When a primitive is drawn, grid cells are replaced with the primitive's colour or left unchanged. The edges of the polygon are jagged because of this all-or-nothing approach of filling in the grid cells. Aliasing is a term used to describe the jagged appearance. The application of methods to reduce aliasing is known as antialiasing.
Surface Tessellation
Display hardware is optimised to process and render triangles. Any surface must be subdivided into these simple shapes before it can be displayed. This subdivision is called tesselation. For many years, several computer graphicists have devised clever techniques to tesselate a parametric surface. Detailed below are three evaluation methods that were developed before the advent of more elegant solutions and alternate surface descriptions.
Polysurface Tessellation
A polysurface is the union of two or more surfaces. Such a union is necessary when a single patch cannot adaquately describe the complexities an artist wishes to produce. This piece-wise approach has several benefits, one of which is the ability to stitch together simple patches that are easy to manipulate and fast to render. The artist also has the freedom to edit parts of the composite surface without having to worry about global side-effects.
Outdoor Lighting
A photon is a quantum of electromagnetic energy. We perceive this energy as visible light if its wavelength falls within the range of four thousand (violet) to eight thousand (red) angstroms. Light either comes from a source (emitter) or is reflected from a surface (receiver). To simulate an outdoor environment, we often use the Sun as the main light source. The Sun, in our model, is a directional light source as is the Moon. The contributions of the stars, planets, zodiacal light, airglow, and diffuse galactic and cosmic light are also important if we wish to accurately portray an outdoor setting. These sources are assumed to be infinitely far away from the scene being lit. This assumption allows us to simplify our lighting model.
Indoor Lighting
Most indoor environments are illuminated by more than one light source. The energy transfers that occur require detailed calculations. For every instance of light bouncing off a surface we need to determine how much of the electromagnetic radiation is absorbed and to where the reflected photons travel next. Acceleration techniques have been developed that increase the efficiency of these calculations. The properties of a surface that receives a stream of photons greatly affects how and to where the light is reflected. This fact is represented very accurately in advanced lighting models.
Haar Wavelets
Wavelets are used to represent functions in an elegant manner. The function can be an image, curve, or surface. With its initial use in approximation theory and signal processing, wavelets can also be applied to image editing and compression [64], global illumination, radiosity, and surface reconstruction and surface approximation. In this introduction to wavelets, it is assumed the reader is familiar with concepts associated with linear algebra.
Almost three decades ago, Chaikin introduced an ingenious method for generating curves. The algorithm was a corner cutting or refinement scheme that produced a smooth curve from a given control polygon. In the following years, many subdivision schemes for modeling smooth surfaces have been developed based on Chaikin's pioneering endeavour. First among these schemes were techniques developed by Doo and Sabin, and Catmull and Clark. The contributions of the latter pair of authors is the focus of this article.
Liang-Barsky Line Clipping
Almost two decades ago, Liang and Barsky developed a fast and efficient parametric line clipping algorithm where the clip region is an upright rectangle in two or three dimensional space. This article is a very brief overview of the algorithm. The region is defined by edges ei having outward pointing normals ni.
Watercolour Rendering
Nonphotorealistic rendering (NPR) techniques have become an increasingly popular topic in research circles. These methods provide a stylistic approach in simulating worlds. Realism is not the goal here. Rather, we wish to achieve styles that are reminiscent of paintings or other forms of artistic illustration. One of more interesting modes of expression is the watercolour process. In this method the artist combines layers of translucent paints to yield the desired colours and opacities. The soft mixture of hues and the hints of curvature and shape can convey a rich, organic and natural feel to a scene.
"Square Root Three" Subdivision
Powerful computer hardware and clever algorithms are two reasons for the growing popularity of subdivision schemes in the efficient generation of freeform surfaces. Such methods are simple, robust and have many practical applications. A relatively new scheme for triangle meshes is called "square root three" subdivision. This rather peculiar name is derived from the fact that if we apply the same subdivision step twice the combined result is the tri-section of each original edge in the mesh. In other words, the scheme creates three edges per two refinement steps for each triangle.
