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108-528: In a 3D-rendering pipeline , when an object is projected on the screen, the depth (z-value) of a generated fragment in the projected screen image is compared to the value already stored in the buffer ( depth test ), and replaces it if the new value is closer. It works in tandem with the rasterizer , which computes the colored values. The fragment output by the rasterizer is saved if it is not overlapped by another fragment. When viewing an image containing partially or fully overlapping opaque objects or surfaces, it

216-500: A r / ( n e a r − f a r ) − 1 0 0 ( n e a r ∗ f a r ) / ( n e a r − f a r ) 0 ) {\displaystyle {\begin{pmatrix}w&0&0&0\\0&h&0&0\\0&0&{far}/({near-far})&-1\\0&0&({near}*{far})/({near}-{far})&0\end{pmatrix}}} The reasons why

324-418: A r {\displaystyle near} is, the less precision there is far away—having the n e a r {\displaystyle near} plane set too closely is a common cause of undesirable rendering artifacts in more distant objects. To implement a z-buffer, the values of z ′ {\displaystyle z'} are linearly interpolated across screen space between

432-429: A r − f a r ) − 1 0 0 n e a r / ( n e a r − f a r ) 0 ) {\displaystyle {\begin{pmatrix}2.0/w&0&0&0\\0&2.0/h&0&0\\0&0&1.0/({near-far})&-1\\0&0&{near}/({near}-{far})&0\end{pmatrix}}} For reasons of efficiency,

540-557: A three-dimensional (3D) scene into a two-dimensional (2D) representation on a screen. Once a 3D model is generated, the graphics pipeline converts the model into a visually perceivable format on the computer display. Due to the dependence on specific software , hardware configurations, and desired display attributes, a universally applicable graphics pipeline does not exist. Nevertheless, graphics application programming interfaces (APIs), such as Direct3D , OpenGL and Vulkan were developed to standardize common procedures and oversee

648-475: A bit pattern to each character , digit , or multimedia object. Many standards exist for encoding (e.g. character encodings like ASCII , image encodings like JPEG , and video encodings like MPEG-4 ). By adding bits to each encoded unit, redundancy allows the computer to detect errors in coded data and correct them based on mathematical algorithms. Errors generally occur in low probabilities due to random bit value flipping, or "physical bit fatigue", loss of

756-493: A computer a brief window of time to move information from primary volatile storage into non-volatile storage before the batteries are exhausted. Some systems, for example EMC Symmetrix , have integrated batteries that maintain volatile storage for several minutes. Utilities such as hdparm and sar can be used to measure IO performance in Linux. Full disk encryption , volume and virtual disk encryption, andor file/folder encryption

864-424: A database) to represent a string of bits by a shorter bit string ("compress") and reconstruct the original string ("decompress") when needed. This utilizes substantially less storage (tens of percent) for many types of data at the cost of more computation (compress and decompress when needed). Analysis of the trade-off between storage cost saving and costs of related computations and possible delays in data availability

972-702: A drive. When the computer has finished reading the information, the robotic arm will return the medium to its place in the library. Tertiary storage is also known as nearline storage because it is "near to online". The formal distinction between online, nearline, and offline storage is: For example, always-on spinning hard disk drives are online storage, while spinning drives that spin down automatically, such as in massive arrays of idle disks ( MAID ), are nearline storage. Removable media such as tape cartridges that can be automatically loaded, as in tape libraries , are nearline storage, while tape cartridges that must be manually loaded are offline storage. Off-line storage

1080-493: A freely programmable, shader-controlled pipeline, which allows direct access to individual processing steps. To relieve the main processor, additional processing steps have been moved to the pipeline and the GPU. The most important shader units are vertex shaders , geometry shaders, and pixel shaders. The Unified Shader has been introduced to take full advantage of all units. This gives a single large pool of shader units. As required,

1188-463: A more common range which is [0, 1] by substituting the appropriate conversion z 2 ′ = 1 2 ( z 1 ′ + 1 ) {\displaystyle z'_{2}={\frac {1}{2}}\left(z'_{1}+1\right)} into the previous formula: Simplifying: Second, the above formula is multiplied by S = 2 d − 1 {\displaystyle S=2^{d}-1} where d

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1296-417: A new coordinate system, allowing for flexible extensions. For instance, an aircraft's propeller, modeled separately, can be attached to the aircraft nose through translation, which only shifts from the model to the propeller coordinate system. To render the aircraft, its transformation matrix is first computed to transform the points, followed by multiplying the propeller model matrix by the aircraft's matrix for

1404-404: A recent addition, aiming to overcome the bottlenecks of the geometry pipeline fixed layout. Computer storage Computer data storage or digital data storage is a technology consisting of computer components and recording media that are used to retain digital data . It is a core function and fundamental component of computers. The central processing unit (CPU) of a computer

1512-400: A relatively simple processor may keep state between successive computations to build up complex procedural results. Most modern computers are von Neumann machines. A modern digital computer represents data using the binary numeral system . Text, numbers, pictures, audio, and nearly any other form of information can be converted into a string of bits , or binary digits, each of which has

