Outline — where it appears
Named by 5 essays across 4 fields — each of them below, with the objects they name alongside it.
One picture of a ball
The outline of a ball in a photograph fixes the cone of rays that graze it, so the cone's axis is the direction of the ball's centre and its half-angle is the arcsine of radius over distance — both exactly, and neither of them separately. A ball a hundred and thirty-seven times larger, a hundred and thirty-seven times further away, draws the identical conic. And the drawn ellipse's own centre is not the image of the ball's.
The ball a drawing does not draw round
An orthographic drawing of a sphere is a circle wherever the sphere is, and its centre is the image of the sphere's centre, exactly. A cavalier oblique drawing of the same sphere is an ellipse of aspect exactly √2 — and the drawing office reaches for a circle template. One formula covers both and the camera as well, and only the camera moves the centre.
Facing the reader is not being reachable
A face turns toward the eye or it does not, and that is a dot product any reader can compute. Whether the eye’s rays actually land on it is a different question with a different answer — on a seating rake, three faces of ten that face the reader receive nothing, and they are 27 per cent of the facing area. On a corner the same test loses nothing at all, which is what makes the gap occlusion rather than arithmetic.
Two outlines are two curves
The whole method of multiview drawing is the transfer line — a feature at a position in the front view is at the same position along that axis in the top view. On a flat-faced solid the feature is a vertex and the rule is exact. On a ball the two views draw two different great circles, meeting in exactly two points, and the transfer line joins places that are √2 radii apart.
A curved surface made of straight lines
A hyperboloid of one sheet carries two families of exactly straight lines, so a photograph of a cooling tower is full of straight lines bounding nothing flat — 28 of them here, drawn to 2.3e-13 px of straightness against a parallel of the same surface that bows 120 pixels. Both families' directions satisfy one asymptotic equation, so their vanishing points lie on one conic in the picture and not on two, to 1.6e-12 px with no fitting anywhere.
Named alongside it
The objects these essays reach for when they reach for this one.
QuadricConicContour generatorDemonstrationcentre of projectionDrawing systemOrthographicAffine mapAnamorphosisAngular sizeAxis scaleCalibration