The Rendering Equation
Surface detail is often conveyed using clever lighting algorithms to simulate a variety of physical properties. The basis of these techniques lies in estimating the amount of light energy being transmitted, reflected or absorbed at a given point on a surface. All such methods are derived from the rendering equation, a very important contribution to the field of computer graphics by James T. Kajiya in 1986. It is this pioneering effort that has led to the truly remarkable visuals we see today in a variety of contexts such as film and interactive entertainment. Here, we (re)introduce the original rendering equation as it was presented decades ago.
Cel shading is a common nonphotorealistic rendering (NPR) technique. Objects are rendered using a very limited colour palatte. Transitions in colour are often abrupt so roundness is implied and not explicitly detailed. The silhouette and any creases are traced with thick, dark lines. Raskar developed a cel shading technique that does not require any connectivity information among the polygons of a given mesh. The same shading rules are applied to every polygon. Only the vertex positions, vertex normals and the current viewing direction are used. The method assumes the mesh consists of oriented, convex polygons. The method can also be easily integrated with any hardware-accelerated rendering pipeline.
Computer Image File Formats
Motion picture films have become increasing subject to digital manipulation. Old films, for example, are restored to their original luster when artists remove blemishes and other visual artifacts. Colours may also be enhanced and/or replaced. More ambitious endeavours include inserting new objects or characters into a scene. The special edition of one film, in particular, raised the ire of some people for this very reason. Regardless of where people stand on the use of computer graphics (CG) in motion pictures, one cannot deny the incredible levels of realism achieved thus far. A component of CG that aids in this realism is colour. Computer image file formats, employed by CG artisians, must be able to represent even the most subtle shifts in hue and saturation. To this end, there are specialised file formats that represent colour information at extraordinarily high levels of precision.
Outdoor Lighting Revisited
Methods to illuminate an outdoor scene during the daytime hours is well documented. Less attention has been devoted to accurately, or at least concinvingly, depict nighttime outdoor environments. Recent attempts, however, have proved very successful as noted below in a rendering by Pramod Kumar Sharma and Guillaume Poncin. Herein we will briefly touch upon some details of a simple nightsky model and the associated sources of natural illumination.
High Dynamic Range Rendering
Current display devices have a limited gamut of intensities. Our eyes, however, are much more sensitive by several orders of magnitude. To better mimic how we perceive colour in the real-world we use high dynamic range (HDR) rendering. The dynamic range is the ratio between the maximum and minimum intensities. We can increase the overall perceived contrast of a scene by making local changes to contrast. There are several ways to approach HDR rendering, two of which are described herein.
Appendix
High definition media
Scarlett Johansson
File format: AVI (XviD 1.x)
File size: 139 534 964 bytes
Audio stream: MPEG-1 Layer 3
Video dimensions: 1920 x 1080i
Publication date: April 21, 2007 (Saturday Night Live Episode #32.18)
Copyright holder: NBC Universal, Inc.
