A ray-traced scene

Ray tracing is a general technique from geometrical optics of modelling the path taken by light by following rays of light as they interact with optical surfaces. It is used in the design of optical systems, such as camera lenses, microscopes, telescopes and binoculars. The term is also applied to mean a specific rendering algorithmic approach in 3D computer graphics, where mathematically-modelled visualisations of programmed scenes are produced using a technique which follows rays from the eyepoint outward, rather than originating at the light sources. It produces results similar to ray casting and scanline rendering, but facilitates more advanced optical effects, such as accurate simulations of reflection and refraction, and is still efficient enough to frequently be of practical use when such high quality output is sought.  ©  This image is copyrighted. ...  ©  This image is copyrighted. ... See also list of optical topics. ... In optics, a ray is an idealized narrow beam of light. ... Photographic lens One of Canons most popular wide angle lenses - 17-40 f/4 L The zoom lens of the Canon Elph A photographic lens (or more correctly, objective) is an optical lens or assembly of lenses used in conjunction with a camera body and mechanism to make images... A microscope (Greek: micron = small and scopos = aim) is an instrument for viewing objects that are too small to be seen by the naked or unaided eye. ... 50 cm refracting telescope at Nice Observatory. ... Binoculars A set of binoculars (from Latin, bi-, two-, and oculus, eye) is a hand-held tool used to magnify distant objects by passing the image through two adjacent series of lenses, and erecting prisms. ... Rendering is the process of generating an image from a model, by means of a software program. ... The rewrite of this article is being devised at Talk:3D computer graphics/Temp. ... In computer graphics, Ray-casting is a pseudo-3D rendering technique, a special case of ray tracing. ... Scanline rendering is a rendering algorithm in 3D computer graphics that works on a point-by-point basis rather than polygon-by-polygon basis. ... Spheres reflecting the floor and each other. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ...

Broad description of ray tracing computer algorithm

Three spheres, that reflect off the floor and each other

Ray tracing describes a more realistic method than either ray casting or scanline rendering, for producing visual images constructed in 3D computer graphics environments. It works by tracing in reverse, a path that could have been taken by a ray of light which would intersect the imaginary camera lens. As the scene is traversed by following in reverse the path of a very large number of such rays, visual information on the appearance of the scene as viewed from the point of view of the camera, and in lighting conditions specified to the software, is built up. The ray's reflection, refraction, or absorption are calculated when it intersects objects and media in the scene. Image File history File links Download high resolution version (1024x768, 292 KB) Summary Some spheres reflecting off the floor and each other. ... Image File history File links Download high resolution version (1024x768, 292 KB) Summary Some spheres reflecting off the floor and each other. ... The rewrite of this article is being devised at Talk:3D computer graphics/Temp. ... Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific context, electromagnetic radiation of any wavelength. ...

Scenes in raytracing are described mathematically, usually by a programmer, or by a visual artist using intermediary tools, but they may also incorporate data from images and models captured by various technological means, for instance digital photography.

Following rays in reverse is many orders of magnitude more efficient at building up the visual information than would be a genuine simulation of light interactions, since the overwhelming majority of light rays from a given light source do not wind up providing significant light to the viewers eye, but instead may bounce around until they diminish to almost nothing, or bounce off to infinity. A computer simulation starting with the rays emitted by the light source and looking for ones which wind up intersecting the viewpoint is not practically feasible to execute and obtain accurate imagery.

The obvious shortcut is to pre-suppose that the ray ends up at the viewpoint, then trace backwards. After a stipulated number of maximum reflections has occurred, the light intensity of the point of last intersection is estimated using a number of algorithms, which may include the classic rendering algorithm, and may perhaps incorporate other techniques such as radiosity. Radiosity is a global illumination algorithm used in 3D computer graphics rendering. ...

