Many of the things we can see in a science fiction movie actually end up with the passage of time. One of the most interesting ideas that I could see in the movie “Prometheus” was the use of a small “drones” sphere-shaped allowing exploration, automatically, del entorno en… (leer más)
One of the first problems we must learn to work in projective geometry is the determination of homologous elements. To start the study will use the methodology to be used as usual model-based elements “points”, since it is easier to interpret. Therefore we will consider the determination of homologous elements in series projective:
Given two projective series defined by three pairs of elements (points) counterparts, determine the counterpart of a given point.
Conic curves, further treatment of the metric based on the notions of tangency, have a projective treatment that relies on the concepts of sets and projective bundles.
We will see two definitions of conic adapted to “World points” o al “world of straight” according to the interest, in what is defined as the definitions “point” or “tangential” of conic curves.
Using the laws of duality in projective models can get a set of properties and dual theorems from other previously deducted. Obtaining homologous elements in the projective case series was performed by obtaining intermediate pespectividades allowed perspectival do we get what we have called “projective axis”. We will see that in the case of projective bundles, Dual reasoning leads us to determine projective centers.
The operational prospects relationships is reduced to the concepts of belonging, so we will use these techniques to suit projective models simplify obtaining homologous elements.
How can we define two projective series? On how many homologous elements are necessary to determine a projectivity?How can we obtain homologous elements?
The relationship called “cuaterna” or “double ratio of four elements” to define the general homographic transformations perspectivity and projectivity.
Projective foundations are based on the definitions of "ordered triples of elements" and “quaternions for defining the cross ratio”, and relationships called “perspectives” between elements of identical or different nature.
These perspectives relations, that will be used in determining projections representation systems, defined from two projective operators:
Projection
Section
Among the most important curves are studied in geometry is called “Conic curves”. Another common name for these curves is the “Conic Sections” because the first definition given for them, by Apollonius of Perge, was from the sections in a cone of revolution.
One of the most geometric games there is the “Billiard game”, in which using a drum with a wad (a pool cue) on a ball, we must ensure that this impact on one or more other arranged in a rectangular table. With the “The taco de bill” effects can be given to balls, but if you just hit them in the center, behavior can be compared to the classical transformations that are studied in the axial symmetries.
An interesting development in a total communication pasohacia through networks are the projects that are being developed at the MIT Media Lab to interact between the physical and the logical or virtual world. Bits sharing the same physical space with atoms.
In particular I was struck by the presentation of a surface in three-dimensional display form of variable that allows remote physically interact.
Tool applications typically exceed the limits for which they were originally conceived.
Blender is designed for computer animation how to make majors: Pixar, Disney …
Sin embargo, motivated use hands we are showing lines of application that can be handled individually. One of them is presented below: Use as a tool to create an educational presentations.
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