Marisa Miller
File format: AVI (XviD 1.x)
File size: 197 941 248 bytes
Audio stream: MPEG-1 Layer 3
Video dimensions: 1280 x 720
Publication date: February 12, 2008 (Late Night with David Letterman)
Copyright holder: Worldwide Pants Incorporated
Natalie Portman
File format: AVI (XviD 1.x)
File size: 151 971 840 bytes
Audio stream: MPEG-1 Layer 3
Video dimensions: 1280 x 720
Publication date: February 28, 2008 (Late Night with David Letterman)
Copyright holder: Worldwide Pants Incorporated
Forbidden Kingdom
File format: MOV (H.264)
File size: 114 159 819 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 534
Theatrical Release Date: April 18, 2008
Copyright holders: Casey Silver Productions, Relativity Media, Huayi Brothers and Lionsgate
Wanted
File format: MOV (H.264)
File size: 24 363 517 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 690
Theatrical Release Date: June 27, 2008
Copyright holders: Spyglass Entertainment, TopCow Productions and Universal Pictures
Wall·E
File format: MOV (H.264)
File size: 60 479 836 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 720
Theatrical Release Date: June 27, 2008
Copyright holders: Pixar Animation Studios and Walt Disney Pictures
Iron Man
File format: MOV (H.264)
File size: 24 913 357 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1248 x 702
Theatrical Release Date: May 2, 2008
Copyright holders: Marvel Enterprises and Paramount Pictures
Speed Racer
File format: MOV (H.264)
File size: 89 448 856 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 720
Theatrical Release Date: May 9, 2008
Copyright holders: Warner Bros. Pictures, Silver Pictures and Village Roadshow Pictures
Kung Fu Panda
File format: MOV (H.264)
File size: 50 716 618 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 544
Theatrical Release Date: June 6, 2008
Copyright holders: DreamWorks Animation and Data Pacific Images (PDI)
Ratchet and Clank Future: Tools of Destruction trailer two and three
File format: MP4 (H.264)
File size: 100 577 291 and 77 493 321 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): October 23, 2007
Published by: Sony Computer Entertainment
Developed by: Insomniac Games
Uncharted: Drake's Fortune - Massive Attack trailer
File format: MP4 (H.264)
File size: 246 522 877 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): November 20, 2007
Published by: Sony Computer Entertainment
Developed by: Naughty Dog Software
Call of Duty 4: Modern Warfare
File format: MP4 (H.264)
File size: 86 223 177 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): November 6, 2007
Published by: Activision
Developed by: Infinity Ward
Gran Turismo 5 Prologue Leipzig 2007 trailer and Nissan GT-R commercial (Japanese)
File format: WMV (Windows Media Video 9)
File size: 111 014 474 and 29 909 622 bytes
Audio stream: WMA (Windows Media Audio)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): March 2008
Published by: Sony Computer Entertainment
Developed by: Polyphony Digital
Race Driver: GRID gameplay trailer
File format: MP4 (H.264)
File size: 65 057 623 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): June 30, 2008
Published by: Codemasters
Developed by: Codemasters
Street Fighter IV
File format: WMV (Windows Media Video 9)
File size: 172 706 171 bytes
Audio stream: WMA (Windows Media Audio)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): 2008
Published by: Capcom
Developed by: Capcom
Grand Theft Auto IV - final trailer
File format: WMV (Windows Media Video 9)
File size: 78 423 792 bytes
Audio stream: WMA (Windows Media Audio)
Video dimensions: 1280 x 720
Release Date (PlayStation 3): April 29, 2008
Published by: Take-Two Interactive
Developed by: Rockstar North
Standard definition media
The Dark Knight
File format: MOV (H.264)
File size: 54 181 617 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 848 x 360
Theatrical Release Date: July 18, 2008
Copyright holders: Warner Bros. Pictures, Legendary Pictures and DC Comics
Indiana Jones and the Kingdom of the Crystal Skull
File format: MOV (H.264)
File size: 73 362 832 bytes
Audio stream: AAC, Stereo (L R)
Video dimensions: 850 x 362
Theatrical Release Date: May 22, 2008
Copyright holders: Lucasfilm, Amblin Entertainment and Paramount Pictures
Dao huo xian (Flash Point) (Yen Ji-Dan, Koo Tin Lok and Chou Hsiao-Lung)
File format: AVI (XviD 1.x)
File size: 110 110 720 bytes
Audio stream: MPEG-1 Layer 3
Video dimensions: 704 x 304
Release Date: August 9, 2007 (Hong Kong)
Copyright holders: Mandarin Films Distribution Co. and Chang Ying Group
Christina Aguilera
File format: AVI (XviD 1.x)
File size: 147 251 200 bytes
Audio stream: MPEG-1 Layer 3
Video dimensions: 725 x 544
Publication date: February 20, 2008 (Ellen DeGeneres Show)
Copyright holder: WAD Productions, Inc. and Warner Bros. Entertainment Group