Detailed description of ray tracing computer algorithm and its genesis

What happens in nature

In nature, a light source emits a ray of light which travels, eventually, to a surface that interrupts its progress. One can think of this "ray" as a stream of photons travelling along the same path. In a perfect vacuum this ray will be a straight line. In reality, any combination of three things might happen with this light ray: absorption, reflection, and refraction. A surface may reflect all or part of the light ray, in one or more directions. It might also absorb part of the light ray, resulting in a loss of intensity of the reflected and/or refracted light. If the surface has any transparent or translucent properties, it refracts a portion of the light beam into itself in a different direction while absorbing some (or all) of the spectrum (and possibly altering the color). Between absorption, reflection, and refraction, all of the incoming light must be accounted for, and no more. A surface cannot, for instance, reflect 66% of an incoming light ray, and refract 50%, since the two would add up to be 116%. From here, the reflected and/or refracted rays may strike other surfaces, where their absorptive, refractive, and reflective properties are again calculated based on the incoming rays. Some of these rays travel in such a way that they hit our eye, causing us to see the scene and so contribute to the final rendered image. Attempting to simulate this real-world process of tracing light rays using a computer can be considered extremely wasteful, as only a minuscule fraction of the rays in a scene would actually reach the eye. In quantum physics, the photon (from Greek φως, phōs, meaning light) is the quantum of the electromagnetic field (light). ... Absorption, in optics, is the process by which the energy of a photon is taken up by another entity, for example, by an atom whose valence electrons make a transition between two electronic energy levels. ... Spheres reflecting the floor and each other. ... The straw seems to be broken, due to refraction of light as it emerges into the air. ... This article needs to be cleaned up to conform to a higher standard of quality. ... In optics, transparency is the property of being transparent, or allowing light to pass. ... The visible spectrum is the portion of the optical spectrum (light or electromagnetic spectrum) that is visible to the human eye. ...

Ray casting algorithm

The first ray casting (versus ray tracing) algorithm used for rendering was presented by Arthur Appel in 1968. The idea behind ray casting is to shoot rays from the eye, one per pixel, and find the closest object blocking the path of that ray - think of an image as a screen-door, with each square in the screen being a pixel. This is then the object the eye normally sees through that pixel. Using the material properties and the effect of the lights in the scene, this algorithm can determine the shading of this object. The simplifying assumption is made that if a surface faces a light, the light will reach that surface and not be blocked or in shadow. The shading of the surface is computed using traditional 3D computer graphics shading models. One important advantage ray casting offered over older scanline algorithms is its ability to easily deal with non-planar surfaces and solids, such as cones and spheres. If a mathematical surface can be intersected by a ray, it can be rendered using ray casting. Elaborate objects can be created by using solid modelling techniques and easily rendered. Scanline rendering is a rendering algorithm in 3D computer graphics that works on a point-by-point basis rather than polygon-by-polygon basis. ... In common usage and elementary geometry, a cone (Greek: κώνος) is a solid object obtained by rotating a right triangle around one of its two short sides, the cones axis. ... A sphere (< Greek σφαίρα) is a perfectly symmetrical geometrical object. ... Solid modelling (or modeling) is the unambiguous representation of the solid parts of an object, that is, models of solid objects suitable for computer processing. ...

Ray casting for producing computer graphics was first used by scientists at Mathematical Applications Group, Inc., (MAGI) of Elmsford, New York, New York. In 1966, the company was created to perform radiation exposure calculations for the Department of Defense. MAGI's software calculated not only how the gamma rays bounced off of surfaces (ray casting for radiation had been done since the 1940s), but also how they penetrated and refracted within. These studies helped the government to determine certain military applications ; constructing military vehicles that would protect troops from radiation, designing re-entry vehicles for space exploration. Under the direction of Dr. Philip Mittelman, the scientists developed a method of generating images using the same basic software. In 1972, MAGI became a commercial animation studio. This studio used ray casting to generate 3-D computer animation for television commercials, educational films, and eventually feature films – they created much of the animation in the film Tron using ray casting exclusively. MAGI went out of business in 1985. Mathematics Application Group, Inc. ... Elmsford is a village located in Westchester County, New York. ... Official language(s) None, English de facto Capital Albany Largest city New York City Area  Ranked 27th  - Total 54,520 sq mi (141,205 km²)  - Width 285 miles (455 km)  - Length 330 miles (530 km)  - % water 13. ... The radiation warning symbol (trifolium). ... The United States Department of Defense, abbreviated as DoD or DOD and sometimes called the Defense Department, is a civilian Cabinet organization of the United States government. ... This article is about electromagnetic radiation. ... An educational film is a film or movie whose primary purpose is to educate. ... Tron is a 1982 Walt Disney Productions science fiction movie starring Jeff Bridges as Kevin Flynn (and Clu), Bruce Boxleitner as Alan Bradley (and Tron), Cindy Morgan as Lora (and Yori)and Dan Shor as Ram. ...