1620-427: A reverse painter's algorithm cannot be used as an alternative to Z-culling (without strenuous re-engineering), except as an optimization to Z-culling. For example, an optimization might be to keep polygons sorted according to x/y-location and z-depth to provide bounds, in an effort to quickly determine if two polygons might possibly have an occlusion interaction. The range of depth values in camera space to be rendered

1728-427: A scene contains light sources placed at different positions to make the lighting of the objects appear more realistic. In this case, a gain factor for the texture is calculated for each vertex based on the light sources and the material properties associated with the corresponding triangle. In the later rasterization step, the vertex values of a triangle are interpolated over its surface. A general lighting (ambient light)

1836-477: A significant chunk of the available memory bandwidth . Various methods have been employed to reduce the performance cost of z-buffering, such as lossless compression (computer resources to compress/decompress are cheaper than bandwidth) and ultra-fast hardware z-clear that makes obsolete the "one frame positive, one frame negative" trick (skipping inter-frame clear altogether using signed numbers to cleverly check depths). Some games, notably several games later in

1944-574: A source to read instructions from, in order to start the computer. Hence, non-volatile primary storage containing a small startup program ( BIOS ) is used to bootstrap the computer, that is, to read a larger program from non-volatile secondary storage to RAM and start to execute it. A non-volatile technology used for this purpose is called ROM, for read-only memory (the terminology may be somewhat confusing as most ROM types are also capable of random access ). Many types of "ROM" are not literally read only , as updates to them are possible; however it

2052-563: A surface from a light's point-of-view permits the creation of shadows by the shadow mapping technique. Even with small enough granularity, quality problems may arise when precision in the z-buffer's distance values are not spread evenly over distance. Nearer values are much more precise (and hence can display closer objects better) than values that are farther away. Generally, this is desirable, but sometimes it will cause artifacts to appear as objects become more distant. A variation on z-buffering which results in more evenly distributed precision

2160-443: A surface, the color and lighting of the point on the surface where the ray hit is calculated. In 3D polygon rendering the reverse happens- the area that is given the camera is calculated and then rays are created from every part of every surface given the camera and traced back to the camera. A graphics pipeline can be divided into three main parts: Application, Geometry, and Rasterization. [REDACTED] The application step

2268-491: A translation matrix that moves the aircraft to the desired point in our world: T x , y , z = ( 1 0 0 0 0 1 0 0 0 0 1 0 x y z 1 ) {\displaystyle T_{x,y,z}={\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\x&y&z&1\end{pmatrix}}} . Now we could calculate

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2376-490: A value of 0 or 1. The most common unit of storage is the byte , equal to 8 bits. A piece of information can be handled by any computer or device whose storage space is large enough to accommodate the binary representation of the piece of information , or simply data . For example, the complete works of Shakespeare , about 1250 pages in print, can be stored in about five megabytes (40 million bits) with one byte per character. Data are encoded by assigning

2484-427: Is a form of volatile memory that also requires the stored information to be periodically reread and rewritten, or refreshed , otherwise it would vanish. Static random-access memory is a form of volatile memory similar to DRAM with the exception that it never needs to be refreshed as long as power is applied; it loses its content when the power supply is lost. An uninterruptible power supply (UPS) can be used to give

2592-425: Is a level below secondary storage. Typically, it involves a robotic mechanism which will mount (insert) and dismount removable mass storage media into a storage device according to the system's demands; such data are often copied to secondary storage before use. It is primarily used for archiving rarely accessed information since it is much slower than secondary storage (e.g. 5–60 seconds vs. 1–10 milliseconds). This

2700-400: Is a point in the world. Many points are used to join the surfaces. In special cases, point clouds are drawn directly, but this is still the exception. A triangle is the most common geometric primitive of computer graphics. It is defined by its three vertices and a normal vector - the normal vector serves to indicate the front face of the triangle and is a vector that is perpendicular to

2808-557: Is almost never used since it has too little precision. Z-buffering is a technique used in almost all contemporary computers, laptops, and mobile phones for performing 3D computer graphics . The primary use now is for video games , which require fast and accurate processing of 3D scenes. Z-buffers are often implemented in hardware within consumer graphics cards . Z-buffering is also used (implemented as software as opposed to hardware) for producing computer-generated special effects for films. Furthermore, Z-buffer data obtained from rendering

2916-404: Is applied to all surfaces. It is the diffuse and thus direction-independent brightness of the scene. The sun is a directed light source, which can be assumed to be infinitely far away. The illumination effected by the sun on a surface is determined by forming the scalar product of the directional vector from the sun and the normal vector of the surface. If the value is negative, the surface is facing

3024-595: Is called w-buffering (see below ). At the start of a new scene, the z-buffer must be cleared to a defined value, usually 1.0, because this value is the upper limit (on a scale of 0 to 1) of depth, meaning that no object is present at this point through the viewing frustum . The invention of the z-buffer concept is most often attributed to Edwin Catmull , although Wolfgang Straßer described this idea in his 1974 Ph.D. thesis months before Catmull's invention. On more recent PC graphics cards (1999–2005), z-buffer management uses

