By default, a background preview is displayed in the Canvas so that you can preview your work directly inside the mapping shapes. You can disable it in View → Show Preview. You also have the option to open a windowed projection to preview your work on your computer in Output → Windowed.
As for the fullscreen projection of your mapping from your video projector, make sure you have configured your computer’s display settings properly first. Then, in HeavyM, if you only need to project on a single 1920x1080 display, go to Output → Fullscreen and select the desired display.
If you need a more advanced projection setup (for instance with a different resolution, or multiple displays), please head over to the "Canvas & Output Setup" chapter of our online guide.