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Another type of sphere arises from a 4-ball, whose three-dimensional surface is the 3-sphere: points equidistant to the origin of the euclidean space R 4. If a point has coordinates, P ( x , y , z , w ) , then x 2 + y 2 + z 2 + w 2 = 1 characterizes those points on the unit 3-sphere centered at the origin.
Three-dimensional ambigram, ABC. A 3D ambigram is a design where an object is presented that will appear to read several letters or words when viewed from different angles. Such designs can be generated using constructive solid geometry , a technique used in solid modeling , and then physically constructed with the rapid prototyping method.
3D computer graphics, computer graphics that use a three-dimensional representation of geometric data; 3D display, a type of information display that conveys depth to the viewer; 3D film, a motion picture that gives the illusion of three-dimensional perception; 3D modeling, developing a representation of any three-dimensional surface or object
A three-dimensional Euclidean space is a special case of a Euclidean space. In Bourbaki's terms, [2] the species of three-dimensional Euclidean space is richer than the species of Euclidean space. Likewise, the species of compact topological space is richer than the species of topological space. Fig. 3: Example relations between species of spaces
For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points ...
The three possible plane-line relationships in three dimensions. (Shown in each case is only a portion of the plane, which extends infinitely far.) In analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. It is the entire line if that line is embedded in the plane, and is ...
The word "tessella" means "small square" (from tessera, square, which in turn is from the Greek word τέσσερα for four). ... Tessellating three-dimensional ...
A form is an artist's way of using elements of art, principles of design, and media. Form, as an element of art, is three-dimensional and encloses space. Like a shape, a form has length and width, but it also has depth. Forms are either geometric or free-form, and can be symmetrical or asymmetrical.