3132-410: Is computer data storage on a medium or a device that is not under the control of a processing unit . The medium is recorded, usually in a secondary or tertiary storage device, and then physically removed or disconnected. It must be inserted or connected by a human operator before a computer can access it again. Unlike tertiary storage, it cannot be accessed without human interaction. Off-line storage

3240-584: Is defined by: After an orthographic projection , the new value of z {\displaystyle z} , or z ′ {\displaystyle z'} , is defined by: where z {\displaystyle z} is the old value of z {\displaystyle z} in camera space, and is sometimes called w {\displaystyle w} or w ′ {\displaystyle w'} . The resulting values of z ′ {\displaystyle z'} are normalized between

3348-408: Is done before deciding whether to keep certain data compressed or not. For security reasons , certain types of data (e.g. credit card information) may be kept encrypted in storage to prevent the possibility of unauthorized information reconstruction from chunks of storage snapshots. Generally, the lower a storage is in the hierarchy, the lesser its bandwidth and the greater its access latency

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3456-609: Is estimable using S.M.A.R.T. diagnostic data that includes the hours of operation and the count of spin-ups, though its reliability is disputed. Flash storage may experience downspiking transfer rates as a result of accumulating errors, which the flash memory controller attempts to correct. The health of optical media can be determined by measuring correctable minor errors , of which high counts signify deteriorating and/or low-quality media. Too many consecutive minor errors can lead to data corruption. Not all vendors and models of optical drives support error scanning. As of 2011 ,

3564-582: Is executed by the software on the main processor ( CPU ). During the application step, changes are made to the scene as required, for example, by user interaction using input devices or during an animation. The new scene with all its primitives , usually triangles, lines, and points, is then passed on to the next step in the pipeline. Examples of tasks that are typically done in the application step are collision detection , animation, morphing, and acceleration techniques using spatial subdivision schemes such as Quadtrees or Octrees . These are also used to reduce

3672-1109: Is from the CPU. This traditional division of storage to primary, secondary, tertiary, and off-line storage is also guided by cost per bit. In contemporary usage, memory is usually fast but temporary semiconductor read-write memory , typically DRAM (dynamic RAM) or other such devices. Storage consists of storage devices and their media not directly accessible by the CPU ( secondary or tertiary storage ), typically hard disk drives , optical disc drives, and other devices slower than RAM but non-volatile (retaining contents when powered down). Historically, memory has, depending on technology, been called central memory , core memory , core storage , drum , main memory , real storage , or internal memory . Meanwhile, slower persistent storage devices have been referred to as secondary storage , external memory , or auxiliary/peripheral storage . Primary storage (also known as main memory , internal memory , or prime memory ), often referred to simply as memory ,

3780-433: Is necessary to determine the visible, closer to the observer fragment, in the case of overlapping polygons. A Z-buffer is usually used for this so-called hidden surface determination . The color of a fragment depends on the illumination, texture, and other material properties of the visible primitive and is often interpolated using the triangle vertex properties. Where available, a fragment shader (also called Pixel Shader )

3888-429: Is not possible to fully see those objects that are farthest away from the viewer and behind other objects (i.e., some surfaces are hidden behind others). If there were no mechanism for managing overlapping surfaces, surfaces would render on top of each other, not caring if they are meant to be behind other objects. The identification and removal of these surfaces are called the hidden-surface problem . To check for overlap,

3996-465: Is not storing color information. The buffer has the same dimensions as the screen buffer for consistency. Primary visibility tests (such as back-face culling ) and secondary visibility tests (such as overlap checks and screen clipping) are usually performed on objects' polygons in order to skip specific polygons that are unnecessary to render. Z-buffer, by comparison, is comparatively expensive , so performing primary and secondary visibility tests relieve

4104-399: Is often defined between a near {\displaystyle {\textit {near}}} and far {\displaystyle {\textit {far}}} value of z {\displaystyle z} . After a perspective transformation , the new value of z {\displaystyle z} , or z ′ {\displaystyle z'} ,

4212-414: Is often the most intuitive because the rotation causes the compass direction to coincide with the direction of the "nose". There are also two conventions to define these matrices, depending on whether you want to work with column vectors or row vectors. Different graphics libraries have different preferences here. OpenGL prefers column vectors, DirectX row vectors. The decision determines from which side

4320-416: Is primarily useful for extraordinarily large data stores, accessed without human operators. Typical examples include tape libraries and optical jukeboxes . When a computer needs to read information from the tertiary storage, it will first consult a catalog database to determine which tape or disc contains the information. Next, the computer will instruct a robotic arm to fetch the medium and place it in

4428-700: Is readily available for most storage devices. Hardware memory encryption is available in Intel Architecture, supporting Total Memory Encryption (TME) and page granular memory encryption with multiple keys (MKTME). and in SPARC M7 generation since October 2015. Distinct types of data storage have different points of failure and various methods of predictive failure analysis . Vulnerabilities that can instantly lead to total loss are head crashing on mechanical hard drives and failure of electronic components on flash storage. Impending failure on hard disk drives

