Short throw projectors (mostly) solve these problems. These devices use a lens system that enlarges the image more strongly, which means they need a lot less distance. There is no exact definition for the ‘short throw’ concept, but the term is often used for devices that have a projection distance shorter than the width of the projected image.
A good example of this is the BenQ W1210ST projector that is part of this test. The device has a range of 0.69 to 0.89 times the image width, which means that you can project a 2 meter wide image at a distance of at least 1.38 meter from the screen. In practice this means that you can project a relatively large image should you place this projector in front of you on a coffee table, for example.
The advantage of these types of projectors is that while the lens system has more requirements than a long throw projector, manufacturers are still able to project a distortion free image that is sharp without extremely high costs. Downside is that a short throw projector is not great for permanent installation, unless you are fine with always having a projector on the coffee table. Mounting it to the ceiling is also an option, but in that case a short throw model does not offer a lot of advantages compared with a traditional model.