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In mathematics, a hidden line is a geometric edge line[1] that is not visible from an observer's view of a shape or object.
A common practice is to draw the visible edges as solid lines and the hidden lines as dotted lines, dashed lines,[2] or thinner lines than the visible lines.
Hidden lines can help visualize geometric objects in three-dimensional space. Hidden lines add geometric information about the unseen sides of an object.
A three-dimensional object drawn with solid visible and hidden lines is a wire-frame model of the object.
Objects without hidden lines
[edit]When a student is first introduced to a geometric cube, a cube without hidden lines looks like a closed box which they are familiar. Drawing an object without hidden lines, matches an observer's view of the object. Less lines makes an object easier to draw.
To draw higher dimensional cubes, hypercubes, without hidden lines, make the faces opaque. Then, the hidden lines are no longer visible, they are removed from the observer's view. This works with a cube in three-dimensional space, a Tesseract in four-dimensional space, a hypercube in five-dimensional space, and will work with higher dimensions as well.
Removing hidden lines is also important in computer design and graphics applications. There are algorithmic solutions to remove hidden lines or partially hidden lines during an object's rendering.
See also
[edit]References
[edit]- ^ Weisstein, Eric W. "Polytope Edge". From Wolfram MathWorld.
- ^ TeX software(TeX), Draw cube with dashed hidden lines. From TeX StackExchange.