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3D

3D is an abbreviation for three-dimensional, denoting a form, space, or representation that incorporates the three spatial dimensions of length, width, and depth, distinguishing it from two-dimensional (2D) entities confined to length and width.^[1]^[2]^[3] In mathematics and physics, 3D space constitutes the framework of the physical world, where points are specified by three orthogonal coordinates (typically x, y, z) in a Cartesian system, enabling precise modeling of volumes, trajectories, and interactions observed empirically.^[4]^[2] This dimensionality aligns with human perception via binocular vision and is foundational for causal analyses in mechanics, where forces and motions unfold across all three axes.^[5] The concept's applications span engineering, where 3D modeling simulates structural integrity through finite element analysis; computer graphics, rendering photorealistic scenes with depth cues like shading and perspective; and manufacturing via additive processes that build objects sequentially in three dimensions.^[2]^[6] Pioneering insights into 3D visualization emerged in 1838 with Charles Wheatstone's stereoscope, which exploited retinal disparity to evoke depth from paired 2D images, laying groundwork for later stereoscopic cinema and virtual reality systems.^[5] While 3D technologies have advanced computational efficiency in fields like aerospace prototyping, challenges persist in rendering accurate occlusion and scaling without optical distortions.^[7]

Science and Mathematics

Three-Dimensional Space and Geometry

Three-dimensional space refers to a geometric framework requiring three mutually perpendicular directions—typically length, width, and depth—to specify the position of any point relative to a fixed origin. This structure is formalized in Euclidean geometry as \mathbb{R}^3, the set of all ordered triples (x, y, z) of real numbers, where each coordinate measures displacement along one of three orthogonal axes.^[8] Unlike one-dimensional space, confined to a line with a single parameter, or two-dimensional space, limited to a plane with two parameters, three-dimensional space accommodates volume and enables the representation of solid objects with non-zero thickness in all directions.^[9] The Cartesian coordinate system provides an algebraic foundation for three-dimensional geometry, extending René Descartes' 1637 innovation from two to three dimensions by incorporating a z-axis perpendicular to the x-y plane. Points, lines, and surfaces are defined via equations such as the line parametric form \mathbf{r}(t) = \mathbf{r_0} + t\mathbf{d}, where \mathbf{d} is a direction vector in \mathbb{R}^3. In solid geometry, volumes of polyhedra follow from these coordinates; for a rectangular prism with dimensions l, w, and h, the volume is V = l \times w \times h, derived by multiplying the base area l \times w by height h, reflecting the invariant measure under rigid transformations. Euclid's Elements, Book XI (c. 300 BCE), establishes core principles of three-dimensional geometry, including intersections of planes and volumes of parallelepipeds, through axiomatic proofs without coordinates.^[10] In physics, three-dimensional space underpins Newtonian mechanics, where position \mathbf{r}, velocity \mathbf{v} = d\mathbf{r}/dt, and force \mathbf{F} are vectors in \mathbb{R}^3, obeying \mathbf{F} = m d^2\mathbf{r}/dt^2 for causal motion prediction. This framework empirically matches observations, such as projectile trajectories under gravity, verifiable since Galileo's 1638 experiments. Crystal structures exemplify three-dimensional periodicity, with atomic lattices like face-centered cubic arrangements confirmed by X-ray diffraction, revealing translational symmetry in all three directions as first demonstrated by von Laue in 1912. Biological forms, from protein folding to organ shapes, occupy and navigate this space, constrained by causal interactions like diffusion and mechanical forces. Modern extensions include differential geometry for curved spaces, as in general relativity's three spatial dimensions embedded in four-dimensional spacetime, where Ricci curvature quantifies deviations from flat Euclidean metrics.^[11] Topology further abstracts three-dimensional properties, classifying manifolds by invariants like Euler characteristic \chi = V - E + F, invariant under homeomorphisms and applied to phenomena such as knotted DNA strands.