Ray tracing algorithm

The next important research breakthrough came from Turner Whitted in 1979. Previous algorithms cast rays from the eye into the scene, but the rays were traced no further. Whitted continued the process. When a ray hits a surface, it could generate up to three new types of rays: reflection, refraction, and shadow. A reflected ray continues on in the mirror-reflection direction from a shiny surface. It is then intersected with objects in the scene; the closest object it intersects is what will be seen in the reflection. Refraction rays traveling through transparent material work similarly, with the addition that a refractive ray could be entering or exiting a material. To further avoid tracing all rays in a scene, a shadow ray is used to test if a surface is visible to a light. A ray hits a surface at some point. If the surface at this point faces a light, a ray (to the computer, a line segment) is traced between this intersection point and the light. If any opaque object is found in between the surface and the light, the surface is in shadow and so the light does not contribute to its shade. This new layer of ray calculation added more realism to ray traced images.

Advantages of ray tracing

Ray tracing's popularity stems from its basis in a realistic simulation of lighting over other rendering methods (such as scanline rendering or ray casting). Effects such as reflections and shadows, which are difficult to simulate using other algorithms, are a natural result of the ray tracing algorithm. Relatively simple to implement yet yielding impressive visual results, ray tracing often represents a first foray into graphics programming. Shadows on a pavement A shadow is a region of darkness where light is blocked. ...

Disadvantages of ray tracing

A serious disadvantage of ray tracing is performance. Scanline algorithms and other algorithms use data coherence to share computations between pixels, while ray tracing normally starts the process anew, treating each eye ray separately. However, this separation offers other advantages, such as the ability to shoot more rays as needed to perform anti-aliasing and improve image quality where needed. Although it does handle interreflection and optical effects such as refraction accurately, traditional Ray Tracing is also not necessarily photorealistic. True photorealism occurs when the rendering equation is closely approximated or fully implemented. Implementing the rendering equation gives true photorealism. As the equation describes every physical effect of light flow. However, this is usually infeasable given the computing resources required. The realism of all rendering methods, then, must be evaluated as an approximation to the equation, and in the case of Ray Tracing, it is not necessarily the most realistic. Other methods, including photon mapping, are based upon raytracing for certain parts of the algorithm, yet give far better results. In digital signal processing, anti-aliasing is the technique of minimizing aliasing (jagged or blocky patterns) when representing a high-resolution signal at a lower resolution. ... In computer graphics, the rendering equation describes the flow of light energy throughout a scene. ... A crystal ball with caustics In computer graphics, photon mapping is a global illumination algorithm based on ray tracing used to realistically simulate the interaction of light with different objects. ...

Reversed direction of traversal of scene by the rays

The process of shooting rays from the eye to the light source to render an image is sometimes referred to as backwards ray tracing, since it is the opposite direction photons actually travel. However, there is confusion with this terminology. Early ray tracing was always done from the eye, and early researchers such as James Arvo used the term backwards ray tracing to refer to shooting rays from the lights and gathering the results. As such, it is clearer to distinguish eye-based versus light-based ray tracing. Research over the past decades has explored combinations of computations done using both of these directions, as well as schemes to generate more or fewer rays in different directions from an intersected surface. For example, radiosity algorithms typically work by computing how photons emitted from lights affect surfaces and storing these results. This data can then be used by a standard recursive ray tracer to create a more realistic and physically correct image of a scene. In the context of global illumination algorithms, such as photon mapping and Metropolis light transport, ray tracing is simply one of the tools used to compute light transfer between surfaces. Radiosity is a global illumination algorithm used in 3D computer graphics rendering. ... Global illumination algorithms used in 3D computer graphics are those which, when determining the light falling on a surface, take into account not only the light which has taken a path directly from a light source (direct illumination), but also light which has undergone reflection from other surfaces in the... A crystal ball with caustics In computer graphics, photon mapping is a global illumination algorithm based on ray tracing used to realistically simulate the interaction of light with different objects. ... This SIGGRAPH 1997 paper by Eric Veach and Leonidas J. Guibas describes an application of a variant of the Monte Carlo method called the Metropolis-Hastings algorithm to the rendering equation for generating images from detailed physical descriptions of three dimensional scenes. ...

Algorithm: classical recursive ray tracing

 For each pixel in image { Create ray from eyepoint passing through this pixel Initialize NearestT to INFINITY and NearestObject to NULL For every object in scene { If ray intersects this object { If t of intersection is less than NearestT { Set NearestT to t of the intersection Set NearestObject to this object } } } If NearestObject is NULL { Fill this pixel with background color } Else { Shoot a ray to each light source to check if in shadow If surface is reflective, generate reflection ray: recurse If surface is transparent, generate refraction ray: recurse Use NearestObject and NearestT to compute shading function Fill this pixel with color result of shading function } } 

Ray tracing in real time

There has been some effort for implementing ray tracing in real time speeds for interactive 3D graphics applications such as computer and video games. This article is about computer and video games. ...

