In regard to cutting fabric or clothing the bias-cut is a cut obliquely or diagonally across the grain.
When working with woven textiles the grain refers to the orientation of the weft and warp threads. The three named grains are straight grain, cross grain, and the bias grain. In sewing, a pattern piece can be cut from fabric in any orientation, and the chosen grain or orientation will affect the way the fabric hangs and stretches and thus the fit of a garment. Generally speaking a piece is said to be cut on a particular grain when the longest part of the pattern or the main seams of the finished piece are aligned with that grain.
- Non-woven materials such as felt, interfacing or leather do not have a grain.
The bias grain of a piece of woven fabric, usually referred to simply as "the bias", is any grain that falls between the straight and cross grains. When the grain is at 45 degrees to its warp and weft threads it is referred to as "true bias." Every piece of woven fabric has two biases, perpendicular to each other. A garment made of woven fabric is said to be "cut on the bias" when the fabric's warp and weft threads are on one of the bias grains.
You may find the following terms to be of possible interest for further research.
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