The factors that determine the coarseness or softness of a material are:

1. **Grain or Fiber Size**: The size of the individual grains or fibers in a material can greatly affect its perceived coarseness. Larger grains or fibers tend to make a material feel coarser, while smaller grains or fibers usually result in a softer feel. For example, the size of the grains in sand can affect whether it feels coarse or soft to the touch.

2. **Grain or Fiber Shape**: The shape of the grains or fibers also plays a role. Rounded grains or fibers can slide against each other more easily, leading to a softer feel, while angular grains or fibers may feel coarser.

3. **Arrangement of Grains or Fibers**: The way the grains or fibers are arranged can affect the feel of a material. A tightly packed arrangement might feel harder and coarser, while a looser arrangement could feel softer.

4. **Material Composition**: The chemical makeup of a material can influence its coarseness. For example, materials made up of softer substances, such as polymers in certain plastics or rubber, can feel softer. Materials made up of harder substances, such as metals or ceramics, can feel harder and coarser.

5. **Surface Treatment**: The treatment applied to the surface of a material can affect its perceived coarseness. For example, a material might be sanded, polished, or coated to change its feel.

6. **Temperature and Humidity**: The environmental conditions can also impact the feel of a material. Some materials might feel coarser in colder temperatures or in less humid conditions, while others might feel softer in warmer temperatures or in more humid conditions.

7. **Molecular Structure**: The structure of the molecules in a material can also play a role. For instance, bottlebrush polymers, which have a unique structure with additional polymers attached to a linear backbone, can form extremely soft elastomers.

Here's a table summarizing the above points:

| Factor                  | Coarser feel | Softer feel |
|-------------------------|--------------|-------------|
| Grain/Fiber Size        | Larger       | Smaller     |
| Grain/Fiber Shape       | Angular      | Rounded     |
| Arrangement             | Tightly packed | Loosely arranged  |
| Material Composition    | Harder substances | Softer substances |
| Surface Treatment       | Roughened    | Smoothed    |
| Temperature and Humidity| Colder/Less Humid | Warmer/More Humid |
| Molecular Structure     | Rigid structures | Flexible structures |
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