Other Mathematical and Physical Concepts

In differential topology, three-dimensional manifolds are smooth spaces locally diffeomorphic to Euclidean \mathbb{R}^3, distinguished by properties such as orientability, which permits a global consistent choice of orientation via nowhere-vanishing volume forms. Compact orientable 3-manifolds decompose uniquely into connected sums of prime factors, as proven by Hellmuth Kneser's finiteness and uniqueness theorem in 1929, facilitating classification efforts like the geometrization conjecture resolved by Perelman's Poincaré conjecture proof in 2003.^[12] Not all such manifolds embed smoothly in \mathbb{R}^4; for instance, certain prime 3-manifolds exhibit embedding obstructions due to topological invariants like Euler characteristic or fundamental group relations.^[13] In general relativity, 4-dimensional Lorentzian spacetime manifolds are decomposed into 3-dimensional spacelike hypersurfaces foliating the geometry, representing constant-time spatial slices that evolve under the ADM formalism, enabling numerical simulations of gravitational dynamics such as black hole mergers.^[14] In solid-state physics, crystalline solids are modeled as infinite 3-dimensional Bravais lattices, where atomic periodicity generates a reciprocal lattice whose first Brillouin zone—a Wigner-Seitz polyhedron—defines the irreducible domain for electron wavevectors \mathbf{k}, essential for computing band gaps and Fermi surfaces via Bloch's theorem.^[15] Higher-order Brillouin zones extend this framework, capturing diffraction conditions where plane waves satisfy Bragg's law at zone boundaries, influencing phonon dispersion and electrical conductivity in materials like semiconductors. Empirical determination of these 3D lattice parameters relies on X-ray crystallography, which reconstructs atomic coordinates from diffraction intensities measured on detectors, achieving resolutions below 1 Å as in the 1913 analysis of NaCl's face-centered cubic structure by William and Lawrence Bragg, confirming interatomic distances of approximately 2.81 Å.^[16] Dimensional analysis underscores how physical laws encode spatial dimensionality through scaling; the inverse-square form of Newton's gravitational law F \propto 1/r^2 and Coulomb's electrostatic force arises because conserved flux (e.g., gravitational or electric field lines) dilutes over a hypersurface whose area scales as r^{d-1} in d spatial dimensions, yielding $1/r^{d-1} intensity for d=3.^[17] This dimensionality dependence manifests causally in phenomena like atomic stability, where in fewer than three dimensions, inverse-power potentials fail to support bound states akin to planetary orbits—per Bertrand's 1873 theorem, only the inverse-square potential permits stable, closed Keplerian orbits for all bound energies in 3D, contrasting with logarithmic potentials in 2D or higher-power falls in 4D that destabilize trajectories.^[18] Such scalings highlight why observed macroscopic physics, from stellar dynamics to molecular bonding, aligns with three spatial dimensions, as deviations would alter critical exponents in phase transitions or wave propagation.^[17]

Technology and Engineering

Computer Graphics and 3D Modeling

Computer graphics in three dimensions involves the algorithmic representation, manipulation, and rendering of virtual objects within a simulated spatial environment, typically using vector mathematics to define positions, orientations, and surface properties. Core techniques include polygonal meshes, which construct models from interconnected vertices, edges, and faces—often triangles or quadrilaterals—for efficient topology and subdivision in real-time applications.^[19] ^[20] NURBS (non-uniform rational B-splines) provide parametric surfaces for precise curvature control in industrial design, contrasting meshes by enabling smooth, mathematically exact representations without tessellation artifacts.^[21] Ray tracing simulates light paths by intersecting rays with scene geometry to compute reflections, refractions, and shadows, yielding photorealistic images at the cost of high computational expense compared to rasterization.^[22] Pioneering work began with Ivan Sutherland's Sketchpad system in 1963, which introduced interactive graphical manipulation on the TX-2 computer, laying foundational principles for constraint-based drawing that influenced subsequent 3D extensions despite its initial 2D focus.^[23] By the 1980s, advancements like Pixar's RenderMan software, released in 1988, standardized ray-tracing pipelines for film production, enabling complex shading models and global illumination in works such as Toy Story (1995).^[24] These milestones shifted from wireframe approximations to filled polygons and texture mapping, driven by hardware like the Evans & Sutherland LDS-1 display (1969) for vector-based 3D visualization.^[25] Prominent software tools include Blender, an open-source suite originating in 1994 and maintained by the Blender Foundation since 2002, supporting mesh editing, NURBS, and scripting for broad accessibility.^[26] Autodesk Maya, developed from 1998 by Alias|Wavefront, excels in professional animation and rigging with node-based workflows for deformable models.^[27] Interchange standards encompass OBJ format, an ASCII-based specification from Wavefront Technologies for geometry, textures, and normals, and STL, a triangulated mesh format introduced in 1987 by 3D Systems for surface approximation.^[28] ^[29] Recent integrations of artificial intelligence leverage neural radiance fields (NeRF), introduced in 2020, to reconstruct 3D scenes from sparse images via volume density and color prediction, accelerating text-to-3D generation.^[30] By 2025, tools like Adobe's Firefly-powered Text to 3D feature employ transformers to derive multi-view consistent models from prompts, reducing manual sculpting while supporting stylization and dynamic edits.^[31] Market projections indicate AI-driven 3D generators reaching $2 billion in value, enabling rapid prototyping but requiring fine-tuning for geometric accuracy in engineering contexts.^[32] These methods underpin computer-aided design (CAD) for micron-level precision in aerospace components and virtual reality simulations approximating physical interactions via physics engines.^[33] However, photorealistic ray tracing demands exponential compute scaling with scene complexity, often necessitating offline processing despite GPU advancements following Moore's Law trends of doubling transistor density roughly every two years.^[34] Aliasing—jagged edges from undersampling—persists in real-time rasterization, mitigated imperfectly by multisampling but introducing temporal inconsistencies in motion.^[35] ^[36] Data scarcity for training implicit representations further hampers generalization, underscoring ongoing trade-offs in efficiency versus fidelity.^[34]

