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Computer Animation  
  
953   01:43 صباحاً   date: 6-1-2016
Author : So You Want To Learn About Animation
Book or Source : So You Want To Learn About Animation
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Even a basic understanding of the technology, the complex mathematics (expedited by computer software), and the hours of manpower behind the making of a movie such as Toy Story (1995) or A Bug’s Life (1998) could change the way a viewer watches computer-animated movies. Knowing more about computer animation helps one better appreciate scenes in which Buzz and Woody careen down the street, passing other cars and whizzing by trees in a background so near to real life that it is easy to forget that the entire movie is fully computer animated.

Animation

The word “animate” means “to give life to,” and animating is the process of moving something that cannot move itself. Computer animation creates the illusion of movement through a succession of computer-generated still images. Fully appreciating the high-speed efficiency and the complexity of computer animation requires a basic understanding of how animation was achieved before the days of the computer.

In traditional animation, sequential images were painted or hand-drawn on paper or plastic sheets called “cels.” They were then filmed, one frame at a time, and played back at high speeds. This tricked the eye-brain response into perceiving movement of the characters and other objects displayed in the drawings, thus creating the illusion of movement.

The underlying process involved in preparing a computer-animated production has not changed much from the process of traditional hand-drawn animation. What is different is the speed with which it is done. It would take many, many pages of hand-written mathematical equations to illustrate the work that a computer does in a fraction of a second.

The Computer Animation Process

Computer animation begins with an idea, followed by the preliminary story. Next, the action scenes are sketched out in frames, with corresponding written explanations, thereby creating a storyboard. Then the detailed story is developed, the sound track is completed, and the key frames are identified.

Another set of animators will later do the “in-betweening,” which is the work of determining—through mathematical computations—a series of midpoint locations between key frames at which images must be  interpolated to create more fluid movement.

Computer animation depends on a combination of scientifically based, mathematically calculated and produced steps. Computer animators focus on making three main determinations:

• how to make a single object on a two-dimensional screen look realistic;

• how to make the object’s entire environment look real; and

• how to add realistic movement to the objects and scenes.

The clever animator knows the effects yielded by a range of “tricks of the trade”—all of which are based on scientific knowledge of perception.

Computer animation capitalizes on a number of principles of human perception in order to trick the viewer into believing that the images seen on a flat, two-dimensional screen are three-dimensional: that is, in addition to height and width, the picture also has depth. Whereas two-dimensional images are useful in providing certain types of information, such as simple directions found in billboards or signs, three-dimensional images provide a

great deal more information, and the effort required to provide this information is considerably greater.

The Illusion of Surface.

 A three-dimensional image begins as a geometric shape, or a combination of shapes—squares, rectangles, parallelograms,  circles,  rhomboids, and especially triangles. An image of a human body might require a combination of thousands of shapes put together into a structure called the wireframe, which in its early development may be recognizable only as the symbol of whatever it will eventually depict. Next, the wireframe is given color and surface texture, and the effects of lighting, or reflectance, is determined. The wireframe surfaces must be lit from all possible angles to create the desired effect. The use of shading and shadow is especially important in enhancing the appearance of reality. Shading is what makes a ball look round or the folds in a blanket look soft and deep, whereas shadow produces the illusion of weight. The variations of these features,  used according to mathematical models, can also give the impressions of warm and cold, soft and hard, smooth, scaly, and so forth.

The Illusion of Distance.

Computer animators use the age-old knowledge of perception in creating an illusion of distance. Animators use “single point perspective,” which is an everyday occurrence in which objects at a distance appear to  converge to a single point just before they fade from view. By calculating the relative sizes of objects to make some appear nearer (larger) and others farther away (smaller), animators can mimic this natural principle of perception.

Depth of field is used to diminish the size and clarity of objects at greater and greater distances from the viewer. In anti-aliasing, the computer adds grayed-out pixels (the smallest individual picture elements on the computer screen) to smooth out the naturally angular shapes that comprise computer images, thus creating the fuzzy illusion associated with distance. For example, trees at a distance appear to be smaller and fuzzier than

at close range.

The Illusion of Movement.

