堅持傳統2D手繪動畫。他說服 Disney 的動畫師加入 DreamWorks，製作策劃中的2D動畫電影。不符合他期望的動畫師，就被分配到製作《史力加》。
Katzenberg 要求更改《史力加》的故事，因為原著只討好小朋友。他認為童話故事應該是老少咸宜。最後故事版本，與典型的迪斯尼童話完全相反【E6】。
Click to enlarge (click again to close)點擊放大(再擊關閉)
Here are some examples of fantasy worlds in computer animations from DreamWorks (see posters above):
| year | animated movie | fantasy world | animation technology |
|------|-----------------|-----------------|------------------------|
| 2001 | Shrek | Ogre and donkey rescuing a princess in a castle | Modern fairy-tale world and a fire-shooting dragon |
| 2008 | Kung Fu Panda | Panda takes martial art lessons from five masters | Facial expressions, incredible fighting poses |
| 2009 | Monsters vs. Aliens | Girl turns into a giant on her wedding day | Chaos in a city under alien attack |
| 2010 | How to Train Your Dragon | Boy and dragon become flying partners in the sky | Design flying scenes from dragons's viewpoint |
| 2014 | Mr. Peabody and Sherman | Smart dog takes its time machine into adventures | World is in danger of annihilation when past meets present |
Not to be left behind, Disney Animation established a computer animation studio in 1990. They were eager to catch up, marketing under a new brandname Disney Digital 3-D.
In 2006, Disney acquired Pixar for $7.4 billion. Pixar would produce animated movies, to be distributed by Disney. Indeed, the board considered closing Disney Animation Studios for good.
Both Ed Catmull and John Lasseter were fans of classical Disney. They would regret the closure, so rejected the board's recommendation. Instead, they dedicated themselves to revitalizing Disney Animation Studios, by introducing new animation technology and making major changes in management.
In 2014, "Frozen" was launched by Disney. This was a refreshing masterpiece, smashing box-office records【E7】.
迪士尼動畫不甘後人，於1990年成立電腦動畫工作室。他們急起直追，以新品牌 Disney Digital 3-D 進行營銷。
2006年，Disney 出價74億美元併購 Pixar。動畫電影由 Pixar 製作，交 Disney 發行。事實上，董事局曾考慮，讓迪士尼動畫工作室，關門大吉。
Ed Catmull 和 John Lasseter 均是經典迪士尼迷，對關閉感到可惜，拒絕董事局的建議。相反，他們致力振興迪士尼動畫工作室，引入新動畫技術，人事進行大革新。
2014年，Disney 推出佳作《魔雪奇緣》，耳目一新，刷新票房【E7】。
Click to enlarge (click again to close)點擊放大(再擊關閉)
Here are some examples of fantasy worlds in computer animations from Disney (see posters above):
| year | animated movie | fantasy world | animation technology |
|------|-----------------|-----------------|------------------------|
| 2010 | Tangled | Princess born with magic hair is trapped in a high tower | Ever growing hair becomes outrageously long |
| 2014 | Frozen | Girl freezes everything she touches, hiding herself in ice castle | Instant freeze, heaps of snow and snowflakes |
| 2016 | Moana | Chief's daughter finds out her destiny, fulfilling a legend | Oceans and volcanoes are characters in the legend |
| 2019 | The Lion King (remake) | Young lion follows guidance to be king of jungle | Details of forest and jungle inhabitants |
| 2021 | Raya and the Last Dragon | Warrior princess protects a gem with magic belonging to a female sea dragon | Mythical form-morphing dragon and fighting tribes |
That's the beauty of animation!
This thrilling animation is a co-production by Pearl Studio【F1】 and DreamWorks.
The main character of the story is a Chinese teenage girl, helping a yeti to return home. The movie depicts an epic 3,000 mile journey from the bustling streets of Shanghai to the breathtaking Himalayan snowscapes.
Imagine the technical challenges in building digital models for the following scenes:
* the Shanghai night view from rooftop,
* the Shanghai shore fabulous night show,
* street-level view of cities and towns,
* the picturesque landscapes of China,
* and the precipitous Himalayas.
This travelogue of China follows famous postcard landmarks,
including the Yellow Mountain in southern Anhui,
the Lake of Thousand Islands, a man-made freshwater Qiandao Lake in Zhejiang,
the Gobi Desert, and the Leshan Giant Buddha in Sichuan.
They look so realistic and colorful,
but remember that they are all computed — that's math!