The OpenRT project includes a highly-optimized software core for ray tracing along with an OpenGL-like API in order to offer an alternative to the current rasterization based approach for interactive 3D graphics. OpenRT is an effort to develop a standard API for ray tracing, similar to what OpenGL is for rasterization. ... OpenGL official logo OpenGL (Open Graphics Library) is a standard specification defining a cross-language cross-platform API for writing applications that produce 3D computer graphics (and 2D computer graphics as well). ...

Ray tracing hardware, such as the experimental Ray Processing Unit developed at the Saarland University, has been designed to accelerate some of the computationally intensive operations of ray tracing. Ray tracing hardware is a special purpose computer hardware design for accelerating real-time ray tracing. ... Ray Processing Unit (RPU) is an experimental ray tracing hardware, developed at the Saarland University. ... The Saarland University (German Universität des Saarlandes) is a university located in Saarbrücken, Germany. ...

Some real-time software 3D engines based on ray tracing have been developed by hobbyist demo programmers since the late 1990's. The ray tracers used in demos, however, often use inaccurate approximations and even cheating in order to attain reasonably high frame rates. [1] The demoscene is a computer subculture that came to prominence during the rise of the 16/32-bit micros (the Atari ST and the Amiga), but demos first appeared during the 8-bit era on computers such as the Commodore 64 and ZX Spectrum. ... A frame part of an animation displayed in real time. ...

In optical design

Ray tracing in computer graphics derives its name and principles from a much older technique used for lens design since the 1900s. Geometric ray tracing is used to describe the propagation of light rays through a lens system or optical instrument, allowing the image-forming properties of the system to be modeled. This is used to optimize the design of the instrument (e.g. to minimize effects such as chromatic and other aberrations) before it is built. Ray tracing is also used to calculate optical path differences through optical systems, which are used to calculate optical wavefronts, which in turn are used to calculate system diffraction effects such as point spread function, MTF, and Strehl ratio. It is not only used for designing lenses, as for photography, but can also be used for longer wavelength applications such as designing microwave or even radio systems, and for shorter wavelengths, such as ultraviolet and X-ray optics. Optical lens design is the science/art of calculating the various lens construction parameters (variables) that will meet or at least approach desired performance requirements while staying within required constraint values. ... Optical redirects here. ... Chromatic aberration is caused by the dispersion of the lens material, the variation of its refractive index n with the wavelength of light. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In optics and telecommunication, the term optical path length has the following meanings: In a medium of constant refractive index, n , the product of the geometric distance and the refractive index. ... In optics, a wavefront is the locus (a line or surface in an electromagnetic wave) of points having the same phase. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The point spread function (PSF) defines the propagation of electromagnetic radiation from a point source. ... The Modulation Transfer Function (MTF) is a property of imaging systems. ... The modern definition of the Strehl ratio is the ratio of the observed peak intensity at the detection plane of a telescope or other imaging system from a point source compared to the theoretical maximum peak intensity of a perfect optical system working at the diffraction limit. ... The wavelength is the distance between repeating units of a wave pattern. ... Ultraviolet (UV) light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than soft X-rays. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz...

The principles of ray tracing for computer graphics and optical design are similar, but the technique in optical design usually uses much more rigorous and physically correct models of how light behaves. In particular, optical effects such as dispersion, diffraction and the behaviour of optical coatings are important in lens design, but are less so in computer graphics. Dispersion of a light beam in a prism. ... An optical coating is a thin layer of material placed on an optical component such as a lens or mirror which alters the way in which the optic reflects and transmits light. ... Optical lens design is the science/art of calculating the various lens construction parameters (variables) that will meet or at least approach desired performance requirements while staying within required constraint values. ...

Before the advent of the computer, ray tracing calculations were performed by hand using trigonometry and logarithmic tables. The optical formulas of many classic photographic lenses were optimized by rooms full of people, each of whom handled a small part of the large calculation. Now they are worked out in optical design software such as OSLO or TracePro from Lambda Research, Code-V or Zemax. A simple version of ray tracing known as ray transfer matrix analysis is often used in the design of optical resonators used in lasers. A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ... Wikibooks has more about this subject: Trigonometry Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. ... In mathematics, if two variables of bn = x are known, the third can be found. ... Photography is the process of making pictures by means of the action of light. ... County Oslo NO-03 District Viken Municipality NO-0301 Administrative centre Oslo Mayor (2004) Per Ditlev-Simonsen (H) Official language form Neutral Area  - Total  - Land  - Percentage Ranked 224 454 km² 426 km² 0. ... TracePro® is a general raytracing program for illumination analysis, optical analysis, radiometry analysis, and photometry analysis. ... CODE V is a commercial software package developed by Optical Research Associates. ... Zemax is a commercial optical design program designed by Ken Moore and has been developed since the 1980s. ... Ray transfer matrix analysis (also known as ABCD matrix analysis) is a type of ray tracing technique used in the design of some optical systems, particularly lasers. ... This page meets Wikipedias criteria for speedy deletion. ... Lasers range in size from microscopic diode lasers (top) with numerous applications, to football field sized neodymium glass lasers (bottom) used for inertial confinement fusion, nuclear weapons research and other high energy density physics experiments. ...

