Notice how the title of this section ends. surfaces not with facets? This is because (as you already know) individuals in SketchUp are always flat - no exceptions. When you see a non-flat surface, it actually consists of several faces. You cannot see the edges between them because they were smoothed out.
Choosing a View → Hidden Geometry provides all curved surfaces for what they really are.
How you are going to map the image to a curved surface in SketchUp depends on what type you have. With this in mind, curved surfaces fall into two general categories:
Unidirectional Curves: A cylinder is a classic example of a surface that curves in only one direction. In SketchUp, a cylinder is essentially a series of rectangles set side by side. Most of the curved walls that you see on buildings are the same; they do not taper or rise.
Another way to think about unidirectional curves is to consider how they could be made. If the curved surface you are looking at may be the result of a single push / push operation (for example, turning a circle into a cylinder), there is a great opportunity in one-way direction.
To display an image on a surface with one curve, you can use the "Adjacent Faces" method, it works well and does not stretch your image.
Multidirectional Curves: Landscapes, saddles, and curtains are all simple examples of surfaces that curve in more than one direction at a time. They always consist of triangles - they are never basic rectangles.
To map an image to this type of curved surface, you must use the Projected Texture method.