Additive Manufacturing and 3D Printing

Additive manufacturing, commonly known as 3D printing, involves the layer-by-layer fabrication of physical objects from digital models, typically using materials such as polymers, metals, or ceramics deposited or solidified sequentially to build complex geometries unattainable through subtractive methods.^[37] This process enables precise control over internal structures, reducing material waste compared to traditional casting or machining by adding only necessary volume.^[38] Empirical efficiencies arise from on-demand production, which minimizes inventory and logistics costs, though material science constraints like thermal gradients during layering introduce mechanical inconsistencies.^[39] The foundational technology emerged in the 1980s with Chuck Hull's invention of stereolithography in 1984, which employed a UV laser to cure liquid photopolymers layer by layer, patented in 1986 and commercialized via 3D Systems.^[40] This was followed by Scott Crump's fused deposition modeling (FDM) in 1989, extruding thermoplastic filaments to form parts, and Carl Deckard's selective laser sintering (SLS) around 1987, fusing powder beds with lasers for metal and polymer applications.^[41] These innovations shifted manufacturing from mass production paradigms to iterative, low-volume customization, driven by causal reductions in setup times inherent to digital-to-physical translation without tooling.^[42] In aerospace, additive manufacturing has empirically shortened prototyping cycles and lowered costs by enabling rapid iteration of lightweight components, such as turbine blades, where traditional methods require extensive machining.^[43] Industry applications demonstrate on-demand spare parts production, cutting lead times from weeks to days and reducing dependency on global supply chains.^[44] Custom prosthetics exemplify patient-specific outcomes, with 3D printing fabricating lightweight limbs tailored to individual anatomy, slashing production costs and times versus conventional molding while improving fit and accessibility in underserved regions.^[45] Decentralized fabrication further empowers small-scale innovators by obviating large capital investments, fostering rapid experimentation in fields like biomedical devices.^[46] Scalability remains constrained for high-volume output, as layer-by-layer deposition is inherently slower than injection molding, which achieves economies through parallel cavity filling and cycle times under 30 seconds per part.^[47] Material weaknesses, including anisotropy from interlayer bonding deficits, yield parts with directional strength variations—often 20-50% weaker perpendicular to layers—limiting load-bearing applications without post-processing like annealing.^[37] Controversies surround 3D-printed firearms, epitomized by Defense Distributed's 2013 release of the Liberator pistol files, prompting legal battles over distribution rights.^[48] Despite regulatory concerns, empirical data reveal no verifiable surge in crime rates attributable to such weapons; U.S. law enforcement encounters remain negligible relative to millions of annual firearm incidents, with global studies documenting fewer than 200 cases from 2014-2023, underscoring unsubstantiated fears of proliferation against evidence of limited practical adoption due to durability issues.^[49] This supports causal realism favoring individual fabrication capabilities over preemptive restrictions, as homemade guns predate 3D printing without analogous panic.^[50] By 2025, advancements include multi-material bioprinting techniques accelerating engineered tissue production via enhanced extrusion precision, and large-format printers for construction enabling on-site building of structures with concrete composites.^[51] MIT's innovations feature dissolvable, recyclable supports that minimize waste in complex geometries, allowing reuse in subsequent prints and addressing environmental critiques of single-use scaffolds.^[52] These developments, grounded in iterative material science, expand viable applications while contending with persistent challenges in uniformity and speed.^[53]

Stereoscopic Imaging and 3D Displays

Stereoscopic imaging exploits binocular disparity, the slight horizontal offset between images captured by each human eye, to simulate depth perception as in natural vision, where the brain fuses these offsets into a three-dimensional percept.^[54] This technique relies on presenting separate left- and right-eye views, separated by optical means to prevent crosstalk, thereby inducing stereopsis without requiring physical depth.^[55] Common methods include anaglyph systems, which use color filters (typically red-cyan) to differentiate eye views, though they reduce color fidelity; polarized systems, employing orthogonally polarized filters for each eye to enable passive viewing; and active shutter systems, where liquid crystal displays in glasses alternately block one eye in sync with the display's 120 Hz refresh rate to deliver full-color, high-resolution images.^[54]^[56] Polarized and shutter approaches dominate cinema due to better image quality, with shutter providing twice the resolution of passive polarized at equivalent frame rates.^[56] A historical revival occurred in the 1950s amid cinema's competition with television, exemplified by House of Wax (1953), the first color 3D feature from a major studio, released on April 25 using polarized projection to draw over 50 million viewers despite requiring glasses.^[57] IMAX advanced large-format stereoscopy with its first full-color 3D short, Transitions, at Expo 86 in Vancouver, followed by digital projector innovations in 2008 enabling wider multiplex deployment.^[58] Contemporary developments emphasize glasses-free autostereoscopy, directing multiple views via parallax barriers or lenticular lens arrays to viewer positions, enabling multi-user 3D without eyewear, as in medical imaging prototypes tracking eye position for precise depth rendering.^[59] Holographic displays, reconstructing wavefronts for viewpoint-dependent true 3D without disparity limits, project a market expansion from $14.3 billion in 2025 to $75.62 billion by 2035, driven by medical and automotive integrations.^[60] Augmented reality glasses leverage waveguide optics to couple light into thin lenses, achieving lighter designs under 50 grams with 30° fields of view for immersive stereoscopic overlays, as seen in 2025 prototypes minimizing bulk via diffractive elements.^[61]^[62] Empirical studies link stereoscopic viewing to visual fatigue from vergence-accommodation conflict, where eyes converge on perceived depths mismatched to the fixed screen focus plane, increasing asthenopia scores by up to 20% in sessions exceeding 30 minutes.^[63]^[64] Post-2009 Avatar surge, native 3D adoption waned by 2015 as post-conversion films proliferated, yielding dimmer images and higher ticket premiums without proportional engagement, reducing overall 3D screen shares from 50% to under 10% in major markets.^[65]^[66] Despite drawbacks, stereoscopy enhances spatial fidelity in medicine, where 3D endoscopy reconstructions improve surgical precision by 15-20% via better depth cues, and in engineering for anatomic model visualization aiding preoperative planning.^[67]^[68] These benefits stem from reduced cognitive load in interpreting complex geometries, outperforming 2D in tasks requiring volumetric assessment.^[69]

Entertainment and Culture

3D in Film, Television, and Gaming

Stereoscopic 3D in film originated with early experiments in the 1890s using dual-image projection systems, though commercial viability emerged in the 1920s with anaglyph glasses for short films.^[70] The format saw periodic revivals, notably in the 1950s amid competition from television, but digital advancements in the 2000s enabled native 3D production. James Cameron's Avatar (2009) exemplified this shift, grossing $2.75 billion worldwide, with approximately 70% of domestic earnings from 3D screenings due to its immersive depth effects and premium ticket pricing.^[71] ^[72] Post-Avatar, 3D adoption waned as audience "fatigue" set in, evidenced by the drop in 3D's share of box office revenue from 82% for Avatar to under 20% for subsequent releases by 2010, driven by inconsistent conversion quality, viewer discomfort from glasses, and dimmer projected images.^[73] ^[74] Empirical data from studio reports indicate that while 3D boosted initial novelty-driven attendance, sustained premium pricing failed to materialize, with theaters reallocating screens to 2D amid declining uptake. In television, 3D standards like Blu-ray 3D peaked around 2010 but faced low consumer demand; by 2017, LG and Sony—the last major holdouts—discontinued 3D support in new models, citing negligible sales and content scarcity.^[75] In gaming, 3D transitioned from polygonal rendering in the 1990s to stereoscopic and VR immersion, with engines like Unity and Unreal facilitating depth cues in titles such as Half-Life: Alyx (released March 23, 2020), which leveraged VR headsets for interactive environmental manipulation and puzzle-solving, earning acclaim for spatial realism.^[76] ^[77] However, VR-induced motion sickness—symptoms including nausea and disorientation—affects 22-80% of users depending on session length and content velocity, per clinical studies, limiting accessibility due to physiological susceptibility rather than technological maturity alone.^[78] Hardware barriers, such as required head-mounted displays costing $300-1,000 plus high-end PCs, further constrain adoption to niche demographics, undermining narratives of universal engagement; sales data for VR titles like Alyx reflect strong critical reception but modest volume compared to flat-screen counterparts.^[79] Overall, while 3D enhances perceptual depth in controlled scenarios, audience metrics reveal causal trade-offs: technological feasibility yields immersion for subsets, but ergonomic drawbacks and economic premiums hinder mass viability.

3D in Music

Robert Del Naja, a founding member of the Bristol-based trip-hop group Massive Attack formed in 1988, performs under the stage name 3D, contributing vocals, instrumentation, and production to their albums such as Blue Lines (1991) and Mezzanine (1998).^[80] Del Naja's work as 3D extends to solo and collaborative electronic projects, including contributions to the 2016 compilation Electronica 1: The Time Machine curated by Jean-Michel Jarre, where he featured on experimental tracks blending downtempo beats and atmospheric soundscapes. This usage of "3D" reflects personal branding within the 1990s Bristol underground scene, which fused hip-hop, dub, and electronica but remained niche compared to mainstream genres.^[81] Several albums have been explicitly titled 3D, including The Three Degrees' 1979 disco release produced by Giorgio Moroder and Harold Faltermeyer, which included singles like "Jump the Gun" and peaked at number 89 on the US Billboard 200.^[82] Similarly, American R&B group TLC's 3D (2002) debuted at number one on the Billboard 200, selling over 2.4 million copies in the US and featuring tracks such as "Girl Talk," though it received mixed reviews for deviating from their earlier sound.^[83] Other releases, like Romanian rock band Voltaj's 3D (2006), incorporate pop-rock elements but achieved limited international reach.^[84] Tracks explicitly titled "3D" appear sporadically in electronica and techno, often as instrumental or experimental pieces in underground compilations, without achieving chart prominence or broad cultural penetration.^[85] This contrasts with the term's more pervasive applications in visual and technological fields, underscoring its marginal role in music nomenclature and reception data from platforms like Discogs, where such entries garner modest collector interest rather than mass appeal.^[86]

