Laura received her Master's degree in Pure Mathematics from Michigan State University, and her Bachelor's degree in Mathematics from Grand Valley State University. She has 20 years of experience teaching collegiate mathematics at various institutions.
Suppose you want someone in another country to design this triangular structure for you. You send them this picture, but it causes some confusion.
Do they consider the green triangle to be in the front or the back of the structure? You don't speak their language, so you can't explain it to them. What do you do?
Thankfully, we have orthographic projections to help in situations like this. Put simply, an orthographic projection is a way of representing a three-dimensional object in two dimensions. It uses different two-dimensional views of the object instead of a single three-dimensional view. This allows you to communicate exactly what you want your structure to look like and eliminates any miscommunication between you and the person creating your design.
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Typically, an orthographic projection drawing consists of three different views: a front view, a top view, and a side view. Occasionally, more views are used for clarity. The side view is usually the right side, but if the left side is used, it is noted in the drawing.
To draw one of the views of an object, use lines to represent changes in depth. For example, consider this object with its right side view orthographic projection:
Notice that there are lines where there are any depth changes in the structure; this changes the right side view of a three-dimensional object into a two-dimensional picture. These next two images show the front view and the top view of the same object:
In an actual orthographic projection, all of the views are included on the same page. Normally, the front view is in the lower left corner of the page, the top view is in the upper left corner, and the right side view is in the lower right corner. The same scale is used for all three of the drawings, and their lengths, widths, and heights are all lined up.
Sometimes, the isometric drawing of the object is included in the upper right corner. An isometric drawing is a view of an object from a corner angle so that all the different views of the object can be seen. Though an isometric drawing is two-dimensional, it appears three-dimensional. The isometric drawing need not be drawn to scale or lined up with the three orthographic projection drawings.
Often, an orthographic projection drawing includes measurements of the dimensions of each of the views. This allows the person creating the design to make it to scale as the designer wishes. This image shows the actual orthographic projection of the object shown earlier:
Let's consider another example. Suppose you want to build a set of steps that you can use to reach the top shelf of a cupboard. You know there are three steps, and you know how tall the steps need to be and the dimensions of each step. The only problem is that you can't build them yourself. The good news is that you can create an orthographic projection of your steps and present it to a builder, and they can build it for you based off your orthographic drawing shown in the image:
In the image, we see that you want a set of steps that are each ten inches high, twelve inches deep, and 36 inches long. This shouldn't be too hard for the builder to make. You will have your set of steps in no time thanks to this drawing!
Orthographic projections are two-dimensional drawings of different views of a three-dimensional object. These projections serve as a sort of universal language when it comes to engineering and building, and allow for smooth communication between designer and builder as to what is expected.
An orthographic projection normally contains three views of the object: the front view in the lower left corner, the top view in the upper left corner, and the right side view in the lower right corner. The drawing often includes an isometric drawing of the object, which is a view of the object from an angle that shows all three of the different views. Measurements and dimensions are also normally included in the drawing. Orthographic projections are extremely important in mathematics, engineering, and the like, so it's great to be familiar with them.
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Orthographic Projection: Definition & Examples
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