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Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions , to describe the sizes or locations of objects in the everyday world.
Stereolithography is a 3D-printing technique that uses photopolymerization to bind substrate that has been laid layer upon layer, creating a polymeric network. As opposed to fused-deposition modeling, where the extruded material hardens immediately to form layers, 4D printing is fundamentally based in stereolithography, where in most cases ultraviolet light is used to cure the layered ...
4D film is a presentation system combining motion pictures with synchronized physical effects that occur in the theater. Effects simulated in 4D films include motion, vibration , scent , rain, mist, bubbles, fog, smoke, wind, temperature changes, and strobe lights.
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space.
The square is two-dimensional (2D) and bounded by one-dimensional line segments; the cube is three-dimensional (3D) and bounded by two-dimensional squares; the tesseract is four-dimensional (4D) and bounded by three-dimensional cubes. The first four spatial dimensions, represented in a two-dimensional picture.
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4DX is a 4D film presentation system developed by CJ 4DPlex, a subsidiary of South Korean cinema chain CJ CGV. It allows films to be augmented with various practical effects, including motion-seats, wind, strobelights, simulated snow, and scents. First debuted in 2009, it presents films in both stereoscopic 3D and monoscopic 2D formats. [1]
Rotations in 3D space are made mathematically much more tractable by the use of spherical coordinates. Any rotation in 3D can be characterized by a fixed axis of rotation and an invariant plane perpendicular to that axis. Without loss of generality, we can take the xy-plane as the invariant plane and the z-axis as the fixed axis.