Hidden line

In mathematics, a hidden line is a geometric edge line that is not visible from an observer's view of a shape or object.

Cubes with hidden lines: dotted, dashed, and thin lines. Cubes with no hidden lines, and a cube with dotted lines to give 3 dimensional reference

A common practice is to draw the visible edges as solid lines and the hidden lines as dotted lines, dashed lines, or thinner lines than the visible lines.

There are advantages for excluding hidden lines. When a student is first introduced to a geometric cube, a cube without hidden lines looks like a closed box which they are familiar. Also, a cube without hidden lines is easier to draw. Drawing an object without hidden lines, matches an observer's view of the object.

Hidden lines can help us visualize geometic objects in three-dimensional space. Hidden lines add geometric information about the unseen sides of an object.

Sample rendering of a wire-frame cube, icosahedron, and sphere

A three-dimensional object drawn with solid visible and hidden lines is a wire-frame model of the object.

A wire-frame image using hidden-line removal

Removing hidden lines is important in computer design and graphics applications. There are algorithmic solutions to remove hidden lines or partially hidden lines during an object's rendering.

References

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