El Sistema de Planos Acotados

• The following is a summary about the system of bounded planes:

Generalidades

• This system involves a cylindrical orthogonal projection onto a single horizontal coordinate plane.
• It is suited for problems with significantly smaller vertical than horizontal dimensions.

Elementos Clave

• Points projected are represented by x, y coordinates and the z coordinate, the elevation
• Each point has projections, is marked with apostrophes, and can be unfolded
• The horizontal P plane serves as the frame or comparison plane.
• "Point elevation" refers to a point's height above the reference P plane
• Elevation can be positive or negative, based on the point's location
• Negative elevations are avoided by ensuring all points are above the reference plane.
• Measurement units consist of cm for class practice and m for real-world applications.

Representación del Punto

• The drawing plane (P) acts as the reference plane
• Points are determined by an orthogonal projection on P and its elevation
• A'(2) indicates point A's projection has a value of 2
• Points can be above the reference plane, with a positive elevation (A'(2)
• Points can be on the reference plane, marking zero elevation (B'(0))
• Points can be below the reference plane with a negative elevation (C'(-4))
• The difference in elevation is found algebraically using the values, the difference between A and C equals 6, given by (2-(-4))=6

Plano de Comparación

• The plane of comparison, with a level of zero, is the Sea Level
• The origin for elevation is the tangent on the Earth on the beach of Spanish Postiguet
• Positive levels are called Altitudes and negative elevations are Depths or Sounds.
• Higher levels are made possible by the planes considered for the reference point and the lower value found

Representación de la Recta

• A line is defined by two points, and its projection is obtained this way
• Lines can be perpendicular, parallel, or oblique relative to the plane, occupying three general positions
• Where the line intersects with the plane is the trace of the line, having a value of 0

Elementos de la Recta

• Inclination in a line is defined by:
• It is tangent to forms on the plane of the reference point: p=tgα=h/d
• The above is expressed as a percentage by multiplying with 100 the tag of the following: p = 100*tag α = 100 * (h/d)
• Ratio between vertical and horizontal distance: p = h/d
• Vertical Distance, h, between two line points is differences in elevation or value
• Horizontal Distance (d) which is the distance between two projected points

Intervalo o Módulo

• It is the projected length difference between line points, and a value of “i” is to denote it
• Said difference allows it to be run horizontally depending on the number of areas with the term slope, or module
• The formula used is p = tgα = 1/i

Cálculo Gráfico

• The slope and interval can be graphically calculated

Graduación de la Recta

• It is the number of parts found in divisions to know the values, that are present as values on the same line
• By having a value in its entirety, it is easier to situation and have points that are whole lines

Posiciones de la Recta

• Straight perpendicular projects form, and is perpendicular to the plane
• Being its direction is the value letter since there exists length. Its range is 0, and inclination is infinite
• The Straight, flat plane horizontal line consists of consistent marks with an infinite range

Intersección de Rectas

• Lines can be split, and split differently depending on the value of the sides:
• This is when the marks exist on a certain end as opposed to flat and horizontal to each other
• Lines can be traversed

Rectas que se cortan fuera de los Límites del Papel

• Projections exist on auxiliaries over the original length based mark projections

Representación del Plano

• Planes can be marked by levels over given planes:
• The level over line on the angle over that, the highest angle over planes

Horizontales del Plano

• Lines exist with said characteristics over certain marks, which consist of straight lines projecting in said forms and ways

Definición del Plano

• Planes have many variables with straight lines that differ in points and concurrent parallels

Pendiente del Plano

• Angles that forms and is measured by a plane

Ejercicios: Hallar el Plano Formado por Tres Puntos Noalineados

• By measuring plane and line segments of values and line over angles, we have defined forms

Punto Contenido en el Plano

• Points contained in a plane consist of lines that fall on those defined by lengths:
• They are measured from points on the slope with said values over lengths, areas with all kinds of lines

Posiciones del Plano

• Position on planes, related to forms and levels:
• Parallel
• Oblique
• Perpendicular

Plano Oblicuo

• Oblique Planes measure inclination and area slopes

Plano Paralelo

• Equal Lines are on said areas, being parallel with certain areas and flat as their main feature

Plano Perpendicular

• Perpendicular Planes consist of infinite length with a value that is constant over flat marks with thin widths.

Intersección de Planos

• Two-plane intersections consist of a result as the intersection of values on the same level

Intersección de Tres Planos

• They are meant to split the intersection on the points with 2, and intersections on wanted points

Intersección de Recta y Plano

• A line is traversed by another depending on the slope

Caso General

• Forms and lines are measured that all consist of an intersection on sought forms and sides

Distancias

• The main distance on this is measured by its components and length depending on measure points

Distancia Entre Dos Puntos

• Using trigonometric laws on the sides, they make up parts of triangles

Distancia de un Pto a un Plano/Recta

• From A to a plane/line perpendicular over forms dependent on the side is to measure distances

Distancia Entre Dos Rectas Paralelas

• Over planes measuring a side point the length can define the volume from side measurements

Distancia Entre Dos Planos Paralelos

• Levels using lengths, the distance is a constant width measured by those said constant lengths

Mínima Distancia Entre Dos Rectas Que Secruzan

• Distances with minimums are defined given intersecting lines