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The next diagram shows the images of the unit cube for various angles and foreshortenings and gives some hints for how to make these personal choices. Various axonometric images of a unit cube. (The image plane is parallel to the y-z-plane.) The left and the far right images look more like prolonged cuboids instead of a cube.
Classification of Axonometric projection and some 3D projections "Axonometry" means "to measure along the axes". In German literature, axonometry is based on Pohlke's theorem, such that the scope of axonometric projection could encompass every type of parallel projection, including not only orthographic projection (and multiview projection), but also oblique projection.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane, known as the projection plane or image plane, where the rays, known as lines of sight or projection lines, are parallel to each other. It is a basic tool in descriptive geometry.
Lincity tiles 2D axonometric graphical elements to form a pseudo-3D game environment.. In axonometric projection and oblique projection, two forms of parallel projection, the viewpoint is rotated slightly to reveal other facets of the environment than what are visible in a top-down perspective or side view, thereby producing a three-dimensional effect.
Example of the use of descriptive geometry to find the shortest connector between two skew lines. The red, yellow and green highlights show distances which are the same for projections of point P. Given the X, Y and Z coordinates of P, R, S and U, projections 1 and 2 are drawn to scale on the X-Y and X-Z planes, respectively.
The foreshortening factor (1/2 in this example) is inversely proportional to the tangent of the angle (63.43° in this example) between the projection plane (colored brown) and the projection lines (dotted). Front view of the same. Oblique projection is a type of parallel projection: it projects an image by intersecting parallel rays (projectors)
Plot of the Duffing map showing chaotic behavior, where a = 2.75 and b = 0.15. Phase portrait of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior. The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic ...