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# Descriptive Geometry-Visualization II Study Guide

Updated: Aug 17, 2022

**Descriptive Geometry**

The graphical solution to three-dimensional spatial problems.

**Isometric**

A pictorial view that shows three sides of an object, usually the top, front, and right side, that they are equally foreshortened.

**Surfaces**

The exterior of an object.

**Line of Sight (LOS)**

An imaginary straight line from the eye of the observer to a point on the object or the direction the observer is looking. An arrow is used to show the direction. It is always perpendicular to a projection plane. All lines for a particular view are assumed to be parallel.

Projection plane

A flat surface that the view of the object is projected onto, such as paper, blackboard, or the face of a plastic box. Your (the observer's) lines of sight are always perpendicular to it.

Projection lines

Lines that are parallel to the lines of sight and perpendicular to the projection plane. They transfer the two-dimensional shape from the object to the projection plane, but are rarely shown on a finished drawing.

Plastic box

A six-sided transparent box. The sides represent six possible projection planes which are at 90 degrees to each other. The object is set inside with the majority of the surfaces parallel to the sides.

Principal planes

Six projection plans that the lines of sight must always be perpendicular to.

Horizontal planes (H)

Level planes. The lines of sight for these are vertical ( perpendicular to the level planes). This rule holds true for three-dimensional & two-dimensional drawings.

Frontal planes (F)

Vertical planes. The lines of sight for frontal planes are horizontal (perpendicular to the frontal planes).

Profile planes (P)

Vertical planes perpendicular to frontal planes. The lines of sight for profile planes are also in a horizontal (perpendicular to the profile planes) position.

Dimensions

True height, width, and depth are perpendicular to the planes.

Height

Is used to indicate the dimension perpendicular to the horizontal planes.

Width

Is used to indicate the dimension perpendicular to the profile planes.

Depth

Is used to indicate the dimension perpendicular to the frontal planes.

Orthographic projection

Two or more views projected at right angles to each other. It is a method of drawing that uses parallel lines of sight at right angles to a projection plane. Visualize the plastic box opened up into what is called third-angle projection. All views must be aligned in their projectable position.

Reference line (fold line or hinged line)

Edges of the plastic box or the intersection of the perpendicular planes. The reference line is only drawn when needed to aid in constructing additional views. It may be placed anywhere, but once it has been referred to, do not move it. All projection lines will be perpendicular to its corresponding hinged line. This line is represented by a phantom line. Draw short dashes 1/8", gaps 1/16", and long dashes 3/4" to 1-1/2".

Origin

A starting point that may be located anywhere on the object or near it. Many computer-aided-drafting (CAD) packages use the lower left corner for this. Coordinates are 0, 0, 0 (0 width, 0 height, 0 depth).

Adjacent views

Views aligned next to each other to share a common dimension. The front and side views share the height projection lines; therefore they are neighbor views.

Related views

Views adjacent to the same view, sharing a common dimension which must be transferred. The dimension may be transferred using dividers or a scale. Students familiar with the mitered method will only be able to use it when transferring dimensions between related principal views.

Elevation view

A view in which the lines of sight are level. The front, right, and top-adjacent views, all have one feature in common--they show the perpendicular distance between horizontal planes referred to as elevation or true height.

Points

Indicate the coordinates of a location in space. They are drawn with 1/8"-long intersecting perpendicular lines.

What is the primary purpose of a multiview drawing?

The primary purpose of this drawing style, or orthographic projection, is to present views of an object on which actual measurements can be shown. Sometimes additional projection planes (auxiliary planes) are required to show all of the necessary details of the object.

Why are the projection planes unfolded?

The projection planes are unfolded to show a three-dimensional object two-dimensionally in a single plane, such as a sheet of paper. This representation is called a multiview drawing.

In a standard multiview drawing, including the three primary views, (a) which two views will show the height of the object viewed, and (b) which two views will show the overall width of the object?

(a) front & right side view (b) front & top view

What relationship do the projection lines have to the lines of sight and reference lines?

Projection lines are parallel to the LOS and perpendicular to the reference line.

true length

actual length of the line

point view

end view of the line

foreshortened

line is viewed between true length and point view positions, making it appear shorter than it really is

Whatever principal plane the line is true length in is the ____ ____.

line type

frontal

the line is true length in the front view (frontal plane)

oblique

the line appears foreshortened--not true length or point view--in any of the principal views

vertical

straight up and down in relation to the horizontal projection plane.

horizontal (level)

parallel to the horizontal projection plane

inclined line

parallel to front plane, but not the horizontal plane

profile

the lines are true length in the right-side view

If you are given a three-view (front, top, right side) orthographic drawing of an object: (a) In which view(s) are you able to see the distance that the object lies below the horizontal plane? (b) In which view(s) do you see the distance that the object lies behind the frontal plane?n (c) In which view(s) do you see the distance that the object lies to the left of the right profile plane?

