Graphic PIZiadas

Graphic PIZiadas

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Categorías Sistemas de representación

Diédrico System: Distance from a point to a line

We can define the distance from a point P to a line r as the smallest of the distances from the point P to the infinite points on the line r. To determine this distance must obtain the line perpendicular to the line r from the point P and get their point of intersection I. The distance d from P to R is the minimum distance from this point to the line r.

This problem can have two different approaches to determining the solution sought.

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” .

Diédrico System: Distance from a point to a plane

We can define the distance from a point P to a α as the smallest of the distances from the point P up to the infinite points of the plane α. To determine this distance we get the straight perpendicular to the plane α from the point P and I get your point of intersection. The distance from P to I will be the minimum distance to the plane α.

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.

The problem of the CAP with three forms

One of the first problems posed in my classes is that call “The CAP with three forms”.

It serves as introduction to the descriptive geometry and forces to make a spatial analysis of great interest for the training of students.

The problem is to determine a plug used to fill three holes that we have made in a wooden box.

Diédrico System: Straight lines in a plane parallel to the projection

Under the so-called category “notable lines” plane are those that are parallel to the planes of projection diedricos. These lines are very useful in the operation that we will develop in this system of representation.

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?

Diédrico System: Projection of the plane

A plane is determined by three unaligned points, so adding a new point to a straight line projections can define it. In this case we will give at least two related dimensions on each plane of projection in order to become independent projections of these plans support of representation. We will learn to represent maps and items belonging to them.

Intersections in outlook: straight and cuboids

One of the classic problems of representation systems is to find the intersection of two elements, such as determining the intersection point between a line and a plane. Topological nature are problems in which the concepts of belonging prevail.

The problems are based on topological relationships are independent projection type in which they are.