Example

As a demonstration of the principles involved in raytracing, let us consider how one would find the intersection between a ray and a sphere. The general equation of a sphere, where I is a point on the surface of the sphere, C is its centre and r is its radius, is . Equally, if a line is defined by its starting point S (consider this the starting point of the ray) and its direction d (consider this the direction of that particular ray), each point on the line may be described by the expression

where t is a constant defining the distance along the line from the starting point (hence, for simplicity's sake, d is generally a unit vector). Now, in the scene we know S, d, C, and r. Hence we need to find t as we substitute in for I: In mathematics, a unit vector in a normed vector space is a vector (most commonly a spatial vector) whose length is 1. ...

Let for simplicity, then

Now this quadratic equation has solutions

This is merely the math behind a straight ray-sphere intersection. There is of course far more to the general process of raytracing, but this demonstrates an example of the algorithms used. This article needs more context around or a better explanation of technical details to make it more accessible to general readers and technical readers outside the specialty, without removing technical details. ...

See also

• Actual state
• Beam tracing
• BRL-CAD
• Cone tracing
• Distributed ray tracing
• Global illumination
• Line-sphere intersection
• Pencil tracing
• Philipp Slusallek
• Photon mapping
• POV-Ray
• Powerwall
• Radiosity
• Radiance (software)
• Target state
• YafRay

Beam tracing is a derivative of the ray tracing algorithm that replaces rays, which have no thickness, with beams. ... BRL-CAD is a powerful Constructive Solid Geometry (CSG) solid modeling Computer-aided design (CAD) system. ... Cone tracing is a derivative of the ray tracing algorithm that replaces rays, which have no thickness, with cones. ... Distributed ray tracing, also called distribution ray tracing and stochastic ray tracing, is a refinement of ray tracing that allows for the rendering of soft phenomena. ... Global illumination algorithms used in 3D computer graphics are those which, when determining the light falling on a surface, take into account not only the light which has taken a path directly from a light source (direct illumination), but also light which has undergone reflection from other surfaces in the... This article needs more context around or a better explanation of technical details to make it more accessible to general readers and technical readers outside the specialty, without removing technical details. ... A crystal ball with caustics In computer graphics, photon mapping is a global illumination algorithm based on ray tracing used to realistically simulate the interaction of light with different objects. ... The Utah teapot, rendered in POV-Ray. ... A Powerwall is the generic term for large, non-tiled high-resolution display walls used for projecting large computer generated images. ... Radiosity is a global illumination algorithm used in 3D computer graphics rendering. ... Radiance is a suite of tools for performing lighting simulation originally written by Greg Ward. ... External link YafRay homepage Categories: Stub | 3D graphics software ...

References

• Glassner, Andrew (Ed.) (1989). An Introduction to Ray Tracing. Academic Press. ISBN 0-12-286160-4.
• Shirley, Peter and Morley Keith, R. (2001) Realistic Ray Tracing,2nd edition. A.K. Peters. ISBN 1-56881-198-5.
• Henrik Wann Jensen. (2001) Realistic image synthesis using photon mapping. A.K. Peters. ISBN 1-56881-147-0.
• Pharr, Matt and Humphreys, Greg (2004). Physically Based Rendering : From Theory to Implementation. Morgan Kaufmann. ISBN 0-12-553180-X.

External links

• The Ray Tracing News - short research articles and new links to resources
• Games using realtime raytracing
• A series of tutorials on implementing a raytracer using C++
• Mini ray tracers written equivalently in various languages

Raytracing software

• POV-Ray
• PBRT - a Physically Based Raytracer
• Tachyon
• Rayshade
• OpenRT - realtime raytracing library
• Raster3D
• RealStorm Engine - a realtime raytracing engine
• BRL-CAD
• More ray tracing source code links
• Zemax
• Radiance
• Yafray
• OSLO - Lens design and optimization software; OSLO-EDU is a free download
• TracePro - Straylight and illumination software with a CAD-like interface