At a horse trial that I attended last month there was a very unusual approach to the water if you were trying not to cross your path. Afterwards the TD explained to me that on xc you are allowed to cross a previous path. In other words, to get from jump #14 to #15 you can cross the path you took from #12 to #13. Has anyone had any experience with this?
Yes. And in fact nearly collided with a friend in the process. You had to cross the path between two early fences toward the end of the course. I was a tick over the time, and a friend, just starting, and I came very close to one of us T-boning the other.
That wasn't the first time, but it was definitely the most memorable.
Hah! Amanda, you are making me remember in the way-back machine....to Menfelt (remember Menfelt?). At one point a friend and I were the only ones on course...and we passed within 10 feet of each other, coming and going, waving merrily at each other all the way....
Anyway, to the OP, the only time you cannot cross your line is as an approach to any given fence (ie, a circle, once "presented"), or in between obstacles numbered A, B, C. If you want to throw in a circle between 13 and 14, have at it.
Once I actually collided with a loose horse--he was running for home and came around a tree line and nailed us. I came off and the 2 beasts ran off together . . . once caught the organizers were very kind and let me pick up my ride, much later.
But to answer the question, Asterix is correct--the course can cross itself, and you can even circle, outside of approaches to obstacles.
In stadium, the course can cross itself, but you cannot circle anywhere without it counting as a refusal (basically the whole course is considered an approach to a fence).