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Visualization

Visualization is an important aspect in understanding what an object or group of objects shown in a drawing is representing in the real world. Visualization involves looking for clues, and understanding how conventional representation of 3-d objects is translated into 2-d space, like a sheet of paper. A photograph is a representation of the 3-d world on a sheet of paper. Drawings used as construction documents are different though, because they use a technique of projection called orthographic projection. This type of projection results in a loss of a physical dimension in each of the basic orientations, or views causing objects to appear to be flattened out.

One of the problems in presenting visualization material is that the goal is to teach someone to visualize objects, but during the learning process it is impossible to present all of the possibilities that one might encounter. Therefore a set of common objects will be used to provide a starting point for discussing how to look at an object, and understanding it's configuration. First, start by defining a method of orientation for objects, and then look at the basic elements that are used to describe 3-d objects in 2-d space.

Orientation

The placement of an object can be determined by deciding which orientation should be used to best represent the object. When objects are represented in orthographic views they have a specific orientation with respect to the viewers world. There is a top or plan view, a front elevation, and also a right elevation. Most of the time in architectural drawings the compass determines how the views are arranged. North is usually used as the up direction for plans on a drawing sheet. A group of planes called a glass box is a theoretical group of transparent planes connected at 90 degrees with each other. The size of the box is elastic, it is always as large as the object that is contained within it. In the theoretical world the direction of orientation is set so that the observer can see three sides of an object at once. These views are represented on the 3-d glass box.

One more step is necessary to get from 3-D, as shown above, to 2-D which represents the sheet of drawing paper.

The common edge between each plan could be hinged, and folded out so the planes will be flat. Each hinge is referred to as a fold line, and will be used to represent the viewing planes on paper. This is a method used for separating views and providing a means for referencing dimensions. Here the connecting edges or fold lines are highlighted in green.

Insert an object into the glass box, and look at the orientation with respect to the box planes. In the glass box an object such as the line A-B seen below, is projected (blue lines) onto the plan view. The drawing on the right shows what the line looks like after projection. Notice that one dimension is missing, in this case the height. It is no longer possible to tell if A or B is closer to the top plane.

Next the line A-B is projected onto the front plane, and the resulting orthographic view seen to the right. The orientation of the line was purposely set so that the front elevation would look exactly like the plan view. Again a dimension is missing from the view. This time it is the depth dimension, but it is not possible to tell if A is closer than B.

It is necessary to have both views to get the information about a drawing. To determine if A is closer to the plane than B, when looking at the front view, check the plan view.

To determine if A is closer to the plane than B, when looking at the plan view, check the front view.

While the Orthographic views shown in the last two frames are very similar in orientation they are not. The plan view is showing length and depth information about line A-B. While the front view is showing length and height information.

Basic Drawing Elements

1. A point, which defines a physical position in space, is often used as a reference location.

2. A line which is mathematically made up of a lot of points, can be described by the endpoints or boundary of the line.

3. The last basic element is a plane. A basic plane is made up of at least 3 points, and 3 lines or edges. In a plane the lines are referred to as edges, and form the boundary of the plane. 3-D solid objects are represented by combining multiple planes.

Lines

In the figure seen below there are 3 different line orientations. Each shows two views (previously defined) which are commonly used, top and front.

The top row shows line 1-2 from the plan or top view. That means the observer is looking down from on above of the line.

Along the bottom row, lines are represented as if the observer is standing in front of the lines, called the front view. Refer to the orientation section previously discussed. So the top view is located directly above the front view. The line orientations seen below represent how they look in a 2-d orthographic top, and front view. Note that the green lines are the fold lines, separating the views.

On the left side of the panel, line 1-2 is parallel to the fold line, or viewer. When a line is parallel with the reference plane the length is not distorted, or foreshortened. Since the view is not foreshortened the observer sees the exact dimension of the line, which is referred to as the true length of the line.

Because the line 1-2 is parallel with the green reference line (fold line) in the front view. The plan view can be said to show a true length line.
Also, since line 1-2 is parallel with the reference line in the plan view, it is also said a true length line in the front view.

Next, in the middle panel, the top view of line 1-2 is rotated by 45 degrees, and the front view reflects that rotation. The front view of the line is an example of how lines in orthographic views are foreshortened due to rotation of an object. That is, the same length of line appears to be shorter than it appeared in the figure to the left.

The front view of line 1-2 is foreshortened.
Look in the front view, and notice that the line 1-2 is parallel with the green line.
Since the front view is parallel with the reference line this means that the plan view is a true length line.

Then on the right side, the same line is once again rotated by another 45 degrees, to an angle of 90. Now the front view of the line appears as a point. The end view of a line is a point. Notice that the point is numbered 1,2. This notation is used to define the orientation of the line, stating that point 1 is closest to the observer.

Now the line has been rotated so much that the front elevation is seen as a point. Kind of the ultimate foreshortening.
Since the front view shows a point, it means that the line is parallel with the reference line, and that the plan view represents the true length view of the line 1-2.