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4536-416: Is run in the rastering step for each fragment of the object. If a fragment is visible, it can now be mixed with already existing color values in the image if transparency or multi-sampling is used. In this step, one or more fragments become a pixel. To prevent the user sees the gradual rasterization of the primitives, double buffering takes place. The rasterization is carried out in a special memory area. Once

4644-488: Is slow and memory must be erased in large portions before it can be re-written. Some embedded systems run programs directly from ROM (or similar), because such programs are rarely changed. Standard computers do not store non-rudimentary programs in ROM, and rather, use large capacities of secondary storage, which is non-volatile as well, and not as costly. Recently, primary storage and secondary storage in some uses refer to what

4752-480: Is the depth of the z-buffer (usually 16, 24 or 32 bits) and rounding the result to an integer: This formula can be inverted and derived in order to calculate the z-buffer resolution (the 'granularity' mentioned earlier). The inverse of the above f ( z ) {\displaystyle f(z)\,} : where S = 2 d − 1 {\displaystyle S=2^{d}-1} The z-buffer resolution in terms of camera space would be

4860-442: Is the only one directly accessible to the CPU. The CPU continuously reads instructions stored there and executes them as required. Any data actively operated on is also stored there in a uniform manner. Historically, early computers used delay lines , Williams tubes , or rotating magnetic drums as primary storage. By 1954, those unreliable methods were mostly replaced by magnetic-core memory . Core memory remained dominant until

4968-405: Is typically automatically fenced out, taken out of use by the device, and replaced with another functioning equivalent group in the device, where the corrected bit values are restored (if possible). The cyclic redundancy check (CRC) method is typically used in communications and storage for error detection . A detected error is then retried. Data compression methods allow in many cases (such as

5076-505: Is typically measured in milliseconds (thousandths of a second), while the access time per byte for primary storage is measured in nanoseconds (billionths of a second). Thus, secondary storage is significantly slower than primary storage. Rotating optical storage devices, such as CD and DVD drives, have even longer access times. Other examples of secondary storage technologies include USB flash drives , floppy disks , magnetic tape , paper tape , punched cards , and RAM disks . Once

5184-420: Is used in a similar sense for the pipeline in processors : the individual steps of the pipeline run in parallel as long as any given step has what it needs. The 3D pipeline usually refers to the most common form of computer 3-Dimensional rendering called 3D polygon rendering , distinct from Raytracing and Raycasting . In Raycasting, a ray originates at the point where the camera resides, and if that ray hits

5292-496: Is used to transfer information since the detached medium can easily be physically transported. Additionally, it is useful for cases of disaster, where, for example, a fire destroys the original data, a medium in a remote location will be unaffected, enabling disaster recovery . Off-line storage increases general information security since it is physically inaccessible from a computer, and data confidentiality or integrity cannot be affected by computer-based attack techniques. Also, if

5400-682: Is what manipulates data by performing computations. In practice, almost all computers use a storage hierarchy , which puts fast but expensive and small storage options close to the CPU and slower but less expensive and larger options further away. Generally, the fast technologies are referred to as "memory", while slower persistent technologies are referred to as "storage". Even the first computer designs, Charles Babbage 's Analytical Engine and Percy Ludgate 's Analytical Machine, clearly distinguished between processing and memory (Babbage stored numbers as rotations of gears, while Ludgate stored numbers as displacements of rods in shuttles). This distinction

5508-500: The N64 's life cycle, decided to either minimize Z buffering (for example, rendering the background first without z buffering and only using Z buffering for the foreground objects) or to omit it entirely, to reduce memory bandwidth requirements and memory requirements respectively. Super Smash Bros. and F-Zero X are two N64 games that minimized Z buffering to increase framerates. Several Factor 5 games also minimized or omitted Z buffering. On

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5616-466: The Window-Viewport transformation , must be applied. This is a shift, followed by scaling. The resulting coordinates are the device coordinates of the output device. The viewport contains 6 values: the height and width of the window in pixels, the upper left corner of the window in window coordinates (usually 0, 0), and the minimum and maximum values for Z (usually 0 and 1). On modern hardware, most of

5724-476: The disk read/write head on HDDs reaches the proper placement and the data, subsequent data on the track are very fast to access. To reduce the seek time and rotational latency, data are transferred to and from disks in large contiguous blocks. Sequential or block access on disks is orders of magnitude faster than random access, and many sophisticated paradigms have been developed to design efficient algorithms based on sequential and block access. Another way to reduce

5832-433: The vertices of the current polygon , and these intermediate values are generally stored in the z-buffer in fixed point format. To implement a w-buffer, the old values of z {\displaystyle z} in camera space, or w {\displaystyle w} , are stored in the buffer, generally in floating point format. However, these values cannot be linearly interpolated across screen space from

5940-690: The 1970s, when advances in integrated circuit technology allowed semiconductor memory to become economically competitive. This led to modern random-access memory (RAM). It is small-sized, light, but quite expensive at the same time. The particular types of RAM used for primary storage are volatile , meaning that they lose the information when not powered. Besides storing opened programs, it serves as disk cache and write buffer to improve both reading and writing performance. Operating systems borrow RAM capacity for caching so long as it's not needed by running software. Spare memory can be utilized as RAM drive for temporary high-speed data storage. As shown in

