Lignes de fuite

06:51 Aug 13, 2015 

Yes, I agree with Robin's suggestion for 3 "lines".

21:35 Aug 12, 2015 

Yes, Claude-Andrew. I agree with your suggestions. The literal terms are what is there. Any figurative readings works in English as in French.

20:26 Aug 12, 2015 

The 3 terms used here in French are the equivalents, in perspective drawing, of the three cartesian axes: X,Y and Z measured by topographers with a sextant and compass. The ST nonetheless refers to 3 lignes, so the English also needs 3 lines, no points. There are several variants for these terms; the ones I learnt many years ago are:
- lignes de fuite - vanishing lines (oblique lines representing horizontal features of the scene, which point towards the (one or several) vanishing points)
- ligne de mire - sight line (the visual axis of the observer's eyes)
- ligne d'horizon - a horizintal line through all the vanishing points (but not necessarily through the sight line).

Note that there are always multiple vanishing lines (even if there is only one vanishing point), so you must retain the plural, but there can be only one sight line and one horizon line.

19:40 Aug 12, 2015 

Although Nikki's suggestion is worth thinking about, I would suggest using the precise terms artists use: vanishing line, vanishing point and horizon line. The fearless sculptor in his perilous position is only thinking about his art.

19:18 Aug 12, 2015 

I think you need to consider figurative and literal meanings of
- ligne de fuite
- ligne de mire
- ligne d'horizon
A literal and figurative interpretation is possible in cotnext for each of the three expressions. Bear in mind the artisitc element (sculpture which has three dimensions) and how the expressions are used in the sentences of the extract you have provided. There are three dimensions there too.
Height, direction, orientation, distance, emptiness, objectives, far off limits, the never-ending. Consider all of those and then try to render all three in a cohrent way that fits with the rest of the text and the stylistic choices you have already made.
Your first step will be a FR/FR dictionary to get the literal contextual and then figurative meanings.