# System dihedral: Fundamentals of auxiliary projections, changes in plane

To represent an object in the dihedral system usually use the projections on the three planes of the reference trihedron, as we have seen when studying the fundamentals of dihedral system.

In general it is sufficient to use only two of the three possible planes, It is represented for example by a straight projections on the horizontal plane and the vertical. Sometimes it may be desirable, or even necessary, obtain new projections in different directions projection, in which case the call her “auxiliary projections” .

# Perpendicular to a plane

One of the basic problems that we learn by studying the systems of representation are those in which there are elements that are perpendicular to other. All the problems of determining distances make use of these concepts.

Let's see how to determine the line perpendicular to a plane in dihedral system working directly on the main system projections.

# Fall line

By studying the true magnitude of a line we saw that we could turn calculate the angle of this line with respect to a projection plane, namely, its slope.

In a plane we can determine endless lines with different direction contained therein. One of these lines form the maximum angular condition with respect to the projection plane.

# Diédrico System: Theorem of the three perpendicular

One of the most important theorems of descriptive geometry is the so-called “Theorem of the three perpendicular”, It establishes a relation between two lines perpendicular when one of them is parallel to a plane of projection.

# Diédrico System: Projection of points in the plane

Can you get from a projection of a belonging to a flat point another projection on the plane dihedral to the full? For example, If give us the horizontal projection and vertical of a plane and a point in the latter as determinaríamos the projection on the horizontal plane?

# Fundamentals del System dihedral

We have seen in presenting Representation Systems descriptive geometry that is the set of techniques that allows to represent geometric character three dimensional space on a two dimensional surface.

In particular we explore in detail the so-called “System dihedral” based on the prospects ratios appearing in the cylindrical projection on two planes orthogonal projection.

# Classification Representation Systems

The representation of technical objects is performed by one or more images that are determined by projecting the objects on an imaginary plane.

The display system is therefore defined by the position of said plane and the center of projection.

The position of the object relative to the center plane and can vary its representation, determining convergence in the projection, varying mediated, lines which are parallel in space.

# Representation systems : Incidence (Intersections) [ Descriptive geometry ]

Incidence problems trying to identify common elements of two geometric figures; can be defined as special cases of belonging.

Starting from the line and plane elements, We can apply the concepts of duality to analyze the possible problems that may occur.

# Representation systems : Foreign prospects [ Descriptive geometry ]

We have seen a general model that relate the different types of projections: Conical, orthogonal and oblique cylindrical cylindrical.

Let's see an example applied spectivity relations in the projections.

# Representation systems : Projections [ Descriptive geometry ]

The so-called representation systems encompasses a set of techniques and projection models for viewing items in a three dimensional space on a two dimensional plane.

Each of the systems provides a number of advantages that make it particularly useful in certain applications. So, systems that are included in the set of perspectives, are especially useful to give a simple three-dimensional view of the object. Cylindrical nature systems facilitate operations orthogonal measure to reduce them to obtain Pythagorean triangles (rectangles), models while central conical or approximate how the human eye works.