In 3D computer graphics, ray tracing is a technique for modeling light transport for use in a wide variety of rendering algorithms for generating digital images. On a spectrum of computational cost and visual fidelity, ray tracing-based rendering techniques, such as ray casting, recursive ray tracing, distribution ray tracing, photon mapping and path tracing, are generally slower and higher fidelity than scanline rendering methods. Thus, ray tracing was first deployed in applications where taking a relatively long time to render could be tolerated, such as still CGI images, and film and television visual effects (VFX), but was less suited to real-time applications such as video games, where speed is critical in rendering each frame. Since 2018, however, hardware acceleration for real-time ray tracing has become standard on new commercial graphics cards, and graphics APIs have followed suit, allowing developers to use hybrid ray tracing and rasterization-based rendering in games and other real-time applications with a lesser hit to frame render times. Ray tracing is capable of simulating a variety of optical effects, such as reflection, refraction, soft shadows, scattering, depth of field, motion blur, caustics, ambient occlusion and dispersion phenomena (such as chromatic aberration). It can also be used to trace the path of sound waves in a similar fashion to light waves, making it a viable option for more immersive sound design in video games by rendering realistic reverberation and echoes. In fact, any physical wave or particle phenomenon with approximately linear motion can be simulated with ray tracing. Ray tracing–based rendering techniques that sample light over a domain typically generate multiple rays and often rely on denoising to reduce the resulting noise. == History == The idea of ray tracing comes from as early as the 16th century, when it was described by Albrecht Dürer, who is credited for its invention. Dürer described multiple techniques for projecting 3-D scenes onto an image plane. Some of these project chosen geometry onto the image plane, as is done with rasterization today. Others determine what geometry is visible along a given ray, as is done with ray tracing. Using a computer for ray tracing to generate shaded pictures was first accomplished by Arthur Appel in 1968. Appel used ray tracing for primary visibility (determining the closest surface to the camera at each image point) by tracing a ray through each point to be shaded into the scene to identify the visible surface. The closest surface intersected by the ray was the visible one. This non-recursive ray tracing-based rendering algorithm is today called "ray casting". His algorithm then traced secondary rays to the light source from each point being shaded to determine whether the point was in shadow or not. Later, in 1971, Goldstein and Nagel of MAGI (Mathematical Applications Group, Inc.) published "3-D Visual Simulation", wherein ray tracing was used to make shaded pictures of solids. At the ray-surface intersection point found, they computed the surface normal and, knowing the position of the light source, computed the brightness of the pixel on the screen. Their publication describes a short (30-second) film "made using the University of Maryland's display hardware outfitted with a 16mm camera. The film showed the helicopter and a simple ground-level gun emplacement. The helicopter was programmed to undergo a series of maneuvers including turns, take-offs, and landings, etc., until it eventually is shot down and crashed." A CDC 6600 computer was used. MAGI produced an animation video called MAGI/SynthaVision Sampler in 1974. Another early instance of ray casting came in 1976, when Scott Roth created a flip book animation in Bob Sproull's computer graphics course at Caltech. The scanned pages are shown as a video in the accompanying image. Roth's computer program noted an edge point at a pixel location if the ray intersected a bounded plane different from that of its neighbors. Of course, a ray could intersect multiple planes in space, but only the surface point closest to the camera was noted as visible. The platform was a DEC PDP-10, a Tektronix storage-tube display, and a printer which would create an image of the display on rolling thermal paper. Roth extended the framework, introduced the term ray casting in the context of computer graphics and solid modeling, and in 1982 published his work while at GM Research Labs. Turner Whitted was the first to show recursive ray tracing for mirror reflection and for refraction through translucent objects, with an angle determined by the solid's index of refraction, and to use ray tracing for anti-aliasing. Whitted also showed ray traced shadows. He produced a recursive ray traced film called The Compleat Angler in 1979 while an engineer at Bell Labs. Whitted's deeply recursive ray tracing algorithm reframed rendering from being primarily a matter of surface visibility determination to being a matter of light transport. His paper inspired a series of subsequent work by others that included distribution ray tracing and finally unbiased path tracing, which provides the rendering equation framework that has allowed computer-generated imagery to be faithful to reality. For decades, global illumination in major films using computer-generated imagery was approximated with additional lights. Ray tracing-based rendering eventually changed that by enabling physically based light transport. Early feature films rendered entirely using path tracing include Monster House (2006), Cloudy with a Chance of Meatballs (2009), and Monsters University (2013). == Algorithm overview == Optical ray tracing describes a method for producing visual images constructed in 3D computer graphics environments, with more photorealism than either ray casting or scanline rendering techniques. It works by tracing a path from an imaginary eye through each pixel in a virtual screen, and calculating the color of the object visible through it. Scenes in ray tracing are described mathematically by a programmer or by a visual artist (normally using intermediary tools). Scenes may also incorporate data from images and models captured by means such as digital photography. Typically, each ray must be tested for intersection with some subset of all the objects in the scene. Once the nearest object has been identified, the algorithm will estimate the incoming light at the point of intersection, examine the material properties of the object, and combine this information to calculate the final color of the pixel. Certain illumination algorithms and reflective or translucent materials may require more rays to be re-cast into the scene. It may at first seem counterintuitive or "backward" to send rays away from the camera, rather than into it (as actual light does in reality), but doing so is many orders of magnitude more efficient. Since the overwhelming majority of light rays from a given light source do not make it directly into the viewer's eye, a "forward" simulation could potentially waste a tremendous amount of computation on light paths that are never recorded. Therefore, the shortcut taken in ray tracing is to presuppose that a given ray intersects the view frame. After either a maximum number of reflections or a ray traveling a certain distance without intersection, the ray ceases to travel and the pixel's value is updated. === Calculate rays for rectangular viewport === On input we have (in calculation we use vector normalization and cross product): E ∈ R 3 {\displaystyle E\in \mathbb {R^{3}} } eye position T ∈ R 3 {\displaystyle T\in \mathbb {R^{3}} } target position θ ∈ [ 0 , π ] {\displaystyle \theta \in [0,\pi ]} field of view - for humans, we can assume ≈ π / 2 rad = 90 ∘ {\displaystyle \approx \pi /2{\text{ rad}}=90^{\circ }} m , k ∈ N {\displaystyle m,k\in \mathbb {N} } numbers of square pixels on viewport vertical and horizontal direction i , j ∈ N , 1 ≤ i ≤ k ∧ 1 ≤ j ≤ m {\displaystyle i,j\in \mathbb {N} ,1\leq i\leq k\land 1\leq j\leq m} numbers of actual pixel v → ∈ R 3 {\displaystyle {\vec {v}}\in \mathbb {R^{3}} } vertical vector which indicates where is up and down, usually v → = [ 0 , 1 , 0 ] {\displaystyle {\vec {v}}=[0,1,0]} - roll component which determine viewport rotation around point C (where the axis of rotation is the ET section) The idea is to find the position of each viewport pixel center P i j {\displaystyle P_{ij}} which allows us to find the line going from eye E {\displaystyle E} through that pixel and finally get the ray described by point E {\displaystyle E} and vector R → i j = P i j − E {\displaystyle {\vec {R}}_{ij}=P_{ij}-E} (or its normalization r → i j {\displaystyle {\vec {r}}_{ij}} ). First we need to find the coordinates of the bottom left viewport pixel P 1 m {\displaystyle P_{1m}} and find the next pixel by making a shift along directions parallel to viewport (vectors b → n {\displaystyle {\vec {b}}_{n
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