3d graphics and operating principles. The Evolution of the Pixel: Little-Known Facts about the History of Computer Graphics. Creating animation and live action appearances

You are probably reading this article on the screen of a computer monitor or mobile device - a display that has actual sizes, height and width. But when you watch, for example, the cartoon Toy Story or play the game Tomb Raider, you are looking at a three-dimensional world. One of the most amazing things about a 3D world is that the world you see could be the world we live in, the world we will live in tomorrow, or a world that lives only in the minds of the movie or game creators. And all these worlds can appear on only one screen - this is at least interesting.

How does a computer trick our eyes into thinking that when we look at a flat screen we see the depth of the picture being presented? How do game developers ensure that we see real characters moving around in a real landscape? Today I will tell you about visual tricks used graphic designers, and how all this is developed and seems so simple to us. In fact, everything is not simple, and to find out what 3D graphics is, go to the cut - there you will find a fascinating story, which, I am sure, you will immerse yourself in with unprecedented pleasure.

What makes an image three-dimensional?

An image that has, or appears to have, height, width, and depth is three-dimensional (3D). A picture that has height and width but no depth is two-dimensional (2D). Remind me where you find two-dimensional images? - Almost everywhere. Remember even the usual symbol on the toilet door, indicating a stall for one gender or another. The symbols are designed in such a way that you can recognize and recognize them at a glance. That's why they only use the most basic forms. More detailed information about a character can tell you what kind of clothing that character wears. little man, hanging on the door, or hair color, for example, the symbolism of the women's restroom door. This is one of the main differences between the way 3D and 2D graphics are used: 2D graphics are simple and memorable, while 3D graphics use more detail and pack significantly more information into a seemingly ordinary object.

For example, triangles have three lines and three angles - all that is needed to tell what the triangle consists of and what it represents in general. However, look at the triangle from the other side - a pyramid is a three-dimensional structure with four triangular sides. Please note that in this case there are already six lines and four corners - this is what the pyramid consists of. See how an ordinary object can become three-dimensional and contain much more information needed to tell the story of a triangle or pyramid.

For hundreds of years, artists have used some visual tricks that can make a flat 2D image look like a real window into the real world. 3D world. You can see a similar effect in a regular photograph that you can scan and view on a computer monitor: objects in the photograph appear smaller when they are further away; objects close to the camera lens are in focus, which means, accordingly, everything behind the objects in focus is blurry. Colors tend to be less vibrant if the subject is not as close. When we talk about 3D graphics on computers today, we're talking about images that move.

What is 3D graphics?

For many of us, gaming on a personal computer, mobile device, or an advanced gaming system in general is the most striking example and common way through which we can contemplate 3D graphics. All of these computer generated games and cool movies must go through three basic steps to create and present realistic 3D scenes:

1. Creating a virtual 3D world
2. Determining which part of the world will be shown on the screen
3. Determining what a pixel on the screen will look like so that the full image appears as realistic as possible

Creating a virtual 3D world
The virtual 3D world is, of course, not the same as the real world. Creating a virtual 3D world - complex work on computer visualization of a world similar to the real one, for the creation of which it is used a large number of tools and which implies extremely high detail. Take, for example, a very small part of the real world - your hand and the desktop underneath it. Your hand has special qualities that determine how it can move and appear externally. The finger joints bend only towards the palm, and not opposite it. If you hit the table, no action will happen to it - the table is solid. Accordingly, your hand cannot pass through your desktop. You can prove that this statement is true by looking at something natural, but in the virtual three-dimensional world things are completely different - in the virtual world there is no nature, there are no natural things like your hand, for example. Objects in the virtual world are completely synthetic - these are the only properties given to them using software. Programmers use special tools and design 3D virtual worlds with extreme care to ensure that everything behaves in a certain way at all times.

How much of the virtual world is shown on the screen?
At any given time, the screen shows only a tiny part of the virtual 3D world created for the computer game. What is shown on the screen are certain combinations of ways in which the world is defined, where you make decisions about where to go and what to see. No matter where you go - forward or backward, up or down, left or right - the virtual 3D world around you determines what you see when you are in a certain position. What you see makes sense from one scene to the next. If you look at an object from the same distance, regardless of direction, it should appear high. Every object must look and move in such a way that you believe that it has the same mass as the real object, that it is as hard or soft as the real object, and so on.