There are special effects, too, also computed:
* the characters launching a flight hanging on a giant dandelion,
* the yeti transforms a field of canola flowers into a floral tidal wave,
* the yeti and the teenagers riding the clouds that look like flying Koi fish,
* and the magical power of the violin with strings made from yeti's hair.
No wonder one of the animators said, "One scene took us six to seven months to properly create despite only being a two and a half minute scene in the finished film."
The voice for the teenage girl, Yi, is Chloe Bennet. Her real name is Chloe Wang（汪可盈）, as her father is Chinese.
The voice of Jin, the handsome friend of Yi, is Tenzing Norgay Trainor.
He is the grandson of Tenzing Norgay who, with Sir Edmund Hillary, was the first man to reach the summit of Mount Everest.
The voice for the magical yeti, Everest, is Joe Izzo. Everest does not talk, but he grunts and hums. Finding Everest's particular sound wasn't easy. As Joe explained,
"When we started, we realised Everest is so big. He's got a huge chest cavity, a huge mouth and he needed to sound a bit bigger." He added, "as big and loud and deep as I could sound, we needed a little help."
They found that help inside a vase on one of the editor's desks. A lot of the grunting and yeti screams were all created with Joe screaming into a vase — that's physics!
Everest’s look was designed to be unpredictable, covering him in a thick white coat of fluffy fur. Much of the effect came from DreamWorks’ proprietary renderer MoonRay, which helped give Everest’s fur a touchable quality 【F2】.
Walt Disney was a visionary innovator. His idea of making a full-length full-color animation feature was not taken seriously by the critics during production. They ridiculed it as "Disney's Folly"【G1】. However, he not only created a dream, but also turned the fairy tale worlds into theme parks!
Edwin Catmull was a computer scientist. His innovative PhD thesis and his subsequent contributions won him a share, with his former co-worker, of the 2019 Turing Award, "for their fundamental contributions to 3D computer graphics, and the revolutionary impact of these techniques on computer-generated imagery (CGI) in filmmaking and other applications."【G2】
John Lasseter was an animation artist. He summed up the concept of making 3D computer animation succinctly, "Art challenges technology, and technology inspires art."【G3】
I love animated movies, because each one is a beautiful example of transforming a story by calculus:
\[
\text{movie} = \int\partial\ \text{story}
\]
Life is like a drama. There is a saying, "Life is just a dream." We live in this dream everyday, and each day updates our lives:
\[
\text{life} = \int\partial\ \text{dream}
\]
Isn't life beautiful? Please listen to the theme song of Abominable.
After downloading to your laptop or smartphone,
try open and play (or simply by double clicking).
Most video players can handle mkv files.
You may need to 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.
下載到筆記本電腦或智能手機後，嘗試打開文件播放（或只是雙擊）。大多數視頻播放器可以處理 mkv 檔案，要弄清楚如何配合設置，以讀取字幕文件。如果有問題，請從 App Store 或 Google Play 或 Microsoft Store 中安裝 VLC，是免費視頻播放器。
【A1】How to Create Your Own Flipbook Animation by MasterClass, 4 November 2021.
Brief history of flipbook animation, and how to create one yourself.翻頁動畫的簡短歷史，以及如何自己製作翻頁動畫書。
【A2】Stop-motion animation定格動畫A good example is "Kubo and the Two Strings" in my webpage Dragon Boat 2021.很好的例子，是《酷寶：魔弦傳說》，在我的網頁 2021年 端午節 中。
【B1】The One That Started It All… The Making Of Snow White by Ben Simon, 26 April 2002.
An account of the early days of Walt Disney, the challenges of making the movie Snow White, and the public reception at its premiere.講述早期的 Walt Disney、製作電影《白雪公主》的挑戰，以及首映時公眾的反應。
Click to enlarge (click again to close)
點擊放大(再擊關閉)
【B2】The Man Behind Snow White And The Seven Dwarfs by William Stull, February 1938.
