Concept

Outline — where it appears

The drawn boundary of a solid in a picture, which is the image of the curve where the surface turns away from the eye. For a quadric it is a conic computable in one line, and it says nothing whatever about which points of the surface produced it.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

the eyecorrect from 9 cm, at 160 mm wideoutlines agree to 6e-12 px

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.

metrology · ballrecovery
orthographicaspect 1.0000cavalieraspect 1.4142a camera, 37° off axisaspect 1.2593correct from 7 cm, at 160 mm widecentres 4e-14 / 3e-13 / 2.17 px

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.

parallel · parallelquadric
frontierthe transfer joins points 1.414 R apartone ball, two outlinesmeeting in exactly two points

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.

parallel · parallelquadric

Named alongside it

The objects these essays reach for when they reach for this one.

DemonstrationQuadriccentre of projectionConicDrawing systemOrthographicAffine mapAngular sizeAxis scaleCalibrationContour generatorFrontier point

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