Programmers who write computer games, put a lot of effort into developing 3D virtual worlds and making them so that you can wander around without encountering anything that makes you think, “That couldn't happen in this world!” The last thing you want to see is two solid objects that can pass right through each other. This is a stark reminder that everything you see is a sham. The third step involves at least as many more calculations as the other two steps and must also occur in real time.

On the left is computer graphics, on the right is a mocap actor

Lighting and perspective

When you enter a room, you turn on the light. You probably don't spend a lot of time wondering how it actually works and how the light comes from the lamp and travels around the room. But people working with 3D graphics have to think about this because all the surfaces and surrounding wireframes and things like that need to be lit. One method, ray tracing, involves sections of path that light rays take as they leave a light bulb, bounce off mirrors, walls and other reflective surfaces, and finally land on objects with varying intensities from different angles. This is difficult, because one light bulb can produce one beam, but in most rooms several light sources are used - several lamps, ceiling lamps(chandeliers), floor lamps, windows, candles and so on.

Lighting plays a key role in two effects that give the appearance, weight, and external solidity of objects: obscuration and shadows. The first effect, shading, is where more light falls on an object from one side than from the other. The shading gives the subject a lot of naturalism. This shading is what makes the folds in the blanket deep and soft and the high cheekbones appear striking. These differences in light intensity reinforce the overall illusion that an object has depth as well as height and width. The illusion of mass comes from the second effect - shadow.

Solids cast shadows when light falls on them. You can see this when you observe the shadow that a sundial or tree casts on the sidewalk. Therefore, we are accustomed to seeing real objects and people casting shadows. In 3D, shadow again reinforces the illusion, creating the effect of being in the real world rather than in a screen of mathematically generated shapes.

Perspective
Perspective is one word that can mean many things, but actually describes a simple effect that everyone saw. If you stand on the side of a long, straight road and look into the distance, it appears as if both sides of the road converge at one point on the horizon. Also, if trees are close to the road, trees further away will appear smaller than trees closer to you. In fact, it will appear that the trees converge at a certain point on the horizon formed near the road, but this is not the case. When all the objects in a scene appear to end up converging on one point in the distance, this is perspective. There are many variations of this effect, but most 3D graphics uses the single point of view that I have just described.

Depth of field

Another optical effect successfully used to create three-dimensional graphic objects is depth of field. Using my example with trees, in addition to the above, another interesting thing happens. If you look at trees close to you, trees further away will appear to be out of focus. Film directors and computer animators use this effect, depth of field, for two purposes. The first is to enhance the illusion of depth in the scene the user is viewing. The second purpose is that directors' use of depth of field focuses their attention on the subjects or actors that are considered most important. To draw your attention to someone other than the film's heroine, for example, a "shallow depth of field" may be used, where only the actor is in focus. A scene that is designed to give you a full impression will instead use "deep depth of field" to keep as many objects as possible in focus and thus visible to the viewer.

Smoothing

Another effect that also relies on tricking the eye is anti-aliasing. Digital graphics systems are very good at creating crisp lines. But it also happens that diagonal lines have the upper hand (they appear quite often in the real world, and then the computer reproduces lines that are more reminiscent of ladders (I think you know what a ladder is when you examine the image object in detail)). So, to trick your eye into seeing a smooth curve or line, the computer can add certain shades of color to the rows of pixels surrounding the line. This " gray The pixels are what the computer deceives your eyes, and you, meanwhile, think that there are no more jagged steps. This process of adding extra colored pixels to trick the eye is called anti-aliasing, and it is one of the techniques that are manually created by 3D computer graphics. Another challenging task for a computer is creating 3D animation, an example of which will be presented to you in the next section.

Real examples

When all the tricks I've described above are used together to create a stunningly real scene, the result lives up to the effort. The latest games, movies, and machine-generated objects are combined with photographic backgrounds to enhance the illusion. You can see amazing results when you compare photos and a computer generated scene.