Two important orientations are worth mentioning again, as they will be useful when looking at planes.

1. When a line is parallel with an observer it is said to be true length (TL). That means that there is no foreshortening of the line. The figure seen above is a TL line in both plan and elevation views, because the lines are both parallel with the fold line.

2. If a line has been placed in an orientation which is parallel with the observers line of sight, then the line has maximum foreshortening. It is seen as a point. The plan view is a true length line view because the front elevation is parallel with the green reference line.

Planes

A plane must have a minimum of 3 edges. When looking at drawings, planes are identified by their orientation in space. It is important to be able to read the orientations of these planes to help in visualizing the objects. Also note that these theoretical planes are flat, non-warped, and they have no thickness.

One common orientation is referred to as a normal surface, where the orientation is such that the viewer can look directly at the plane, and see the true area, because all edges are true length there is no foreshortening.
Another type of orientation is the inclined plane. These planes are foreshortened in at least two of the theoretical views.
Still another plane orientation is the edge view. This means that the viewer is looking perpendicular to the normal surface. An edge view of a plane is a line.

The rectangular plane, seen below, is rotated in each of the 3 panels so that the plan is vertical on the left, and horizontal on the right.

Starting from the left side, the top view shows a line, and in the front view a full rectangle is seen. Looking at the combined information from the two views determine if the plane is oriented vertically. How is this determined?

Because the top view is a single line or an edge, the front view is parallel with the viewer. The rectangle is said to be normal with the front elevation, and the true area is visible. One important key is to notice that in the front elevation edge 1,3 is shown as a line, and seen as point 1,3 in the top view.

In the middle group the rectangle is rotated by 45 degrees. Now the edges 1,3 and 2,4 are shorter than they were on the left, in the previous view. They are foreshortened. Due to the way the plane was rotated, both the top and front views appear to be foreshortened.

Notice that in the middle panel all edges of the plane are visible. This represents an inclined plane. Edges 1,2 and 3,4 are still true length, while 1,3 and 2,4 are foreshortened.

In the right panel the plane is rotated another 45 degrees or a total of 90 degrees from the original position. Now, in the front elevation the rectangle is horizontal. Note that now the front elevation is the edge view, and points 3, 4 are closest to the observer.

The plan view is now oriented to represent a normal surface, which shows the true area.
Check line 1,3 in the plan view, which is called out as point 3,1 in the front view. Now the front view shows the edge of the surface.

Looking at 3-D objects

Any 3-D object can be reduced in detail to the point where it is represented by basic planes. The block below could be a simple wood block, or a simplified version of a high rise building. Most of the objects you will see in conjunction with class work are simplified versions of real objects.

An object has planes, or surfaces which are defined by edges, the edges are lines, which have points, or vertices at each end. The principle views of this 3-D object are shown below. Notice the positions of similar numbers in the different views.

Lines or edges are used to represent the boundaries of surfaces, and also the connection of adjacent planes. For instance the front plane (1,2,3,4), and right plane (4,3,7,8) have edge 3,4 in common. Edge 1,4 is common to the top (1,4,8,5), and front planes. Edge 1,2 is common with the front, and left planes.

Look for elements associated with vertices 1,5. In the top and left views, edge 1,5 appears as a line.

1. Where and how does edge 1,5 appear in the front, and right views? A_1

Surfaces in these objects are vertical, horizontal, or inclined. An inclined slope can be connected to a horizontal surface, and or a vertical surface. When looking at objects it is sometimes useful to categorize the surfaces with respect to their orientation.

2. Is the front surface vertical, horizontal, or inclined? How was the answer determined? A_2

3. Is the top surface vertical, horizontal, or inclined? How was the answer determined? A_3

If a line is shown on a surface it means that there is a change in plane at that location. The object shown on the left side below has a line (red) across the middle of the surface, but no change in plane. This condition doesn't occur in orthographic drawings unless it is painted on a surface.

Again, when a line appears in a drawing it indicates that there is a change of plane occurring at that location.
The box on the left side is incorrectly represented.
The right side drawing indicates that there is a change in plane also. A vertical plane is connected to an inclined plane. The red line represents the edge at which they connect.

When the object is drawn using 2-D orthographic views, inclined surfaces appear to be flattened out rectangles. Evaluate possible options for the object seen below, and sketch the profiles.

When reviewing an object, it might be easiest to look at the overall shape.

In this case the object appears to be rectangular.
But not totally rectangular, because there are edges in the middle of the top, and front views.
An edge means that there is a connection between two planes, or a change in plane.
What orientations in the planes would result in the configuration seen above.

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Looking at planes in various views helps to understand what the object is like in 3-D. To get a feeling for what orientation a plane is in, look at the different views identifying the orientation of the plane.

Example Models, and Sketching

One of the best ways to learn visualization is to work with different models, sketching views which can be created by rotating the object. Start with simple shapes, and progress to harder more challenging objects. Rectangular shapes are the easiest, and fasted to start with.

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