This was an article from the magazine American Cinematographer in 1938, right after the national release of Snow White. Most likely the author interviewed Walt Disney and his staff, getting inside information about work practices during production of the animation.1938年《白雪公主》全國上映後不久，《美國電影攝影師》雜誌刊登這篇文章。很有可能，作者訪問 Walt Disney 和工作人員，獲得動畫製作過程中實踐經驗和內部資料。
The Making of Snow White【39:03】
This 40-minute documentary provides fascinating insight into the events leading up to the development of this film.這套40分鐘的紀錄片，對製作此電影發展的事情，提供精闢的見解。
【B3】Snow White and the Seven Dwarfs - Opening Scene【2:59】
Review the first three minutes of Walt Disney's groundbreaking animation movie.回顧 Walt Disney 開創性動畫電影的頭三分鐘。
【B4】The Wonderful World of Disney Episodes There are 18 episodes available.《迪士尼的奇妙世界》，共有18集可供觀賞。
【C1】The Early Years for Pixar Co-founder Ed Catmull by Jay Rao and Jim Watkinson, 19 December 2014.
Ed Catmull's boyhood living room had two posters of his idols, Walt Disney and Albert Einstein. The first one drove him to art, and the second one drove him to science. Since there was no course on animation in universities, he studied a double-major in physics and computer science. Upon graduation, his dream was to make computer graphics so realistic that one day, he could make a movie entirely by computer.童年時代，Ed Catmull 的客廳掛上兩張偶像海報︰Walt Disney 和 Albert Einstein。前者讓他走向藝術，後者讓他走向科學。由於大學裡沒有動畫課程，他主修物理學和電腦科學。畢業後，他的夢想是︰把電腦圖形變得彬彬如生，以至終有一天，完全運用電腦製作電影。
【C2】The Imaginer by Kelley J.P. Lindberg, spring 2013.
University of Utah alum Ed Catmull has taken a path that melds science and artistic endeavor. This is a detailed account of his university days and his career afterwards.猶他大學校友 Ed Catmull 走的道路，致力融合科學和藝術。這篇文章，詳述他在大學的年代，及之後的事業發展。
【D1】3D animation pipeline: A Start-to-Finish Guide by Arash Naghdi abd Payam Adib, 2022.
A tutorial from Dream Farm Studios, a compnay offering 3D animation services. The word 'farm' refers to their hardware: an array of workstations devoted to heavy computations. This tutorial explains, in simple terms, each stage in the 3D animation production process.
Dream Farm Studios 提供3D動畫製作服務，這是公司的教程。「farm」（農場）一詞是指硬件：一組致力於繁重計算的電腦工作站。本教程簡單解釋3D動畫製作過程中每個階段。
【D2】Disney's practical guide to Path Tracing【9:32】cc
Path tracing is a method for generating digital images by simulating how light would interact with objects in a virtual world. The exposition is divided into seven chapters.路徑追踪方法，是模擬光線如何與虛擬世界中的對象互相交錯，來生成數碼圖像。解釋詳細，分有七節。
Disney's Practical Guide to Snow Simulation【6:55】cc
Things in the virtual world need simulation to look real. Environmental effects like water, smoke and fire are governed by equations in physics. Why not let computers do all the heavy computation to solve those equations? The software programs that do such computation are called simulators.虛擬世界中的事物，需要模擬才看似真實。流水、煙霧和火焰等環境效果，由物理方程操控。為什麼不讓電腦做所有繁重的計算，來解決這些方程呢？進行此類計算的軟件程式，稱為「模擬器」。
【D3】How Pixar Animates Human Characters | Movies Insider【14:13】cc<
Various techniques to show faces with features, hair that flows or curls, and muscles that look strong.運用各種技術，展示面部特徵、頭髮飄動或捲曲、以及強壯的肌肉。
How Pixar's Movement Animation Became So Realistic | Movies Insider【13:08】cc
This one shows how to animate fingers playing instruments.關於動畫製作，如何展示手指演奏樂器。
【D4】How Disney's Animation Evolved From 'Frozen' To 'Frozen II' | Movies Insider【13:28】cc
In the sequel Frozen II, animators updated Anna and Elsa's outfits from Frozen. They also figured out how to turn water, wind, fire, and rocks into living, breathing creatures.在續集《魔雪奇緣 II》中，動畫師更新了《魔雪奇緣》中 Anna 和 Elsa 的服飾。他們還想出，如何將海水、旋風、烈火和岩石，變成活生生的、具性格的生物。
Why Lighting Animated Movies Is So Complicated | Movies Insider【7:30】cc
Lighting is essential in 3D animated films for a few reasons: it tells the time of day, makes objects appear more lifelike, and even conveys the mood of a given moment. This is explained by animators from Pearl Studio, who produced Netflix's "Over the Moon".在3D動畫電影中，彩光照明必不可少。原因有︰顯示日夜時間，物體看來更逼真，甚至傳達特定時刻的情緒。東方夢工廠的動畫師，解釋箇中情況。她們製作 Netflix 《飛奔去月球》（Over the Moon）。
【E1】A Computer Animated Hand (1972) HQ【4:46】
In 1972, Ed Catmull made an animated version of his left hand. This clip was eventually picked up by a Hollywood producer and incorporated in the 1976 movie Futureworld. In December 2011, this short film was selected for preservation in the National Film Registry of the Library of Congress.1972年，Ed Catmull 製作自己左手的動畫版本。這段剪輯，最終被荷里活製片人注意到，納入1976年的電影《未來世界》。2011年12月，這齣短片獲選，保存在美國國會圖書館國家電影登記處。
【E2】From Dream to 3-D Reality: The Fascinating Origin of Pixar by Matt Blitz, 13 January 2014.