The photo above shows a typical office that uses the sidewalk as an entrance. In one of the following photographs, a simple plain ball was placed on the sidewalk and the scene was photographed. The third photograph represents the use of a computer graphics program, which created a ball that actually does not exist in this photograph. Can you tell there are any significant differences between these two photographs? I think no.

Creating animation and live action appearances

So far we've looked at tools that make any digital image appear more realistic - whether the image is a still or part of an animation sequence. If it's an animated sequence, then the programmers and designers will use even more different visual tricks to create the appearance of "live action" rather than computer-generated images.

How many frames per second?
When you go to see a blockbuster movie at the local cinema, the sequence of images called frames runs at 24 frames per second. Since our retinas retain an image for slightly longer than 1/24 of a second, most people's eyes will blend the frames into one continuous image of movement and action.

If you don't understand what I just wrote, let's look at it this way: this means that each frame of a movie is a photograph taken at a shutter speed (exposure) of 1/24 of a second. Thus, if you look at one of the many frames of a racing movie, you will see that some of the racing cars are "blurred" because they were driven at high speed while the camera was open. This blurriness of things created by fast movement is what we are used to seeing, and it is part of what makes an image real to us when we look at it on a screen.

However, digital 3D images are not photographs after all, so no blurring effect occurs when the subject moves in the frame during shooting. To make images more realistic, blur must be explicitly added by programmers. Some designers believe that it takes more than 30 frames per second to "overcome" this lack of natural blur, which is why games have been pushed to the next level - 60 frames per second. While this allows each individual image to appear in great detail and display moving objects in smaller increments, it significantly increases the number of frames for a given animated action sequence. There are other certain pieces of imagery where accurate computer rendering must be sacrificed for the sake of realism. This applies to both moving and stationary objects, but that's a completely different story.

Let's come to the end

Computer graphics continues to amaze the whole world by creating and generating a wide variety of truly realistic moving and non-moving objects and scenes. From 80 columns and 25 lines of monochrome text, graphics have advanced significantly, and the result is clear - millions of people play games and run a wide variety of simulations with today's technology. New 3D processors will also make their presence felt - thanks to them, we will be able to literally explore other worlds and experience things we never dared to try before. real life. Finally, back to the ball example: how was this scene created? The answer is simple: the image has a computer-generated ball. It's not easy to say which of the two is genuine, is it? Our world is amazing and we must live up to it. I hope you found it interesting and learned another piece of interesting information.

Those involved in the development of 3D graphics know very well that success in mastering this field depends solely on patience. It is impossible to master this science “at once”; this requires long-term preparation. Using trial and error, reading a lot of educational literature, after repeated tedious waiting for the final scene to be rendered, the insight finally comes: “So this is how it turns out it should have been done!”

Like an athlete honing his skills on sports equipment, a computer graphics designer uses the same template designs over and over again to help him understand the intricacies of working with the program. Familiar pictures and models have been used for testing various functions of the 3D editor for so long that they seem to be quite ordinary tools. Meanwhile, many of them are not at all similar to “standard” products. A teapot model, a 3D monkey head and other strange things - where did they come from?

Many believe that the presence of such unusual models as Suzanne or Teapot in programs for developing 3D graphics is a brilliant find of the developers. Indeed, unlike regular simple objects such as a sphere, cylinder, cube or cone, models with unusual geometry look more natural. There are more of them complex shape allows you to quickly detect deficiencies in lighting and materials. These objects are very convenient to experiment with and practice modeling.

⇡ The difficult life of a simple teapot

The fate of some things sometimes develops very unusually. When Martin Newell and his wife Sandra purchased a teapot from a department store in Salt Lake City in 1974, they could not imagine that in the future the whole world would literally know about this thing.

It was the most ordinary ceramic teapot produced by the German company Melitta. A very simple shape - slightly rounded, with a lid. There wasn't even any design or pattern on it - just a smooth white teapot.

Newell worked on developing rendering algorithms for a graphics editor at the University of Utah. This is where the name of the teapot came from; it began to be called the “Utah teapot.” Interestingly, the teapot model was originally accompanied by a set of cups and teaspoons. It looked like this.

Then the tea set models became confused, and only one teapot remained. The most attentive users probably noticed that, in comparison with the teapot from the 3ds max program, the proportions of the original Utah teapot are somewhat different.