6048-508: The I/O bottleneck is to use multiple disks in parallel to increase the bandwidth between primary and secondary memory. Secondary storage is often formatted according to a file system format, which provides the abstraction necessary to organize data into files and directories , while also providing metadata describing the owner of a certain file, the access time, the access permissions, and other information. Most computer operating systems use

6156-487: The N64 Z Buffering can consume up to 4x as much bandwidth as opposed to not using Z buffering. Mechwarrior 2 on PC supported resolutions up to 800x600 on the original 4 MB 3DFX Voodoo due to not using Z Buffering. In rendering , z-culling is early pixel elimination based on depth, a method that provides an increase in performance when rendering of hidden surfaces is costly. It is a direct consequence of z-buffering, where

6264-637: The X-axis, if one rotates it first by 90° around the X- and then around The Y-axis, it ends up on the Z-axis (the rotation around the X-axis does not affect a point that is on the axis). If, on the other hand, one rotates around the Y-axis first and then around the X-axis, the resulting point is located on the Y-axis. The sequence itself is arbitrary as long as it is always the same. The sequence with x, then y, then z (roll, pitch, heading)

6372-410: The above f ( z ) {\displaystyle f(z)\,} : This shows that the values of z ′ {\displaystyle z'} are grouped much more densely near the near {\displaystyle {\textit {near}}} plane, and much more sparsely farther away, resulting in better precision closer to the camera. The smaller n e

6480-520: The amount of main memory required at a given time. The "world" of a modern computer game is far larger than what could fit into memory at once. The geometry step (with Geometry pipeline ), which is responsible for the majority of the operations with polygons and their vertices (with Vertex pipeline ), can be divided into the following five tasks. It depends on the particular implementation of how these tasks are organized as actual parallel pipeline steps. [REDACTED] A vertex (plural: vertices)

6588-506: The camera and projection matrix are usually combined into a transformation matrix so that the camera coordinate system is omitted. The resulting matrix is usually the same for a single image, while the world matrix looks different for each object. In practice, therefore, view and projection are pre-calculated so that only the world matrix has to be adapted during the display. However, more complex transformations such as vertex blending are possible. Freely programmable geometry shaders that modify

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6696-485: The case of row vectors, this works exactly the other way around. The multiplication now takes place from the left as v o u t = v i n ∗ M {\displaystyle v_{out}=v_{in}*M} with 1x4-row vectors and the concatenation is M = R x ∗ T x {\displaystyle M=R_{x}*T_{x}} when we also first rotate and then move. The matrices shown above are valid for

6804-433: The computer calculates the z-value of a pixel corresponding to the first object and compares it with the z-value at the same pixel location in the z-buffer. If the calculated z-value is smaller than the z-value already in the z-buffer (i.e., the new pixel is closer), then the current z-value in the z-buffer is replaced with the calculated value. This is repeated for all objects and surfaces in the scene (often in parallel ). In

6912-524: The concept of virtual memory , allowing the utilization of more primary storage capacity than is physically available in the system. As the primary memory fills up, the system moves the least-used chunks ( pages ) to a swap file or page file on secondary storage, retrieving them later when needed. If a lot of pages are moved to slower secondary storage, the system performance is degraded. The secondary storage, including HDD , ODD and SSD , are usually block-addressable. Tertiary storage or tertiary memory

7020-447: The coordinate system is defined, is left to the developer. Whether, therefore, the unit vector of the system corresponds in reality to one meter or an Ångström depends on the application. The objects contained within the scene (houses, trees, cars) are often designed in their object coordinate system (also called model coordinate system or local coordinate system) for reasons of simpler modeling. To assign these objects to coordinates in

7128-538: The culled pixels. This makes z-culling a good optimization candidate in situations where fillrate , lighting, texturing, or pixel shaders are the main bottlenecks . While z-buffering allows the geometry to be unsorted, sorting polygons by increasing depth (thus using a reverse painter's algorithm ) allows each screen pixel to be rendered fewer times. This can increase performance in fillrate-limited scenes with large amounts of overdraw, but if not combined with z-buffering it suffers from severe problems such as: As such,

7236-401: The depth of each pixel candidate is compared to the depth of the existing geometry behind which it might be hidden. When using a z-buffer, a pixel can be culled (discarded) as soon as its depth is known, which makes it possible to skip the entire process of lighting and texturing a pixel that would not be visible anyway. Also, time-consuming pixel shaders will generally not be executed for

7344-430: The desired data to primary storage. Secondary storage is non-volatile (retaining data when its power is shut off). Modern computer systems typically have two orders of magnitude more secondary storage than primary storage because secondary storage is less expensive. In modern computers, hard disk drives (HDDs) or solid-state drives (SSDs) are usually used as secondary storage. The access time per byte for HDDs or SSDs