Before making animated movies, Pixar was a high-end computer hardware company. The tale of the most profitable and critically adored animation studio in history is one filled with financial difficulties, struggling to survive. It all started with a dream of Ed Catmull, and he kept the dream alive until the dream came true.在製作動畫電影之前，Pixar 只是一間高檔電腦硬件公司。成為史上最賺錢、最受追捧的動畫工作室，它的演變是一個充滿財務困難、掙扎求存的故事。這一切，始於 Ed Catmull 的夢想。他一直保持夢想，直到夢想成真。
【E3】Pixar Shorts Collection Luxo Jr 1986 YouTube【2:06】
Written and directed by John Lasseter, this two-minute film is the source of Luxo Jr., the mascot of Pixar. With Ed Catmull, they worked around the clock to finish the short film for the 1986 SIGGRAPH. Ultimately, the film took four and a half months to be completed.這齣兩分鐘電影，由 John Lasseter 編劇和導演，是 Pixar 吉祥物 Luxo Jr. 的來源。與 Ed Catmull 一起，他們夜以繼日工作，為趕及1986年 SIGGRAPH 展出短片。最終，花了四個半月才完成。
【E4】Toy Story Celebrates Its 20th Anniversary in Style by Karl Cohen, 19 November 2015.
Creators of Toy Story recounted how they came together to work towards a goal: making the first 3D computer animated movie.《反斗奇兵》各創作者，講述他們如何齊心協力，實現目標︰製作第一部3D電腦動畫電影。
【E5】Steve Jobs at Siggraph (1995)【26:21】cc
Steve Jobs talked about three things: the first is a centenary, the second is scale and complexity, and the third is a place in history.Steve Jobs 談及三要點︰第一是百週年紀念，第二是規模和復雜性，第三是在歷史佔一席位。
【E6】How Jeffrey Katzenberg's Reluctant Embrace of 'Shrek' Helped Shape Modern 3D Animation By Anthony Vieira, 11 March 2022.
Jeffrey Katzenberg insisted on making 2D hand-drawn animations instead of 3D computer animations, even though the former were box-office disasters. How did he change his minid to give 'Shrek' a go, and turned the fate of DreamWorks?Jeffrey Katzenberg 堅持製作2D手繪動畫，而不是3D電腦動畫，儘管前者票房不濟。他如何改變自己的想法，嘗試出品《史力加》，並扭轉 DreamWorks 的命運？
【E7】Frozen: This Disney Princess Movie Is Thaw-some by Richard Corliss, 23 November 2013.
The author takes a provoking view that the story of Frozen might be a metaphor for the friendly rivalry between Walt Disney Studios and Pixar.作者提出發人深省的觀點，即《魔雪奇緣》的故事可能是隱喻，象徵 Walt Disney 工作室與 Pixar 之間的友誼競賽。
【F1】Pearl Studio﹙東方夢工廠﹚
Formerly Oriental DreamWorks, this was founded as a Chinese-American joint venture in 2012 by DreamWorks Animation and Chinese investment companies. The studio produced 1/3 of "Kung Fu Panda 3" in 2016. "Abominable" is their first original animation.「明珠工作室」現稱「東方夢工廠」，由 DreamWorks Animation 與中國投資公司於2012年成立，是中美合資企業。工作室在2016年製作《功夫熊貓3》的三份之一，《雪人奇緣》是他們的第一部原創動畫。
【F2】The Tech Behind DreamWorks' Abominable【3:24】cc
This BBC video shows the digital models for computer animation, including the yeti Everest, and the amount of computation.這段 BBC 視頻，展示電腦動畫的數碼模型，包括雪人「大毛」，以及其中的計算量。
Abominable (2019) - The Magic Violin Scene【3:14】
Standing on the hands of Leshan Buddha, Yi plays her yeti-magic-infused violin.《雪人奇緣》中，阿怡站在樂山大佛的手上，演奏融入雪人魔法的小提琴。
Abominable (2019) - Saving Everest Scene【2:21】
Yi uses her magical violin to save the captured Everest.《雪人奇緣》中，阿怡用她的神奇小提琴，營救被擒的大毛。
【G1】Disney's Folly: The Profound Importance of 'Snow White' by Becky Pitt, 2017.