That's right - the original object is slightly higher than the computer model. Why is that? The “parents” of the first computer model themselves are confused in their explanations. Most likely, the reason is that the frame buffer on the computer Newell was working with had non-square pixels. Instead of distorting the image, Martin asked his colleague Jim Blinn to adjust the scale of the model to eliminate stretched deformations. Jim himself claims that they simply liked the vertically scaled shape of the teapot, which they used in a demonstration in their laboratory.

The teapot has become a favorite object of 3D graphics developers. Somehow, imperceptibly, they began to use it wherever possible. For example, Commodore CBM computers sold in the early 1980s had the Grafikdemo demo program installed. Having launched it, the user could see the frame of the teapot on the screen. This base could be rotated using the keyboard, viewed from all sides. Such simple manipulations were supposed to make a strong impression on users and persuade a potential buyer to make an expensive purchase.

The teapot could also be seen in the popular 3Dpipes screensaver for Windows.

He also appeared every now and then in various 3D animations - for example, in the famous Pixar film Toy Story, where the main character drinks tea from Newell's teapot.

Even the cartoon Homer Simpson in one of the episodes of The Simpsons series suddenly acquired a third dimension, and immediately the Utah teapot came into the frame (for fans, the sixth episode of the seventh season of Treehouse of Horror VI).

And the Utah teapot (after a little editing, it changed its shape) came into the frame while watching another Pixar film, “Monsters Inc.”

By the way, Pixar studio also has a funny tradition. Every year at the next Siggraph exhibition they give away souvenir Utah teapots - walking toys promoting the RenderMan rendering engine. Usually these teapots are packed in a tea box. A wonderful souvenir of the exhibition for a 3D lover.

The three-dimensional model of a teapot has become the hallmark of one of the most popular 3D editors - Autodesk 3ds max. In this program, any user can easily create a teapot, even those who have never done 3D modeling.

Typically, ceramic dishes do not last long. But this rule does not work in the case of Newell's teapot. Not only is it still in excellent condition, but it has also passed into the public domain, so to speak. The owner donated it to the Boston Computer Museum, where it remained until 1990. This exhibit can currently be found at the Computer History Museum in Mountain View, California.

From time to time, the famous teapot travels to various events - like the Siggraph exhibition. Despite his advanced years, he looks clean, shiny and suspiciously new. And although the owners of the rarity convince us that this is the very same teapot with which the history of 3D animation began, given the distances it had to move, it is possible that it could have been secretly replaced by another copy, because similar models are still sold in large quantities.

⇡ Stanford rabbit

For a long time after the appearance of the Utah teapot, 3D graphics developers had no alternative. Need to test rendering? Of course, a Newwell kettle is used. But in the nineties the situation changed slightly. New tools have appeared for 3D modeling and new models for testing. Stanford University researchers Greg Turk and Marc Levoy got involved.

At Easter in 1994, Greg walked down University Avenue and stopped into a store that sold decorative items for the home and garden. There he saw a collection of clay rabbits. He really liked the terracotta color of the red clay, and Turk came up with the idea that this figurine would be ideal for 3D scanning and use in 3D experiments.

“If I had known that this rabbit was so popular, I would have bought them all!” - Greg said a few years later. He purchased this rabbit and brought it to the laboratory, where, together with Mark, they digitized its shape. The rabbit had only one drawback - there were holes in its geometry. To simplify the polygon mesh, Greg simply patched them in by hand. The model of the Stanford rabbit, which was obtained after digitizing the figurine, contained 69,451 triangular surfaces, while the original figurine itself was 19 centimeters in height.

Since then, anyone can download this model directly from the Stanford University website.

In addition to the rabbit, there are many more models posted in the Stanford repository, many of which have also become very popular in the 3D graphics communities. Some of the free 3D models available for download include a happy Buddha figurine, a popular Chinese dragon, a beautiful Thai statue, and so on.

⇡ Monkey in Blender

The Blender 3D editor has no analogues. This is the only free professional package for creating 3D graphics that can compete more or less on equal terms with such “whales” as Maya or Lightwave.