Other Artistic and Media Uses

In contemporary sculpture and installation art, 3D printing technologies have facilitated hybrid digital-to-physical creations, particularly amid the post-2010 proliferation of affordable additive manufacturing tools associated with the maker movement. Artists like Nick Ervinck have utilized large-scale 3D printing in collaborations with firms such as Materialise to produce intricate, organic forms that challenge traditional sculptural constraints, as seen in works blending algorithmic design with material experimentation since around 2010.^[87] Similarly, Morehshin Allahyari employs 3D printing to reconstruct fragmented artifacts from conflict zones, merging digital modeling with physical output to explore themes of cultural loss and reclamation in installations exhibited internationally from 2013 onward.^[88] 3D scanning has advanced the preservation and replication of cultural artifacts by generating high-fidelity digital models without physical contact, enabling detailed analysis and facsimiles for conservation. Organizations like Factum Arte have applied structured light and laser scanning to artifacts such as ancient Egyptian sculptures, producing millimeter-accurate replicas that support non-invasive study and mitigate deterioration risks, with projects documented since the early 2010s.^[89] The Smithsonian Institution has similarly scanned over 1,000 cultural items by 2018 using portable 3D scanners, creating open-access models that facilitate global research while preserving originals from handling wear.^[90] Binaural 3D audio techniques, informed by empirical psychoacoustic studies of head-related transfer functions (HRTFs), have been incorporated into artistic installations to craft immersive spatial soundscapes beyond musical contexts. HRTFs, which model how human anatomy filters sound directionality, enable headphone-based rendering of three-dimensional auditory environments, as validated through listener localization tests achieving up to 90% accuracy in controlled experiments.^[91] In non-musical media, such as interactive exhibits, these methods simulate environmental acoustics for experiential art, with applications in virtual reality heritage reconstructions tested for perceptual fidelity since the mid-2010s.^[92] Dolby Atmos, launched commercially in 2012, has influenced artistic sound design in emerging media by supporting object-based audio placement in three dimensions, independent of fixed channels. This has enabled creators to position discrete sound elements dynamically in installations and interactive narratives, with over 1,700 non-film projects adopting the format by 2023 for heightened spatial immersion.^[93]

Miscellaneous Uses

Historical and Economic References

In pre-decimal British currency systems, the abbreviation "3d" denoted three pence, a subdivision of the pound sterling comprising 20 shillings of 12 pence each, facilitating everyday minor transactions such as purchasing confectionery or newspapers.^[94]^[95] The threepence coin itself, initially silver and later cupro-nickel in a distinctive twelve-sided brass form from 1937 onward, circulated widely within the British Empire for over a century, embodying the system's reliance on duodecimal fractions for practical divisibility in trade and wages.^[96] This notation appeared routinely in historical accounting ledgers as shorthand for threepence amounts, often alongside shillings (s) and pounds (£) in the £sd format derived from Latin librae, solidi, denarii, where "d" stemmed from denarius.^[95] For instance, a price of one shilling and threepence was recorded as 1s 3d, enabling efficient bookkeeping in mercantile and household records prior to mechanical calculators.^[95] The British threepence was demonetized on 1 September 1971, shortly after decimalisation on 15 February 1971, which rendered old pence obsolete and eliminated "3d" from active economic use.^[96] Analogous pre-decimal threepence coins existed in Commonwealth realms like Australia, minted until 1964 and withdrawn following decimal transition on 14 February 1966, after which they held no legal tender status.^[97] Today, "3d" lacks any ongoing economic function, supplanted by decimal notations and overshadowed by non-currency interpretations of "3D," underscoring the notation's historical specificity to imperial monetary practices rather than enduring fiscal relevance.^[94]

Sports, Gaming Mechanics, and Other

In professional wrestling, "3D" refers to the Dudley Death Drop, a signature double-team finishing maneuver popularized by the tag team The Dudley Boyz (Bubba Ray and D-Von Dudley) during their tenure in Extreme Championship Wrestling (ECW) in the mid-1990s and later in World Wrestling Entertainment (WWE) through the 2000s.^[98] The move involves one wrestler lifting the opponent onto their shoulders in a fireman's carry position, while the partner leaps forward to execute a cutter or head-first impact, often driving the victim through a table for dramatic effect, as seen in high-profile matches like ECW's November to Remember 1996 event where the Dudleys used it to retain the ECW World Tag Team Championship.^[99] This technique emphasized teamwork and high-impact visuals, contributing to the team's 23 WWE Tag Team Championship reigns between 1999 and 2004, with rare kickouts reported in only two instances during WWE programming.^[100] In video game mechanics, "3D" denotes the transition to three-dimensional environments and controls, particularly in platformers like Super Mario 64, released on June 23, 1996, for the Nintendo 64, which pioneered analog stick input for fluid, 360-degree character movement and camera manipulation, enabling precise navigation of open-world levels without relying on fixed 2D constraints.^[101] This innovation allowed for mechanics such as variable-speed running, mid-air adjustments, and contextual actions like long jumps or wall kicks, setting standards for spatial awareness and momentum-based physics in subsequent titles, with the game's 24 courses demanding adaptation to depth perception and analog sensitivity for collecting 120 stars. Such 3D mechanics enhanced replayability by introducing non-linear exploration, contrasting earlier 2.5D hybrids like Super Mario World. 3D chess variants extend traditional chess into three dimensions, typically using stacked boards (e.g., 8x8x8 configurations or the 5x5x5 Raumschach board invented in 1907) where pieces move across multiple planes, adding layers of strategic depth through vertical threats, extended ranges for queens and bishops, and complex pawn promotions.^[102] These rules require players to visualize inter-level interactions, such as unicorns (three-dimensional knights) leaping across boards, increasing computational complexity and forcing multidimensional tactical planning, as evidenced in competitive play where standard two-dimensional openings prove insufficient against elevated attacks.^[103] In logistics, "3D" commonly abbreviates three-dimensional bin packing problems (3D-BPP), algorithmic challenges for optimally arranging rectangular items into containers to minimize waste and transport costs, as applied in warehousing since the 1970s with heuristics like first-fit decreasing height for real-time cargo loading.^[104] Solutions involve orientation constraints and stability checks, with recent deep reinforcement learning models achieving up to 15% better space utilization in simulated freight scenarios compared to classical methods.^[105]