An animator knows that the retina of the human eye can retain an image for about 1/24th of a second. So if images, or frames, are run in sequence before the viewer’s eyes at a rate of twenty-four frames per second, the illusion of continuous movement and action will be produced. The addition of “blurring,” produced by speeding up the exposure of images to thirty or even sixty frames per second, heightens the illusion of speed. An example is seeing a residual blur of a car that has just sped away. The complexity of the task, of course, is multiplied when groups of images must be animated to move together as a body and yet maintain each individual’s unique appearance and behavior.

  The massive wildebeest stampede in The Lion King (1994), for example, used a computer to replicate the hand-animated wildebeest from many different angles, creating differences in appearance among them. Similarly, in the crowd scene in The Hunchback of Notre Dame (1996), a number of base characters were programmed into the computer. A program called CROWD then scrambled actions randomly so that the characters in the crowd were doing different things: laughing, clapping, jumping, and so forth.

The Future of Computer Animation

Although computer animation is often thought of in terms of video games and high-action animated movies, it is easy to overlook its many other applications. In fact, computer animation is used extensively in crime investigation, and applications are being developed steadily for fields such fluid dynamics, thermodynamics, meteorology (for the prediction of severe storms and other weather patterns), and the legal system (to reconstruct crime scenes and accidents).

Though remarkable strides have been made in the field of computer animation, technology is currently not able to keep up with the demands for even faster and more powerful computers. The movie industry, in particular, continues searching for ways to increase the speed of production. Although current technology has cut huge chunks of time out of production, still more power and speed are needed.

Computer graphics pioneer Matt Elson predicts that in the first half of the twenty-first century, three-dimensional characters will be created that will have the ability to “think” and to interact with their environments. These virtual characters will be able to understand and to respond to human speech and will be able to perform tasks and take care of many of the details of everyday human life. Elson predicts that when computer and software companies across the world pool their discoveries, a digital character with a “mind of its own” will become a “real” part of the everyday world of its human counterparts.

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Reference

“So You Want To Learn About Animation?” <http://www.art.uiuc.edu/local/anle/ ANIMATION/animation_ptour.html>.

Thalmann, Nadia Margaret, and Daniel Thalmann. “What Is Computer Animation?” <http://miralabwww.unige.ch/ARTICLES/HBCS96.html>.




الجبر أحد الفروع الرئيسية في الرياضيات، حيث إن التمكن من الرياضيات يعتمد على الفهم السليم للجبر. ويستخدم المهندسون والعلماء الجبر يومياً، وتعول المشاريع التجارية والصناعية على الجبر لحل الكثير من المعضلات التي تتعرض لها. ونظراً لأهمية الجبر في الحياة العصرية فإنه يدرّس في المدارس والجامعات في جميع أنحاء العالم. ويُعجب الكثير من الدارسين للجبر بقدرته وفائدته الكبيرتين، إذ باستخدام الجبر يمكن للمرء أن يحل كثيرًا من المسائل التي يتعذر حلها باستخدام الحساب فقط.وجاء اسمه من كتاب عالم الرياضيات والفلك والرحالة محمد بن موسى الخورازمي.


يعتبر علم المثلثات Trigonometry علماً عربياً ، فرياضيو العرب فضلوا علم المثلثات عن علم الفلك كأنهما علمين متداخلين ، ونظموه تنظيماً فيه لكثير من الدقة ، وقد كان اليونان يستعملون وتر CORDE ضعف القوسي قياس الزوايا ، فاستعاض رياضيو العرب عن الوتر بالجيب SINUS فأنت هذه الاستعاضة إلى تسهيل كثير من الاعمال الرياضية.

تعتبر المعادلات التفاضلية خير وسيلة لوصف معظم المـسائل الهندسـية والرياضـية والعلمية على حد سواء، إذ يتضح ذلك جليا في وصف عمليات انتقال الحرارة، جريان الموائـع، الحركة الموجية، الدوائر الإلكترونية فضلاً عن استخدامها في مسائل الهياكل الإنشائية والوصف الرياضي للتفاعلات الكيميائية.
ففي في الرياضيات, يطلق اسم المعادلات التفاضلية على المعادلات التي تحوي مشتقات و تفاضلات لبعض الدوال الرياضية و تظهر فيها بشكل متغيرات المعادلة . و يكون الهدف من حل هذه المعادلات هو إيجاد هذه الدوال الرياضية التي تحقق مشتقات هذه المعادلات.