Straightedge construction — where it appears
Named by 5 essays across one field — each of them below, with the objects they name alongside it.
Carrying a height across the room
A known height at one place on the floor, and the same height wanted at another: two lines settle it, and they settle it exactly, at every camera and every pair of positions. What the recipes never mention is that one of those two lines has to be drawn to a point that is usually not on the paper — 3,300 canvas widths away in the case drawn here — and that the repair is not to extend it further.
A picture with nothing straight in it
Every construction on this site is handed the horizon, and a photograph of a crowd, a hillside or a curved façade has no straight edge to give it. What such a picture does have is repetition — and three things of one height put the horizon exactly where the camera has it, from the picture alone. Two things do not, and three standing abreast do not either, and both refusals are the reader's ordinary situation.
Seven is not a power of two
Halving a receding depth by diagonals is exact, and every book gives it. Halving reaches a half, a quarter, three eighths — and never a third, however many times it is spent, because no power of two is divisible by three. There is a construction that reaches every whole fraction, it costs three lines rather than a stack of quadrangles, and the extra ingredient is not a measurement.
The circle in the square wants a number
Every manual draws a circle in perspective by inscribing it in a square, crossing the diagonals, and marking four more points about seven tenths of the way out. Seven tenths is right — along the diagonal of the real square. Along the drawn one it is 54 mm off a circle two and a half metres across, and the drawn diagonal is the only diagonal on the paper.
The line every nosing is on
Nothing in a staircase points up the pitch. Every surface in it is level or vertical, and its picture has a vanishing point off the horizon all the same — belonging to the line the front edges of the treads lie on. That point is not free: it is collinear with the travel point and the vertical point, and the angle it makes says the rise-to-run the builder chose.
Named alongside it
The objects these essays reach for when they reach for this one.
HorizonIncidenceVanishing pointConditioningCross ratiosingle-view metrologyDyadic rationalForeshorteningGround planeHarmonic conjugatePicture planeProjective invariance