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Who Invented 3D Modeling: A History of Pioneering Technologies
Ivan Sutherland is often regarded as the father of computer graphics. In 1963, he developed Sketchpad, a revolutionary interactive computer graphics program.
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Challenges and Opportunities in 3D Content Generation - arXiv
May 24, 2024 · This paper aims to summary 3D content creation, addressing challenges such as data scarcity and computational resource limitations.
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Aliasing in computer graphics
Mar 15, 2020 · In this article, we look at other manifestations of aliasing in 3D graphics, and attempt to theoretically unify them.
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Learning to predict perceptual visibility of rendering deterioration in ...
Nov 13, 2024 · Aliasing, an artifact stemming from insufficient sampling of 3D scenes, manifests as jagged object edges or fragment disappearance (refer to Fig ...Missing: achievements criticisms
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Additive manufacturing (3D printing): A review of materials, methods ...
Jun 15, 2018 · However, the inferior mechanical properties and anisotropic behaviour of 3D printed parts still limit the potential of large-scale printing.
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3D Printing in Manufacturing: Benefits and Challenges - UltiMaker
Apr 8, 2025 · Reduced Tooling Lead Times: For low-volume production, 3D printing can eliminate the need for expensive and time-consuming mold creation.
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3D printing: What is it & how does it work? | Protolabs Network
One of the biggest limitations of 3D printing is that most parts are inherently anisotropic or not fully dense, meaning they usually lack the material and ...
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3D Printing History: A Complete Timeline of Additive Manufacturing ...
Jun 25, 2024 · 3D printing's roots began with the inventive efforts of Dr. Hideo Kodama. In 1981, he laid the foundation for additive manufacturing.
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https://www.additive-x.com/blog/the-history-of-3d-printing-additive-manufacturing
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3D Printing History - When Was 3D Printing Invented? - Xometry
Mar 29, 2024 · The first 3D printer was invented by Chuck Hull and was awarded a patent in 1986. Around the same time, Scott Crump developed Fused Deposition ...
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3D Printing and Aerospace: Applications, Materials and Advantages
3D printing revolutionises the aerospace industry, improving design, production and cost reduction with lightweight, optimised components.
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How is 3D Printing Used in the Aerospace and Defense Industry?
Aug 12, 2024 · With 3D printing, companies can produce spare parts on-demand, reducing both time and cost. A key benefit of 3D printing spare parts is the ...
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All About 3D Printing Prosthetics | Xometry
Aug 8, 2022 · Using 3D printing to fabricate prosthetics leads to a considerable reduction in the manufacturing time, cost, and weight of prosthetics.
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The Role and Future Directions of 3D Printing in Custom Prosthetic ...
Mar 14, 2025 · Moreover, 3D printing reduces the production time and costs, making high-quality prosthetics more accessible to a broader population, including ...
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3D Printing vs Injection Molding: A Complete Comparison
Aug 26, 2025 · Both 3D printing and injection molding use plastics, but the range of available materials and the performance of finished parts differ greatly.
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An Empirical Overview of the Use of 3D-Printed Firearms by Right ...
Jun 1, 2024 · This article provides an empirical overview of right-wing extremists' adoption of 3D-printed firearms (3DPF) for political violence using a dataset of 35 ...
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Three-Dimensional Printed Hysteria - PMC
Apr 16, 2020 · The Federal Bureau of Investigation does not keep statistics for reported crimes that are specifically linked to 3D printed guns. However ...Missing: firearms rates studies
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Printing Violence: Urgent Policy Actions Are Needed to Combat 3D ...
Jul 17, 2025 · A recent academic study documented 186 international law enforcement encounters with 3D-printed firearms from mid-2014 to August 2023, with the ...
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New 3D bioprinting technique may improve production ... - MIT News
Sep 17, 2025 · New method developed by engineers from MIT and Politecnico di Milano Polimi enhances 3D bioprinting capabilities, accelerating process ...Missing: advancements multi- recyclable
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New 3D printing method enables complex designs and creates less ...
Jun 3, 2025 · MIT engineers developed a technique for making intricate structures with supports that can be dissolved and reused instead of thrown away.Missing: advancements multi-
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Additive manufacturing Technologies: Advances for the construction ...
Additive manufacturing technologies have revolutionized the construction industry by improving operational efficiency, sustainability, housing quality, and ...Missing: multi- bioprinting format
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[PDF] Stereoscopic 3D
Active Shutter glasses Contain LCD lenses that alternately 'black-out' each eye syncronised to the screen so the correct image is presented to the correct eye. ...
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[PDF] Stereo & 3D Display Technologies Introduction - Research
Binocular disparity is the difference in the images projected on the left and right eye retinas in the viewing of a 3D scene. It is the salient depth cue used ...