Read about why the production of Snow White was nearly a disaster. Walt Disney’s daughter Diane recalled, "Dad says that while Snow White was fun, it was a ding-dong, photo-finish race with their budget. He was running out of money, and still had a lot to do when his deadline loomed up in December." It was said that the final print of the film from Technicolor arrived at the theatre only a few hours before the movie was scheduled to begin.暸解為什麼《白雪公主》的製作、幾乎是一場災難。Walt Disney 的女兒 Diane 憶述︰「爸爸說，雖然《白雪公主》很有趣，但製作預算和實際支出，是一場競賽，幾乎叮噹馬頭，要影相決勝負。他的錢財，快將耗盡。十二月來臨，最後期限迫在眉睫，他還有很多事情，尚未完成。」據說，Technicolor 公司的終極版影片，僅在預定放映前數小時，才送抵電影院。
【G2】CACM Jun. 2020 - 2019 ACM A.M. Turing Award【5:29】 cc
Edwin Catmull and Patrick Hanrahan were the recipients of the 2019 Association for Computing Machinery (ACM) Turing Award. This Communications of the ACM (CACM) feature chronicles how these two extraordinary innovators carved their paths in the earliest days of the computer graphics field, and worked together to create tools that would forever transform the way moving images are brought to life. See mext item for the award announcemnt.2019年計算機協會(ACM = Association for Computing Machinery)的圖靈獎（Turing Award）得獎者，是 Edwin Catmull 和 Patrick Hanrahan。這段 ACM 通訊 (CACM = Communications of the ACM) 專題，講述這兩位非凡的創新者，如何在電腦繪圖領域的初期，開拓他們的道路，並共同創建作業工具。這些工具，將永遠改變動畫變得活生生。獲獎公告，參考下一項。
Pioneers of Modern Computer Graphics Recognized with ACM A.M. Turing AwardOfficial announcement of the 2019 Turing Award, descrbing the innovations of Catmull and Hanrahan in detail. They paved the way for today’s 3D animated films. They designed and built the animation rendering system RenderMan, which was widely used in Hollywood movies such as Titanic.2019年圖靈獎（Turing Award）的官方公告，詳述 Catmull 和 Hanrahan 之創新貢獻。他們為今天的3D動畫電影，開拓坦途。他們設計並構建的動畫渲染系統 RenderMan，廣泛使用在荷里活電影中，例如《鐵達尼號》。
【G3】John Lasseter On the Future Of Animation【1:51】cc
On 21 May 2012, John Lasseter talked about the future of animation at The Academy's Development of the Digital Animator in Samuel Goldwyn Theater.2012年5月21日，Samuel Goldwyn 劇院舉行「電影學院數碼動畫師的發展」。John Lasseter 出席會議，談論動畫的未來。
Click to enlarge (click again to close)
Click to enlarge (click again to close)
Click to enlarge (click again to close)
Click to enlarge (click again to close)
Click to enlarge (click again to close)
Click to enlarge (click again to close)
Click to enlarge (click again to close)
Full movie in English, without subtitle. See next item for subtitles.
全高清電影，英語無字幕。若要字幕，請參閱下一項。
Click to enlarge (click again to close)
There are 18 episodes available.
《迪士尼的奇妙世界》，共有18集可供觀賞。
Formerly Oriental DreamWorks, this was founded as a Chinese-American joint venture in 2012 by DreamWorks Animation and Chinese investment companies. The studio produced 1/3 of "Kung Fu Panda 3" in 2016. "Abominable" is their first original animation.
「明珠工作室」現稱「東方夢工廠」，由 DreamWorks Animation 與中國投資公司於2012年成立，是中美合資企業。工作室在2016年製作《功夫熊貓3》的三份之一，《雪人奇緣》是他們的第一部原創動畫。