Ewzary

Auxiliary views

Views projected on any projection plane other than the principal planes.

Primary auxiliary view

Found by projecting onto a plane that is adjacent and thus perpendicular to one of the six principal planes of the orthographic box.

Secondary auxiliary view

Found by projecting onto a plane that is adjacent and thus perpendicular to a primary auxiliary view.

Steps to drawing a primary auxiliary view

I. Determine the LOS II. Draw the reference line perpendicular to the LOS & label to show the two adjacent planes III. Draw the projection lines parallel to the LOS IV. Transfer the points of measurement to the new view from the related view and label lightly V. Connect the points and label true-length lines, edge views, and/or true shapes

Four fundamental views

1. The true length (TL) of a straight line 2. The point of view of a line 3. The edge view (EV) of a plane 4. A plane in its true size (TS) and shape

line type

determined by the principal plane in which the line appears true length.

oblique line

the line is not true length in a principal plane

bearing

direction of a line in the top view, and (true length or oblique) is the compass reading or angle of a line.

slope

the angle between a true length line and a horizontal plane.

Slope of a Line must have:

1. A true-length line 2. In an elevation view (because the front view, side view or top-adjacent view shows one end of the line is higher than the other). 3. Create a construction line parallel to the edge view of the horizontal plane (H/? reference line, such as H/F or H/1). 4. Measure of the slope, between the true-length line and the construction line.

Percent Grade of a Line

1. Using an engineer's scale, measure off 10 equal divisions parallel to the horizontal plane (run), with each unit, equaling 10 units totaling 100 units (Any unit). 2. Measure the vertical distance (rise), using the same scale. 3. An uphill line is positive and a downhill line is negative. If an origin is not given, read the line in the front view from left to right.

Plane

surface which is not curved or warped. It is a surface in which any two points may be connected by a straight line, and the straight line will always lie completely within the surface. Every point on that line is also on the plane.

inclined plane

a plane that appears as an edge view in either the front or side views, and is not perpendicular to a principal view line of sight.

normal plane

a plane that is parallel to any one of the primary projection planes, such as the horizontal or frontal planes, will be seen true shape and size.

oblique plane

a plane that does not appear as an edge view in a principal view.

type of plane

determined by the principal plane in which the plane is true shape.

edge view (EV)

a plane used to determine slope of a roof, highway, or ski slope.

third fundamental view

any plane seen as an edge view (straight line) in a view in which any line on the plane appears as a point. However, sometimes auxiliary views are essential to find the missing information.

compass bearing

a horizontal line measured where any line in the plane is true length in the top

strike

(compass reading) of a horizontal (level) line within a plane

slope of the plane

(dip) is the angle the edge view of the plane makes with the edge view of the horizontal plane.

How to find the strike (compass bearing of a horizontal line)

1. Find a true length line in 2. the top view and 3. measure the acute angle 4. from North. 5. North is assumed to be directed toward the top of the page. 6. The strike is measured independently of the slope (dip).

How to find the Dip of a plane

1. Angle the 2. edge view of the plane makes 3. with the edge view of the horizontal plane (H/1 reference line)

How to find the Dip direction

1. Draw a line perpendicular to 2. true length line in 3. top view towards 4. the low side (found in elevation view)

fourth fundamental view

Used to solve for the true shape of a plane, the line of sight must be perpendicular to the edge view of the plane.

true shape

(TS) may e used to determine the area of a surface in order to calculate how many shingles, ceramic tiles, gallons of paint that may be required.

dihedral /angle

the angle between two planes found in the view where both planes appear as edge views in the same view.

piercing point

a line neither lies in a particular plane nor lies parallel to it, the line will intersect the plane at a single point.

vertex

v, the highest point of a pyramid

transition piece

a sheet metal connector that joins two other pipes, or openings, that are different sizes and shapes.

topographic maps

represent the form of the earth's surface in a single view (top).

contour lines

denotes a series of connected points at a particular elevation. A person walking on this would be on a level path.

index contour line

every fifth line drawn darker and thicker for readability

contour interval

the difference in elevation between adjacent contour lines usually 100 feet.

saddle

two peaks side by side

ridges

small dents in contour lines that bulge toward the lower contour line

ravines

small dents in contour lines that bulge toward higher contour elevations, can also mean a water course exists.

strata

a series of layers below the top soil and loose rock that covers much of earth's surface

veins or lodes

cracks in the rock that often fill with minerals or ores

upper & lower bedding planes

two parallel planes that sandwich a stratum (layer) of rock uniform in thickness

fault

parallel strata interrupted by fractures where one side of the bed shifts in relation to the other

fault plane

plane of a fracture

fault-plane outcrop

fault plane intersects the earth's surface

outcrop

where a stratum of rock, or a vein of ore intersects the earth's surface

dip

slope angle of the plane of the stratum, given in conjunction with the general direction of the downward slope of the plane.