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[PDF] Principles of 3D Video and Blu-ray 3D - Michael Scroggins
Active shutter glasses are capable of providing a picture quality that has twice the pixel resolution of 3D displays that rely on polarized glasses. • Extremely ...
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House of Wax | Horror, Vincent Price, 3D | Britannica
House of Wax, American horror film, released in 1953, that established Vincent Price as a leading actor in the genre. It was one of the first films shot in 3-D.
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The History of 3D Movie Tech - IGN
Apr 23, 2010 · IMAX began to expand its array of 3D films. A turning point for the format came at Expo '86 in Vancouver. The film Transitions became the first ...<|separator|>
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Investigation of Autostereoscopic Displays Based on Various ... - NIH
The autostereoscopic display is a promising way towards three-dimensional-display technology since it allows humans to perceive stereoscopic images with naked ...
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Global Holographic Display Market Set to Grow from $14.3B in 2025 ...
Oct 1, 2025 · The global holographic display market size is estimated to grow from USD 14.30 billion in 2025, to USD 75.62 billion by 2035, at a CAGR of 18. ...
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Designing AR Glasses in 2025 - Medium
Sep 12, 2025 · A 30° FOV allows for stylish AR glasses and provides the same field of view as a MacBook Air at arm's length, giving the ability to cover many ...
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SiC diffractive waveguides for augmented reality: single-layer, full ...
Aug 21, 2025 · The resulting single-layer SiC waveguide achieves rainbow-artifact-free full-color displays while weighing just 3.795 g and measuring only 0.75 ...
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Vergence–accommodation conflicts hinder visual performance and ...
Yano and colleagues concluded that vergence–accommodation conflicts cause visual fatigue and discomfort in conventional 3D displays. This conclusion is not ...Missing: empirical | Show results with:empirical
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[PDF] Visual Discomfort and Visual Fatigue of Stereoscopic Displays
This indicates a conflict between accommodation and vergence for sharp images displayed at screen disparities beyond the 1° limit; the accommodation- vergence ...
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What James Cameron and 'Avatar' Did (and Didn't Do) for 3D ...
Dec 13, 2022 · “Now, you've got people quickly converting movies from 2D to 3D, which is not what we did,” Cameron told Deadline in 2010. “They're expecting ...
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4 Reasons Why 3D Films Have Failed - Brandwatch
May 19, 2015 · 3D successes, Gravity and Avatar, became outnumbered by 3D re-releases and converted 2D films, and viewers realized. 3. Influencers weren't ...
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Application of Stereo-Imaging Technology to Medical Field - PMC
The application of 3D stereo-imaging technology to the medical field will help improve surgical accuracy, reduce operation times, and enhance patient safety.
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Integrating Stereoscopic Video with Modular 3D Anatomic Models ...
Combined with 3D anatomic models, any surgical procedure or pathology could be represented virtually to supplement learning or surgical preoperative planning.
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Application of stereo-imaging technology to medical field - PubMed
Sep 30, 2012 · The application of 3D stereo-imaging technology to the medical field will help improve surgical accuracy, reduce operation times, ...
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The First 3D Movies - Optics & Photonics News
Nov 1, 2021 · Chief among the Kinetoscope design team was a young Scottish–American inventor, William Kennedy-Laurie Dickson (1860-1935)—who, after a falling ...
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Avatar (2009) - Box Office and Financial Information - The Numbers
$$77,025,481 (9.8% of total gross). Legs: 10.19 (domestic box office/biggest weekend). Domestic Share: 26.9% (domestic box office/worldwide). Production Budget ...
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'Avatar' at 10: What Happened to the 3D Box Office Boom? - Variety
Dec 13, 2019 · ... Avatar” would gross $500 million at the domestic box office. This ... 18, 2009, it opened to a solid, but not spectacular, $77 million.
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Film executives scoff at notion of '3D fatigue' - The Hollywood Reporter
Jul 21, 2010 · The 3D-to-2D gross decline follows the phenomenal 82% average 3D share marked by “Avatar” during its record theatrical run. But the Fox ...
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Film executives scoff at notion of "3D fatigue" - Reuters
Jul 21, 2010 · The 3D-to-2D gross decline follows the phenomenal 82% average 3D share marked by "Avatar" during its record theatrical run. But the Fox ...<|separator|>
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Shambling corpse of 3D TV finally falls down dead - CNET
Jan 17, 2017 · 3D TV finally looks dead. LG and Sony, the last two major TV makers to support the 3D feature in their TVs, will stop doing so in 2017.
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Half-Life: Alyx on Steam
In stock Rating 5.0 (58,897) VR was built to enable the gameplay that sits at the heart of Half-Life. Immerse yourself in deep environmental interactions, puzzle solving, world exploration, ...
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Half-Life: Alyx review – a spectacular immersive experience | Games
Mar 25, 2020 · VR, meanwhile, offers the promise of unparalleled immersion, the ability to let players perceive virtual environments and touch objects as if ...
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Clinical predictors of cybersickness in virtual reality (VR ... - Nature
