How does cross-hatching create shadows and volume?

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Watercolor painting by Berthe Morisot showing Edma seated on a sofa in a floral dress with her young daughter Jeanne beside her, both facing slightly right. — Drawing *The Artist's Sister, Edma, with Her Daughter, Jeanne*, watercolor over graphite on paper by Berthe Morisot, 1872; in the collection of the National Gallery of Art, Washington, D.C.

In the context of drawing, cross-hatching is a technique used to create the illusion of shadows, modeling, and volume, particularly when using mediums that do not allow for blending, such as pen and ink.1

Artists achieve these effects through the following principles:

Density and Proximity: The intensity of shading is determined by the number of lines used and how close they are to one another. By placing lines in closer proximity, an artist can create darker, more concentrated areas of shadow.1
Layering: While basic hatching uses parallel lines, cross-hatching involves layering these lines by crossing them with others. This process increases the density of the marks, allowing for a greater range of tonal values and deeper shadows.1
Modeling Volume: By varying the density and direction of these intersecting lines, artists can suggest the curvature and three-dimensional form of an object, effectively modeling volume on a two-dimensional surface.1