Open source, cross-platform and enormous modeling capabilities - we can talk about the advantages of this program for a very long time. The developers have done everything possible to ensure that this program is in no way inferior to its commercial counterparts. And as if in response to the Utah teapot, Blender integrated its own “non-standard” object - a monkey named Suzanne.

The model of this monkey has a not very complex, but non-trivial geometry, which is ideal for test scenes and studying rendering settings. This is a low-poly model consisting of 500 surfaces.

The chimpanzee head first appeared in Blender 2.25. It was then, in January-February 2002, that it became clear that the NaN company, which was promoting the then paid 3D editor Blender, was bankrupt, and therefore would not be able to further develop this project. Its programmers added a monkey as a kind of character easter egg in the latest release of the program created by NaN. After this, the Blender license was changed to the GNU GPL, money was raised from creditors, and the 3D editor became free.

The famous monkey was modeled by Willem-Paul van Overbruggen, also known as SLiD3. He gave the name, taking it from a very specific comedy by Kevin Smith, Jay and the Silent Bob Strike Back. This film featured an orangutan named Suzanne.

Suzanne has become a real symbol of the free 3D editor. In 2003, a special competition was even established for artists working in Blender. The annual competition is called Suzanne Awards, and the winners are awarded a figurine of Suzanne the monkey as a prize.

⇡ Cornell box: experiments with light

One of the most important stages work on a three-dimensional scene - visualization. And here, it must be said, not everything depends on the user. In some cases, even a thorough knowledge of rendering parameters is not a guarantee of highly realistic images. The quality of the final image is determined by the visualization conditions and, most importantly, the lighting calculation algorithm.

In the real world, everything is governed by physical processes. The laws of optics, as well as the properties of materials, determine the picture of the world around us. Glass objects are perceived by our eyes as transparent, lemon peel appears embossed, and icy frost appears matte. The 3D visualization algorithm used for rendering tries to replicate all these phenomena and material properties by simulating physical processes. However, the problem is that this algorithm is imperfect and, like any school physics problem, uses many assumptions and conventions.

For example, the simplest principle for calculating shadows is tracing. It only gives an idea of ​​where the contour of the cast shadow will be. However, in real life, shadows are not always sharp - most often there is multiple re-reflection of light, when the beam is reflected several times from objects, transferring the color of neighboring objects to other areas and making the shadows “soft”. In 3D graphics, this property is described by global illumination algorithms.

In 1984, a team of scientists in the graphics department at Cornell University was developing new light tracing algorithms. Their work was called “Modeling the interaction of light with diffuse surfaces.” For the average person, this name will not mean anything, but a 3D graphics specialist will unmistakably guess in this phrase one of the principles for calculating light in a 3D scene - “global illumination”. In the same year, at the popular Siggraph exhibition, Cornell University specialists demonstrated the advantage of their system using the example of a simple three-dimensional scene - a hollow cube, inside of which the simplest primitives were located.

This cube played the role of a room, an enclosed space, and served as a simplified model for simulating the realistic propagation of light. The model with a box, called the Cornell box, is extremely simple, the light in it makes predictable reflections, and therefore the simple design turned out to be very practical and convenient. So convenient that it is still used by 3D graphics specialists to this day, setting up visualization algorithms and testing new methods for calculating illumination.

The walls of the inside of the Cornell box are painted in different colors. So, left-hand side it is red, the right one is green, the back wall, as well as the “ceiling” and “floor” are white. This is necessary so that the researcher conducting experiments on this model can see the color transfer to adjacent surfaces. You can observe the simplest example of this effect yourself - place something very bright yellow on a clean white sheet of paper, and you will see how the sheet will acquire a yellowish tint along the perimeter of this object. If you render using global illumination algorithms, a similar effect will occur in the Cornell box.

⇡ First 3D computer animations

Bell Laboratories has always been one of the largest and most promising teams of scientists. They dealt with the most pressing problems in various fields of science. Over the years of its existence, Bell Laboratories scientists have been awarded the Nobel Prize seven times.

And it is quite natural that the first three-dimensional simulation was carried out by specialists from this center. In 1963, a Bell Laboratories employee named Edward E. Zajac demonstrated a program written in Fortran to simulate the motion of a satellite.

