What other kinds are there?
Seems to me these are the fundamental elements that make up all other kinds of line.
Lately in my teaching I've been rediscovering the sweeping curved line as a mode of movement and teaching it to my students along with straight lines. It's liberating and leads to freed-up, dynamic drawings that are full of compositional possibilities but also surprisingly accurate.
In art school, a drawing teacher once told us, "There are no straight lines in nature." What I came to understand him to mean was that with straight lines one can draw anything, rectilinear or curved, by breaking the curves into sections (having not gotten much past algebra, I only later came to realize this was calculus).
The sections can get so infinitely small that the resulting 'joints' are almost imperceptible, resulting in a line that reads to the eye as a specific and flowing curve. Given a choice of one or the other, I'd pick straight lines. In fact, until the Collage Paintings, my love affair with the horizontal and vertical was exclusive.
I was musing about this when it suddenly occured to me...what if straight lines are an illusion? What if all the straight lined objects we see - roads, phone poles, skyscrapers, the pillars of a bridge - are actually themselves lying along arcs so enormous we cannot perceive the place where they begin to bend in another direction? Like the arc of the horizon, apparently flat but really part of the great, slow curve of the earth.
What if all lines are actually parts of a curve? What if there are no straight lines?