7452-491: The desired location of data. Then it reads or writes the data in the memory cells using the data bus. Additionally, a memory management unit (MMU) is a small device between CPU and RAM recalculating the actual memory address, for example to provide an abstraction of virtual memory or other tasks. As the RAM types used for primary storage are volatile (uninitialized at start up), a computer containing only such storage would not have

7560-400: The diagram, traditionally there are two more sub-layers of the primary storage, besides main large-capacity RAM: Main memory is directly or indirectly connected to the central processing unit via a memory bus . It is actually two buses (not on the diagram): an address bus and a data bus . The CPU firstly sends a number through an address bus, a number called memory address , that indicates

7668-435: The end, the z-buffer will allow correct reproduction of the usual depth perception: a close object hides one further away. This is called z-culling . The z-buffer has the same internal data structure as an image, namely a 2D-array, with the only difference being that it stores a single value for each screen pixel instead of color images that use 3 values to create color. This makes the z-buffer appear black-and-white because it

7776-477: The former using standard MOSFETs and the latter using floating-gate MOSFETs . In modern computers, primary storage almost exclusively consists of dynamic volatile semiconductor random-access memory (RAM), particularly dynamic random-access memory (DRAM). Since the turn of the century, a type of non-volatile floating-gate semiconductor memory known as flash memory has steadily gained share as off-line storage for home computers. Non-volatile semiconductor memory

7884-456: The fragment shader pipeline that all primitives are rasterized with. In the rasterization step, discrete fragments are created from continuous primitives. In this stage of the graphics pipeline, the grid points are also called fragments, for the sake of greater distinctiveness. Each fragment corresponds to one pixel in the frame buffer and this corresponds to one pixel of the screen. These can be colored (and possibly illuminated). Furthermore, it

7992-409: The geometry can also be executed. In the actual rendering step, the world matrix * camera matrix * projection matrix is calculated and then finally applied to every single point. Thus, the points of all objects are transferred directly to the screen coordinate system (at least almost, the value range of the axes is still -1..1 for the visible range, see section "Window-Viewport-Transformation"). Often

8100-465: The geometry computation steps are performed in the vertex shader . This is, in principle, freely programmable, but generally performs at least the transformation of the points and the illumination calculation. For the DirectX programming interface, the use of a custom vertex shader is necessary from version 10, while older versions still have a standard shader. The rasterization step is the final step before

8208-481: The graphics pipeline of a given hardware accelerator. These APIs provide an abstraction layer over the underlying hardware, relieving programmers from the need to write code explicitly targeting various graphics hardware accelerators like AMD , Intel , Nvidia , and others. The model of the graphics pipeline is usually used in real-time rendering. Often, most of the pipeline steps are implemented in hardware, which allows for special optimizations . The term "pipeline"

8316-420: The graphics pipeline. Primitives that are only partially inside the cube must be clipped against the cube. The advantage of the previous projection step is that the clipping always takes place against the same cube. Only the - possibly clipped - primitives, which are within the visual volume, are forwarded to the final step. To output the image to any target area (viewport) of the screen, another transformation,

8424-410: The image has been completely rasterized, it is copied to the visible area of the image memory. All matrices used are nonsingular and thus invertible. Since the multiplication of two nonsingular matrices creates another nonsingular matrix, the entire transformation matrix is also invertible. The inverse is required to recalculate world coordinates from screen coordinates - for example, to determine from

8532-538: The image space, and the surfaces and volumes are the same size regardless of the distance from the viewer. Maps use, for example, an orthogonal projection (so-called orthophoto ), but oblique images of a landscape cannot be used in this way - although they can technically be rendered, they seem so distorted that we cannot make any use of them. The formula for calculating a perspective mapping matrix is: ( w 0 0 0 0 h 0 0 0 0 f

8640-434: The incremental value resulted from the smallest change in the integer stored in the z-buffer, which is +1 or -1. Therefore, this resolution can be calculated from the derivative of z {\displaystyle z} as a function of z ′ {\displaystyle z'} : Expressing it back in camera space terms, by substituting z ′ {\displaystyle z'} by

8748-568: The information stored for archival purposes is rarely accessed, off-line storage is less expensive than tertiary storage. In modern personal computers, most secondary and tertiary storage media are also used for off-line storage. Optical discs and flash memory devices are the most popular, and to a much lesser extent removable hard disk drives; older examples include floppy disks and Zip disks. In enterprise uses, magnetic tape cartridges are predominant; older examples include open-reel magnetic tape and punched cards. Storage technologies at all levels of

8856-418: The later rastering step. In a perspective illustration , a central projection is used. To limit the number of displayed objects, two additional clipping planes are used; The visual volume is therefore a truncated pyramid ( frustum ). The parallel or orthogonal projection is used, for example, for technical representations because it has the advantage that all parallels in the object space are also parallel in

8964-641: The most commonly used data storage media are semiconductor, magnetic, and optical, while paper still sees some limited usage. Some other fundamental storage technologies, such as all-flash arrays (AFAs) are proposed for development. Semiconductor memory uses semiconductor -based integrated circuit (IC) chips to store information. Data are typically stored in metal–oxide–semiconductor (MOS) memory cells . A semiconductor memory chip may contain millions of memory cells, consisting of tiny MOS field-effect transistors (MOSFETs) and/or MOS capacitors . Both volatile and non-volatile forms of semiconductor memory exist,

