3D computer graphics

• 1. Introduction

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  3D computer graphics began with a single man at Boeing. In 1961, William Fetter coined the term "computer graphics" to describe his work there. That label stuck, even as the technology it described would grow into something Fetter likely never imagined: entire virtual worlds built from points, polygons, and light simulations rendered into images seen by billions of people every day.

  Here is the paradox at the heart of the field. The images are called three-dimensional, but most of them exist on flat, two-dimensional screens. The depth is an illusion. The math behind that illusion involves storing geometric data in Cartesian coordinates, calculating how light would behave, and collapsing a three-dimensional model into a 2D image through a process called rendering. At every step, the computer is doing something philosophically strange: representing a world that does not exist in a space that has no volume.

  Two foundational questions run through 3D graphics. First, how do you build a model? Second, how do you turn that model into a convincing image? The answers involve techniques ranging from decades-old polygon math to real-time rendering engines pushing millions of triangles per second.

• 2. The Earliest Experiments

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  In 1963, the Sketchpad program at MIT's Lincoln Laboratory gave early researchers their first taste of interactive 3D graphics. That experiment came a full thirteen years before 3D graphics reached a movie screen.

  Futureworld, released in 1976, holds a particular place in the history of the field. It was one of the first films to display computer animation. The sequence that made it into that film had originally appeared in a 1972 experimental short called A Computer Animated Hand, made by Edwin Catmull and Fred Parke, both students at the University of Utah. The hand and the face they animated were primitive by any later standard, but the ambition behind them was clear: computers could model organic, moving shapes.

  By the late 1970s, 3D graphics software had reached home computers. The earliest known example is 3D Art Graphics, written by Kazumasa Mitazawa and released in June 1978 for the Apple II. That software represented the first time an ordinary user at home could interact with a 3D graphics tool, more than two decades before the technology became commonplace in living rooms.

• 3. How Models Are Built

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  Every 3D model, no matter how complex, is built from points. Those points are called vertices, and three or more of them define a polygon. A polygon with three vertices is a triangle. A polygon with n points is an n-gon. The overall structure of those polygons determines whether a model can be animated smoothly or whether it will collapse into visual chaos during motion.

  There are two main ways a 3D model enters a computer. An artist or engineer constructs it using a modeling tool, working with methods such as polygonal modeling, patch modeling, or NURBS modeling. The alternative is scanning a real-world object and converting it into digital geometry. Models can also be produced procedurally, meaning a computer generates them from rules, or through physical simulation.

  Once a model exists, software gives users the ability to add, subtract, and stretch the mesh. The model can be viewed from multiple angles simultaneously and rotated freely. Most modeling software also includes ray tracers, texture mapping, and some animation capabilities. Files can be exported in formats such as Blender's .blend, Wavefront's .obj, or DirectX's .fbx, and imported into other applications as long as the metadata are compatible.

• 4. Light, Surfaces, and Rendering

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  Rendering is where a 3D model becomes an image. Two fundamental operations govern how that happens: transport, meaning how much light travels from one place to another, and scattering, meaning how surfaces interact with light when it arrives.

  Materials and textures tell the render engine how to treat light at each surface. A color or albedo map gives the surface its basic color. A bump map or normal map adds the appearance of surface features without changing the model's actual geometry. A displacement map can go further and physically deform the model. Together, those properties allow a flat polygon mesh to look like rough stone, translucent skin, or polished metal.

  Not all rendering aims for photorealism. Non-photorealistic rendering applies an art style instead of simulating light transport. Tools in wide use include Autodesk 3ds Max, Blender, and dedicated rendering engines such as OTOY's Octane Rendering Engine and Maxon's Redshift. The process also involves 3D projection, which is the mathematical step that collapses a three-dimensional scene into the two-dimensional image a screen can actually display.

• 5. Animation and Movement

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  A model placed in a scene is static. Animation is the temporal layer that makes it move. The source of that motion falls into several distinct approaches: keyframing, which defines positions at specific moments in time; inverse kinematics, which calculates how a chain of joints should move to reach a target position; and motion capture, which records the movement of a real performer and applies it to a digital model. In practice, these methods are often combined.

  The 3D production workflow runs through three phases in sequence. First comes 3D modeling, the construction of the object's shape. Second is layout and CGI animation, which positions models, lights, and cameras within a scene and defines how they move. Third is rendering, which computes the final image. Physical simulation can appear in both the animation and the rendering phases.

  After rendering is complete, post-production tools take over. Mid-level studios use programs such as Adobe Premiere Pro or Final Cut Pro for editing and compositing. High-end work involves tools such as Autodesk Combustion, Digital Fusion, or Shake. Match moving software synchronizes computer-generated footage with live-action video as the camera moves. When real-time game engines are used to produce cinematic work rather than interactive games, the result is called machinima.

• 6. Beyond the Screen

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  3D models do not have to produce images at all. A model can serve as the input for non-graphical computer simulations and engineering calculations. Computer-aided design software uses the same fundamental modeling techniques as 3D graphics software, but its outputs feed into computer-aided engineering, computer-aided manufacturing, finite element analysis, product lifecycle management, and computer-aided architectural design.

  3D printing takes the relationship between virtual and physical further. A model can be rendered into an actual physical object, though physical fabrication imposes limits on how closely the printed result can match the virtual original.

  Virtual reality adds yet another output mode. Although the first VR headsets appeared in the late 1950s, the technology did not reach wide popularity until the 2000s. The release of the Oculus in 2012 marked a turning point for consumer VR headsets, and the ecosystem of 3D VR devices has expanded steadily since then. In VR, the usual paradox of 3D graphics is partially resolved: the viewer is surrounded by the image rather than looking at it on a flat plane, though the display panels themselves remain two-dimensional.

• 7. Illusions and Alternatives

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  Not everything that looks three-dimensional actually uses a 3D model. 2D computer graphics can produce photorealistic 3D effects through filters, layering, and manual rendering techniques. The end result can be visually indistinguishable from true 3D rendering, even though no three-dimensional geometry was ever involved.

  Some video games occupy a middle ground called 2.5D. These games use restricted projections of three-dimensional environments, such as isometric viewpoints or virtual cameras locked to fixed angles. The restriction can serve performance goals by reducing the computational load on the game engine, or it can serve stylistic purposes. Games without such restrictions are described as using true 3D.

  Stop motion animation represents a different kind of hybrid. It is not computer-generated in the traditional sense, but 3D software tools now interact with its various forms. Stop motion includes claymation, cutout animation using flat paper materials, silhouette animation in solid black, puppet animation, and pixelation. Examples in the source include Clay Fighter for claymation, Paper Mario for cutout, Limbo for silhouette, Yoshi's Wooly World for puppet, and Shovel Knight for pixelation. The shared trait across all these forms is that physical or visual objects move through time in discrete steps, a structural echo of keyframe animation in 3D software itself.