He didn't set out to create the first 3D animation, but that's exactly what happened.

At that time, he worked in the department of mathematical research and was engaged in mathematical modeling to create mechanisms with a dual-gyroscopic stabilization system, which could be used in the first communication satellites. Using the ORBIT program (written by another Bell Laboratories employee), the scientist processed his calculations, producing a set of punched cards with the results. Using a General Dynamics Electronics Stromberg-Carlson 4020 computer recorder, he printed microfilm of the animation.

Its plot is simple - two objects are connected to each other by the force of gravity and one object rotates around the second like, say, the Moon around the Earth. The graphics, as you can see, are minimal, but this is 1963 and this is truly the first 3D animation.

Another Bell Laboratories employee who sought to find a way to make a computer draw 3D animation was A. Michael Noll.

Using an IBM 7094 computer in 1965-66, he made several short films, such as a “computer ballet”, where, with a good imagination, you can see the figures of one-legged dancers moving in three-dimensional space. Most likely, this is an ice ballet. An articulated structure consisting of several nodal points was taken as “dancers”. This option made it possible to simplify miscalculations.

And so that no one would have any doubt that this animation is three-dimensional, Michael Noll visualized it in stereoscopic mode, drawing the video separately for the right and left eyes. In addition to the “computer ballet,” Michael also had several interesting stereoscopic animations with a four-dimensional cube, a four-dimensional sphere, etc. All images in the animation are “inverted,” that is, on the left is a picture for the right eye, and on the right is a picture for the left eye. So, if you want to watch them, focus your vision in front of the monitor screen.

⇡ First 3D model of a car: how to scan with your hands

The production of many things in the middle of the last century was much slower compared to what it is now. The process of creating a prototype of, say, a car, was very long and complex. But everything changed when Ivan Edward Sutherland began developing an interactive interface that would help humans and computers “communicate” with each other.

Ivan Sutherland was once asked how he could come up with and create so many revolutionary ideas in such a short time, from the concept of the interface of all CAD systems to the object-oriented approach to programming. In response, Sutherland just smiled and spread his hands: “But we didn’t know then that it was all so complicated!”

Back in 1963, as part of his dissertation, Ivan Sutherland demonstrated a “robot draftsman” (this is the unofficial name of the project - Robot Draftsman). This program became the first link in the evolution of computer-aided design systems, which today are known as Sketchpad.

Using a computer and a connected light pen, the operator could draw directly on the display screen. The computer determined the coordinates of the points of contact of the light pen, and then calculated the geometry of the curve, straight line or geometric figure and almost instantly displayed the result on the screen.

Simple by today's standards, Sketchpad required fantastic computing power at the time. It ran on the TX-2 computer, which occupied several rooms at MIT's Lincoln Research Laboratory.

In the video below, Sutherland demonstrates the capabilities of the new human-machine interface.

His system made it possible to do things incredible for the 1960s - draw lines point by point and create real drawings on the screen. Sketchpad also allowed you to make changes as you worked and scale ready-made drawing elements.

One of the most important requirements for Sketchpad that Ivan put forward was that the operator's instructions be followed accurately. This was quite difficult to implement, since the user could “miss” at the desired point, and the data input device itself was imperfect. To eliminate this problem, Sketchpad used a system of so-called limiters. These stops made it possible to manipulate drawing details with absolute precision, such as making straight lines parallel or giving two segments the same length. To use these limiters, a whole set of function keys was used, which was located next to the data entry screen.

But at this presentation, the author of the first CAD software already shows a completely working version of an interactive interface with several projection windows and talks very sensibly about the potential possibilities of working with 3D.

For his development of Sketchpad, Ivan was awarded the Association for Computing Machinery's most prestigious award in computer science, the Turing Award.

Modern educators can learn a lot from Sutherland. This man devoted himself completely to science. Why, he literally did not spare a car for this purpose. Together with his students, Ivan made the first 3D digital scan of a Volkswagen Beetle by hand. Yes, exactly manually.