9072-537: The mouse pointer position the clicked object. However, since the screen and the mouse have only two dimensions, the third is unknown. Therefore, a ray is projected at the cursor position into the world and then the intersection of this ray with the polygons in the world is determined. Classic graphics cards are still relatively close to the graphics pipeline. With increasing demands on the GPU , restrictions were gradually removed to create more flexibility. Modern graphics cards use

9180-598: The near and the far value leads to so-called Z-fighting because of the low resolution of the Z-buffer. It can also be seen from the formula that the near value cannot be 0 because this point is the focus point of the projection. There is no picture at this point. For the sake of completeness, the formula for parallel projection (orthogonal projection): ( 2.0 / w 0 0 0 0 2.0 / h 0 0 0 0 1.0 / ( n e

9288-408: The physical bit in the storage of its ability to maintain a distinguishable value (0 or 1), or due to errors in inter or intra-computer communication. A random bit flip (e.g. due to random radiation ) is typically corrected upon detection. A bit or a group of malfunctioning physical bits (the specific defective bit is not always known; group definition depends on the specific storage device)

9396-572: The point vectors are to be multiplied by the transformation matrices. For column vectors, the multiplication is performed from the right, i.e. v o u t = M ∗ v i n {\displaystyle v_{out}=M*v_{in}} , where v out and v in are 4x1 column vectors. The concatenation of the matrices also is done from the right to left, i.e., for example M = T x ∗ R x {\displaystyle M=T_{x}*R_{x}} , when first rotating and then shifting. In

9504-473: The pool is divided into different groups of shaders. A strict separation between the shader types is therefore no longer useful. It is also possible to use a so-called compute-shader to perform any calculations off the display of a graphic on the GPU. The advantage is that they run very parallel, but there are limitations. These universal calculations are also called general-purpose computing on graphics processing units , or GPGPU for short. Mesh shaders are

9612-402: The position of the aircraft according to the speed after each frame. In addition to the objects, the scene also defines a virtual camera or viewer that indicates the position and direction of view relative to which the scene is rendered. The scene is transformed so that the camera is at the origin looking along the Z-axis. The resulting coordinate system is called the camera coordinate system and

9720-918: The position of the vertices of the aircraft in world coordinates by multiplying each point successively with these four matrices. Since the multiplication of a matrix with a vector is quite expensive (time-consuming), one usually takes another path and first multiplies the four matrices together. The multiplication of two matrices is even more expensive but must be executed only once for the whole object. The multiplications ( ( ( ( v ∗ R x ) ∗ R y ) ∗ R z ) ∗ T ) {\displaystyle ((((v*R_{x})*R_{y})*R_{z})*T)} and ( v ∗ ( ( ( R x ∗ R y ) ∗ R z ) ∗ T ) ) {\displaystyle (v*(((R_{x}*R_{y})*R_{z})*T))} are equivalent. Thereafter,

9828-471: The propeller points. This calculated matrix is known as the 'world matrix,' essential for each object in the scene before rendering. The application can then dynamically alter these matrices, such as updating the aircraft's position with each frame based on speed. The matrix calculated in this way is also called the world matrix . It must be determined for each object in the world before rendering. The application can introduce changes here, for example, changing

9936-530: The result. It would have to be reconfigured to change its behavior. This is acceptable for devices such as desk calculators , digital signal processors , and other specialized devices. Von Neumann machines differ in having a memory in which they store their operating instructions and data. Such computers are more versatile in that they do not need to have their hardware reconfigured for each new program, but can simply be reprogrammed with new in-memory instructions; they also tend to be simpler to design, in that

10044-423: The resulting matrix could be applied to the vertices. In practice, however, the multiplication with the vertices is still not applied, but the camera matrices (see below) are determined first. The order in which the matrices are applied is important because the matrix multiplication is not commutative . This also applies to the three rotations, which can be demonstrated by an example: The point (1, 0, 0) lies on

10152-409: The second case, while those for column vectors are transposed. The rule ( v ∗ M ) T = M T ∗ v T {\displaystyle (v*M)^{T}=M^{T}*v^{T}} applies, which for multiplication with vectors means that you can switch the multiplication order by transposing the matrix. In matrix chaining, each transformation defines

10260-512: The smallest and the greatest distance have to be given here are, on the one hand, that this distance is divided to reach the scaling of the scene (more distant objects are smaller in a perspective image than near objects), and on the other hand to scale the Z values to the range 0..1, for filling the Z-buffer . This buffer often has only a resolution of 16 bits, which is why the near and far values should be chosen carefully. A too-large difference between

10368-413: The storage hierarchy can be differentiated by evaluating certain core characteristics as well as measuring characteristics specific to a particular implementation. These core characteristics are volatility, mutability, accessibility, and addressability. For any particular implementation of any storage technology, the characteristics worth measuring are capacity and performance. Non-volatile memory retains

