Graphic PIZiadas

Graphic PIZiadas

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Categories projective geometric shapes and operations

Category geometric shapes

Geometric shapes are classified into categories.

From a viewpoint parametric, the category of a geometric shape is the number of variables or data necessary for referencing an element thereof.

For example, in the geometry "Flat dotted" (geometrical form containing the infinite points belonging to the same plane or base) two coordinates are needed to identify each of your points; dotted say that the plane is a second class.

The rectilinear series, the straight beam and flat beam its forms of first category.

The forms of second category are dotted plane (the points), radiated plane (of lines) and straight radiation (lines through a given point of the space R3) and radiation levels (planes passing through a point).

The third category forms Points are space (R3 points) or planes.

Projective Operations

Two operations are projective. The operators of our model geometric projective.

  • Projection
  • Section
Projecting from a point R a rectilinear base series b It is to generate a beam that point straight vertex.

Geometrical form containing these elements is based on a flat.

Select by a line r straight beam vertex V.. is to generate a series of points that straight base.

Geometrical form containing these elements is based on a flat.

The resulting shapes of sectioned by a line projecting from a point or other geometric shape are termed "Forms prospects”.

This concept is also generalized for the item "flat".

Perspectividad entre formas de primera categoría.

Perspectivity between-class forms.

The perspectivity is desirable because it provides a simple relationship between the geometric elements (points and lines or planes) the corresponding forms.

In Figure series base r, this is perspective the straight beam vertex R. Each point on the line r corresponds to a straight beam and vice versa.



Projective Geometry