Descriptive Geometry/Understanding Views

Descriptive geometry's primary function is to translate an object in three dimensions into a two dimensional representation of that object. Each such representation is called a view.

From Two Dimensions to One
Rather than begin with views of three dimensional objects, we shall first examine the process of taking one-dimensional views of a two-dimensional figure. Suppose that we have a square, rotated at an angle relative to the angle of the two views we will be taking of it.

Point View
Point view of a line shows a view of a line in which its endpoints coincide. To find point view of a line you must first find it in true length if you have not already done so (the construction for finding true length of a line is described in the following section, True Length). Then you must take a view perpendicular to the true length line, and that will give you the line in point view.





True Length


Finding the true length is a fundamental process in descriptive geometry that advances the problem-solving to the next steps to reach the solution. To find the true length of a line you must take a view parallel to the line; in other words, if a line is a parallel to the folding line in one view, it is shown in true length in the adjacent view. If a line is parallel to the folding line in both adjacent views, as for example in both the top and front views, then it is shown in true length in both of those views, and in such cases no additional work must be done if the only goal is to find the true length of the line.





Edge View
Edge view is a view looking at one side of a plane. Planes in edge view are shown as lines that are the distances of the edges of the shape. To get edge view, take a view parallel to a side of a plane. Then take another view perpendicular to the new line. Alternatively, if you already have front and top views of the plane, to get an edge view you may draw - in either view - a line from one side of the plane to the other that is parallel to the folding line, transfer this line to the other view, and then take a view perpendicular to the line from that second view. Use transfer distances from the first view to get the endpoints of the plane and complete the edge view of a plane.



True Shape
To get your plane into true shape, find the edge view, then draw a folding line parallel to edge view and use transfer distances to transfer all of the points of the plane to this final view. This will get you the true shape of the plane.