10476-422: The stored information even if not constantly supplied with electric power. It is suitable for long-term storage of information. Volatile memory requires constant power to maintain the stored information. The fastest memory technologies are volatile ones, although that is not a universal rule. Since the primary storage is required to be very fast, it predominantly uses volatile memory. Dynamic random-access memory

10584-467: The sun. Only the primitives that are within the visual volume need to be rastered (drawn). This visual volume is defined as the inside of a frustum , a shape in the form of a pyramid with a cut-off top. Primitives that are completely outside the visual volume are discarded; This is called frustum culling . Further culling methods such as back-face culling, which reduces the number of primitives to be considered, can theoretically be executed in any step of

10692-409: The surface. The triangle may be provided with a color or with a texture (image "glued" on top of it). Triangles are preferred over rectangles because their three points always exist in a single plane . The world coordinate system is the coordinate system in which the virtual world is created. This should meet a few conditions for the following mathematics to be easily applicable: How the unit of

10800-1827: The three aircraft axes (vertical axis, transverse axis, longitudinal axis). R x = ( 1 0 0 0 0 cos ⁡ ( α ) sin ⁡ ( α ) 0 0 − sin ⁡ ( α ) cos ⁡ ( α ) 0 0 0 0 1 ) {\displaystyle R_{x}={\begin{pmatrix}1&0&0&0\\0&\cos(\alpha )&\sin(\alpha )&0\\0&-\sin(\alpha )&\cos(\alpha )&0\\0&0&0&1\end{pmatrix}}} R y = ( cos ⁡ ( α ) 0 − sin ⁡ ( α ) 0 0 1 0 0 sin ⁡ ( α ) 0 cos ⁡ ( α ) 0 0 0 0 1 ) {\displaystyle R_{y}={\begin{pmatrix}\cos(\alpha )&0&-\sin(\alpha )&0\\0&1&0&0\\\sin(\alpha )&0&\cos(\alpha )&0\\0&0&0&1\end{pmatrix}}} R z = ( cos ⁡ ( α ) sin ⁡ ( α ) 0 0 − sin ⁡ ( α ) cos ⁡ ( α ) 0 0 0 0 1 0 0 0 0 1 ) {\displaystyle R_{z}={\begin{pmatrix}\cos(\alpha )&\sin(\alpha )&0&0\\-\sin(\alpha )&\cos(\alpha )&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}}} We also use

10908-498: The transformation is called camera transformation or View Transformation . The 3D projection step transforms the view volume into a cube with the corner point coordinates (-1, -1, 0) and (1, 1, 1); Occasionally other target volumes are also used. This step is called projection , even though it transforms a volume into another volume, since the resulting Z coordinates are not stored in the image, but are only used in Z-buffering in

11016-484: The values of -1 and 1, where the near {\displaystyle {\textit {near}}} plane is at -1 and the f a r {\displaystyle {\mathit {far}}} plane is at 1. Values outside of this range correspond to points which are not in the viewing frustum , and shouldn't be rendered. Typically, these values are stored in the z-buffer of the hardware graphics accelerator in fixed point format. First they are normalized to

11124-438: The vertices—they usually have to be inverted , interpolated, and then inverted again. The resulting values of w {\displaystyle w} , as opposed to z ′ {\displaystyle z'} , are spaced evenly between near {\displaystyle {\textit {near}}} and far {\displaystyle {\textit {far}}} . There are implementations of

11232-429: The w-buffer that avoid the inversions altogether. Whether a z-buffer or w-buffer results in a better image depends on the application. The following pseudocode demonstrates the process of z-buffering: Graphics pipeline The computer graphics pipeline, also known as the rendering pipeline, or graphics pipeline , is a framework within computer graphics that outlines the necessary procedures for transforming

11340-451: The world coordinate system or global coordinate system of the entire scene, the object coordinates are transformed using translation, rotation, or scaling. This is done by multiplying the corresponding transformation matrices . In addition, several differently transformed copies can be formed from one object, for example, a forest from a tree; This technique is called instancing. First, we need three rotation matrices , namely one for each of

11448-406: The z-buffer of some duty. The granularity of a z-buffer has a great influence on the scene quality: the traditional 16-bit z-buffer can result in artifacts (called " z-fighting " or stitching ) when two objects are very close to each other. A more modern 24-bit or 32-bit z-buffer behaves much better, although the problem cannot be eliminated without additional algorithms. An 8-bit z-buffer

11556-461: Was extended in the Von Neumann architecture , where the CPU consists of two main parts: The control unit and the arithmetic logic unit (ALU). The former controls the flow of data between the CPU and memory, while the latter performs arithmetic and logical operations on data. Without a significant amount of memory, a computer would merely be able to perform fixed operations and immediately output

11664-441: Was historically called, respectively, secondary storage and tertiary storage . The primary storage, including ROM , EEPROM , NOR flash , and RAM , are usually byte-addressable . Secondary storage (also known as external memory or auxiliary storage ) differs from primary storage in that it is not directly accessible by the CPU. The computer usually uses its input/output channels to access secondary storage and transfer

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