Indeed. As you stated, mutual vanishing points, as used in illustration, are when parallel lines of the scene are extended to infinity and converge. Animation o

Indeed. As you stated, mutual vanishing points, as used in illustration, are when parallel lines of the scene are extended to infinity and converge. Animation of a rotating object requires animation of a set of vanishing points for each frame. This is nearly deja vu for me, as a conversation that I've seen several times at the intersection of arts and computer graphics. I can only conclude that a sub-population have received instruction on "vanishing points" that were overly specific and missed the footnote on how it generalizes. Specifically: the artist and draftsman idioms of 2 or 3-point perspective or vanishing points are short cuts for perspective rendering of subjects which have cartesian layouts, such as rectilinear buildings and street scenes built on a cartesian grid, with lots of parallel or perpendicular edges. The missing footnote is that this does not work for arbitrary subjects. Real perspective rendering has infinite potential vanishing points in one scene. Each point represents nothing more than the infinite continuation of any line segment in the scene, as it would be rendered by a true perspective rendering. The vanishing point of any one line is when the viewing ray converges with that line, to the limit of angular resolution in your rendering. All more distant segments project into the same small picture element, whether formed by raster graphics or your finest pencil, pen, brush, or engraving tool. For a complex scene, the skilled artist would choose [edited to delete typo "three"] different vanishing points appropriate for each set of parallel lines. E.g. a vineyard with parallel rows of plantings might use different points than a road passing by at an odd angle, and a set of high-tension powerlines crossing the scene would have its own vanishing points as well. If the power lines follow a ragged course, each segment between two towers would need its own vanishing points. Furthermore, the artist would have to approximate the parabolic sag of the wire below these projected line segments, perhaps using parallel lines to locate the envelope within which the line sags.