2.2: Orthographic projections

Learning Objectives

By the end of this section, learners will be able to

1. Define surfaces, edges, and vertices.
2. Describe width, depth, and height as the three principal dimensions.
3. Identify and describe the six standard orthographic views and corresponding planes of projection.
4. Explain how the first-angle and third-angle projection methods differ in terms of object placement and arrangement of views.

Surfaces, edges, and vertices

Learning the basic elements of a solid and the terms used to describe them is essential to understand orthographic projections. A solid consists of surfaces, edges, and vertices.

Surfaces - figure 2.2.1(a) - are the outer faces that enclose a solid. They can be planar (flat) or curved. If a flat surface is parallel to one of the standard planes of projection, it is called a normal surface. If it is not parallel to a standard plane of projection, it is either an inclined surface or an oblique surface. Section 2.6 describes how to identify, represent, and interpret normal, inclined, and oblique surfaces.

Edges, shown in red in Figure 2.2.1(b), are formed where two surfaces meet. Depending on the shape of these surfaces, edges can be either straight or curved.

Finally, a vertex is a point where three or more surfaces intersect. Figure 2.2.1(c) illustrates a surface with six vertices.

Figure \(\PageIndex{1}\): Primary elements of a solid: Surfaces (a), edges (b), and vertices (c).

A solid's three principal dimensions are width, depth, and height, as shown in Figure 2.2.2.

Figure \(\PageIndex{2}\): The three principal dimensions: width, depth, and height.

Orthographic Projections

A type of parallel projection, orthographic projection is a projection method in which all projectors are parallel to each other and orthogonal (at a 90-degree angle) to the plane of projection.

A view or projection is a two-dimensional representation of a three-dimensional object. There are six principal (or standard) views: top, bottom, front, rear, left-, and right-side views. Each view provides information about two of the object's three dimensions. Depending on the projection method—either the third-angle or first-angle projection method—these six views are arranged on the drawing sheet in a specific order relative to one another.

Figure \(\PageIndex{3}\): The six standard views.

First- and third-angle projection methods

There are two primary methods for orthographic projection: first-angle and third-angle projection. In the United States, the third-angle method is used, following the ASME Y14.3-2003 standard. Europe, Asia, and most of the world use the first-angle method.

Note

ASME stands for American Society of Mechanical Engineers. The American National Standards Institute (ANSI) is the organization that administers and oversees the development of standards by other organizations, such as ASME.

To understand the difference between these two systems, imagine a vertical plane intersecting a horizontal plane at a right angle, as shown in Figure 2.2.4. The intersection of these two planes forms four distinct regions, called quadrants. Figure 2.2.5 illustrates the four quadrants highlighting the first and third quadrants, which are used in the respective projection methods.

Figure \(\PageIndex{4}\): Horizontal and vertical planes intersecting.

Figure \(\PageIndex{5}\): The four quadrants.

First-angle method

The figure below illustrates the first-angle projection method using the L-shaped object from the previous section, which is placed in the first quadrant (Figure 2.2.6).

Figure \(\PageIndex{6}\): Object placed in the first quadrant.

In this method, the object is positioned above the horizontal plane and in front of the vertical plane, between the observer and the projection planes. Figure 2.2.7 provides a closer view of this quadrant. Three arrows indicate the observer’s lines of sight used to project the front, top, and right-side views.

Figure \(\PageIndex{7}\): First quadrant and lines of sight.

Following the direction of the line of sight, the front view is projected onto the vertical plane across the object, as shown in Figure 2.2.8. The top view is projected onto the horizontal plane below the object, and the right-side view is projected onto a vertical plane placed to the left of the object.

Figure \(\PageIndex{8}\): Projection of top, front, and right-side views in the first-angle method.

By unfolding the planes, we obtain the arrangement of the three views in the first-angle projection.

Figure \(\PageIndex{9}\): First angle projection arrangement of views.

Third-angle projection method

Similarly, the same L-shaped object can be placed in the third quadrant to illustrate the third-angle projection method. In this method, the object is positioned below the horizontal plane and behind the vertical plane, as shown in Figure 2.2.10.

Figure \(\PageIndex{10}\): Object in the third quadrant.

Figure 2.2.11 provides a closer view of this quadrant. In this case, the observer is “outside, looking in,” with the planes of projection located between the observer and the object. Three arrows represent the lines of sight used to project the front, top, and right-side views. The front view is obtained by looking directly at the front of the object, the top view is projected onto the plane above the object, and the right-side view is projected onto the plane to its right (Figure 2.2.12).

Figure \(\PageIndex{11}\): Third quadrant and lines of sight.

Figure \(\PageIndex{12}\): Projection of top, front, and right-side views in the third-angle method.

By unfolding the box, the standard arrangement of views in the third-angle projection is obtained (Figure 2.2.13).

Figure \(\PageIndex{13}\): Third-angle porjection arrangement of views

Ultimately, the difference between first- and third-angle projection lies in the different arrangement of views. To avoid mistakes in the interpretation, international projection symbols are used to distinguish between the two projection methods.

Figure \(\PageIndex{14}\): International projection symbols in first-and third-angle projection.