Jun 9, 2021 · In previous studies, about 22–80% of participants have experienced cybersickness during or after application of VR. Not only do VR users ...
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Factors Associated With Virtual Reality Sickness in Head-Mounted ...
VR sickness may be influenced by technological differences within HMDs such as resolution and refresh rate, however, VR content also plays a significant role.
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https://www.discogs.com/artist/8137824-3D-51
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https://www.discogs.com/artist/4601623-3D-32
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https://www.discogs.com/master/36570-3-Degrees-3D
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https://www.discogs.com/master/51837-TLC-3D
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https://www.discogs.com/master/864970-Voltaj-3D
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https://www.discogs.com/search/?q=3D+techno+track&type=all
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https://www.discogs.com/search/?q=%223D%22+electronica&format_exact=Track&genre_exact=Electronic
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Examples of 3D printed sculptures, installations, and other works of art
Mar 16, 2023 · One example of this is the collaboration between the artist Nick Ervinck and the Belgian 3D printing company, Materialise. Ervinck's work often ...
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The Impact of 3D Printing on Contemporary Sculpture - Prazzle
Dec 24, 2024 · Several contemporary artists have embraced 3D printing to enhance their sculptural works including Morehshin Allahyari, Nick Ervnick, Nandipha ...
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3D SCANNING FOR CULTURAL HERITAGE CONSERVATION
High-resolution 3D recordings of sites, monuments and artifacts allow us to monitor, study, disseminate and understand our shared cultural history.
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[PDF] 3d scanning and replication for museum and cultural heritage ...
3D scanning produces a high-precision digital reference document that records condition, provides a virtual model for replication, and makes possible easy mass ...
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Head-Related Transfer Function and Acoustic Virtual Reality
This book covers all aspects of head-related transfer function (HRTF), from the fundamentals through to the latest applications, such as 3D sound systems.
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A Review on Head-Related Transfer Function Generation for Spatial ...
Using binaural synthesis techniques, HRTFs play a crucial role in creating immersive audio experiences through headphones or loudspeakers, using binaural ...
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Dolby Corporate Facts
Since its launch in 2012 with Disney/Pixar's Brave, 1,700+ movies have been mixed in Dolby Atmos for the cinema. More than 6,000+ theater screens enabled with ...
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Pounds, Shillings and Pence - The Royal Mint Museum
The pre-decimal currency system consisted of a pound of 20 shillings or 240 pence, though at first there were no coins corresponding in value to the shilling ...
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Money - The University of Nottingham
Coins and units of money ; 3d, Three pennies. The coin was sometimes referred to as a 'threepenny bit'. The word was often pronounced 'thrupny', or 'thruppence'.Missing: ledgers | Show results with:ledgers
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British coins: threepence - Retrowow
It was withdrawn from circulation on 1 September 1971. The closest decimal coin in value to the threepence was the new decimal penny. In size, the closest ...<|separator|>
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Australia Threepence KM 57 Prices & Values - NGC
Assess world coin values with the World Coin Price Guide on NGCcoin.com. View Australia Threepence prices, images and mintage info.
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100 Best Wrestling Moves EVER - WhatCulture.com
Feb 27, 2025 · The reaction that bubbles under as it becomes clear that the Dudley Death Drop is on the way is palpable, and the urge to shout “3D!” along ...
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5/16 THIS DAY IN HISTORY | PWInsider.com
May 16, 2013 · The Dudleys attacked Taz afterward and laid him out with the Dudley Death Drop. ... Sabin was sent to the floor, and Team 3D set up Roode for 3D.<|separator|>
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What is the most effective finisher in WWE? : r/SquaredCircle - Reddit
May 6, 2014 · I believe no-one has ever kicked out of Dudley Death Drop in WWE/WWF. ... 3D has only been kicked out of twice, the second time was against ...Missing: maneuver | Show results with:maneuver
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Holism: the Wonderful Worlds of Super Mario 64 - Source Gaming
Jun 21, 2017 · The Joystick allowed a precise degree of analog control ... It's why Nintendo has only had to refine Mario's movement in later 3D games ...
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https://www.houseofstaunton.com/chess-blog/3-dimensional-chess-learn-to-think-differently/
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three dimensional chess - The Book of Threes
Nov 13, 2009 · The difficulty in three-dimensional chess is not just in the strategic depth but also in visualizing and maneuvering pieces in a more complex ...
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An Efficient Deep Reinforcement Learning Framework for the 3D Bin ...
Oct 11, 2025 · The three-dimensional bin packing problem (3D-BPP) is widely applied in logistics and warehousing. Existing learning-based approaches often ...Missing: acronym | Show results with:acronym
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(PDF) A Three-dimensional Bin Packing Algorithm. - ResearchGate
The 3D Bin Packing Problem (3D-BPP) [1] is the 3D extension of the 1D-BPP and 2D-BPP versions (both versions widely studied). Bin Packing is one of the most ...Missing: acronym | Show results with:acronym