The task was very difficult. There were no digital scanners or digital photography back then, so everything had to be done head-on. Students crawled around the car like ants and, using special measuring rulers, drew a polygonal mesh on it, what today 3D graphics experts call a wireframe. three-dimensional model. Before starting work, some parts were removed from the car - wheels, bumper, etc., since one base was “digitized” - from all sides, from top to bottom. Was such a sacrifice justified? Certainly! Thanks to mocking the “bug,” Sutherland developed a technique for projecting polygonal meshes onto an object, which is how modern 3D graphics appeared.

Ivan also managed to interest many people in his work, who continued to develop the direction of 2D and 3D computer graphics. And against the backdrop of success, everyone somehow forgot that the Volkswagen Beetle actually belonged to Ivan’s wife, and her reaction to her husband’s act remained a mystery.

And who were these “ant” students? Among them there were many bright personalities. One of those who made the car model was named John Edward Warnock. Ten years after this story, he will become a co-founder of the well-known company Adobe.

Junior researcher B˘i T˝ờng Phong also took part in the creation of this model. Today Phong's model is used in many 3D engines.

It was on a model of the first 3D car that Phong tested his famous shading system, which later received his name - Phong. In any three-dimensional editor where it is possible to customize materials, among other options, you can select the Phong shading algorithm. Phong's method is based on interpolating surface normals from rasterized polygons and allows you to calculate the color of pixels taking into account the interpolated normal and the light reflection model.

Sutherland's project had virtually no analogues. The only system that had a similar principle was a commercial development by General Motors and IBM, which was called DAC-1 (Design Augmented by Computers). This console was also controlled using a light pen, but was less convenient and also expensive.

⇡ One left: the first computer animation of a hand

The habit of chasing the power of computer hardware has led to widespread among users the belief that without a modern video card it is impossible to obtain a 3D image. But this is not true at all. Imagine that the third dimension was attempted more than half a century ago. Even before that momentous moment when the computer truly became personal, engineers could (and did) do 3D animation. And the future founder and president of Pixar studio, as well as the head of Walt Disney Animation Studios and DisneyToon Studios, Edwin Catmull, had a hand in this.

And he did it in the literal sense of the word - he digitized his left hand and created a demonstration animation of the movements of the fingers on it.

Catmull has been interested in the process of creating animation since childhood. He even had his own homemade stand, where Edwin tried to make the first primitive cartoons. However, like many other graduates of higher education educational institutions, he did not immediately find his calling. Immediately after graduating from the University of Utah, he first went to work for Boeing, but a year later the economic crisis forced Boeing to lay off thousands of employees, and Ed was among them. The recent graduate then returned to the university to pursue graduate studies.

Ivan Edward Sutherland, then a professor at the University of Utah, became a mentor to Catmull and encouraged the young graduate student to study interactive computer graphics. Catmull used the same method as Ivan to digitize his car. The creation of the 3D hand animation was carried out in several stages. Compared to Ivan's large-scale project to digitize the Volkswagen Beetle, Catmull had it a little simpler - he simply painted a cast of his left hand, marking the location of the edges and nodes of the polygonal mesh on it. Next, in the laboratory, this mesh was read by a special device, and a three-dimensional model was compiled from the data obtained.

Catmull wrote a program to animate this model. This animation was rendered and used as a nice addition to graduation project. The surface of the hand was deformed, the fingers bent and unbent, and the hand itself rotated on the screen. For greater effect, Catmull even allowed a “look” inside the model, demonstrating to the viewer that the 3D hand was hollow inside.

The work of young scientists was not in vain. A model of a hand rotating in 3D space was used in the 1976 science fiction film Futureworld. It was about a resort hotel whose staff consists of robots. To imitate high technology, everything was used - both rendered animation and the skeleton of a 3D model.

In addition to this 3D hand, the students created an even more complex work - an animated model of a human head.

It was prepared by Catmull's friend and colleague Fred Parke, who also took part in the digitization of the model of Edward's left hand.

He even tried to synchronize the sound and lip movements of the computer model. And this was in 1974!

The students called the model of a person Baldy, that is, “bald.” Its frame consisted of 900 triangles.

In the mid-eighties, the laboratory of Dominic Massaro continued work on this model and, using a more advanced technique, “revitalized” the head, giving it a large set of verbal facial expressions. Professor Massaro himself slightly changed the name in the Italian style - Baldi and registered it as a trademark. And not so long ago, under his leadership, the release of an application for iOS was launched, in which there is a talking 3D head, made back in the seventies.

The term “computer animation” in the middle of the last century was something very exotic. Computers, as well as printing devices, were only at the disposal of research organizations and, of course, the military. Well, in the Soviet Union people had never heard of computer animation, with the exception of a small group of enthusiasts who assumed that it was quite possible to “draw” animation using computer technology. One of these people is mathematician Nikolai Nikolaevich Konstantinov.

This man is a real legend of Russian mathematics. Konstantinov is one of the most talented and extraordinary scientists who managed not only to make a huge contribution to domestic science and the education system, but also to pass on his knowledge to subsequent generations. Among his students there are many great mathematicians and scientists, not to mention the winners of mathematical competitions and olympiads.

Back in 1968, he created the first one and a half minute computer animation. The object of his attention was the cat, hence the name of the mini-cartoon - “Kitty”.

The mathematician decided to create a cartoon by programming the cat's movements and printing each frame of the animation with a redrawn silhouette. The implementation of such an idea could only arise from a person who not only has an excellent understanding of higher mathematics, but also sees its practical application.

Since the animal’s muscles, when contracting, control the acceleration of certain parts of the body, Konstantinov decided that the basis of the animal’s movement algorithm could well be second-order differential equations. A graphical interpretation of the cat's silhouette was achieved using a character array. The mathematician broke the cat's outline into parametric "bars", and then, using hypothetical formulas describing the animal's gait, recreated a simple movement scenario that included several steps, turning the head and slowing down.

In this work, he was helped by two MSU students - Vladimir Ponomarenko and Viktor Minakhin. Nikolai Nikolaevich later recalled a funny detail of this project: in order to derive the correct formula for the movements of a cat, Victor tried to imitate a cat - he got down on all fours and walked on the floor, trying to understand which muscles were involved in the work.

Although Konstantinov himself subsequently denied the realism of the achieved result, citing the hypothetical nature of the mathematical calculations, it is difficult not to notice how believably the animal moves in the frame.

At the Department of General Problems of Management of the Faculty of Mechanics and Mathematics of Moscow University, the theoretical part of this problem was prepared, and the debugging of the calculation program itself differential equations and its operation was carried out at the Computing Center of the Moscow State Pedagogical Institute. The computer that was used to calculate this animation was proudly called BESM-4 (“Big Electronic Calculating Machine”).

BESM-4 had very little in common with what we call a computer today. Only 30 such devices were released throughout the country. RAM in BESM-4 it was made on ferrite cores (8192 words, 45-bit words, organized into two cubes of 4k words each). The productivity of this “cabinet” was up to forty thousand operations per second. The printer for a large electronic calculating machine had an equally capacious name - the ATsPU-128 alphanumeric printing device.

If you look closely at the frame-by-frame rendering, you can see minor random unwanted artifacts - in their own way, these are the first “glitches” of computer visualization, that is, rendering.

As for the face that the cat makes at the beginning of the short film, this is not the work of a mathematician, but of a merry artist who made animation for the unforgettable Soviet film “ Funny boys" He was also invited to work on this project.

Interestingly, at that time Konstantinov was not the only person in the USSR who used the computer animation method. However, other attempts at computer visualization, such as animation of processes inside a DNA molecule, were boring and unclear to an unprepared viewer.

⇡ Conclusion

Nowadays the computer is a universal tool. It can be used for drawing, creating animation, and preparing videos. The only thing he lacks is creativity. However, perhaps this is a matter of time.

Appearance computer equipment and the development of computer graphics, in a sense, allowed people to take a new look at the world. Much of what was previously inaccessible to human vision, what was too fast or too slow, very small or too large, became obvious and understandable in the computer model. Medicine, technology, engineering, space - computer graphics are used in any field of human activity. What began as an ordinary point of light on a screen, a single pixel, displaying minimal computer information, gradually transformed into a line, a moving image on the screen, and then into virtual and augmented reality. And the limit of this pixel evolution is somewhere far beyond human understanding. And most likely, the most interesting is yet to come.