Where This Spatter Came From ORIGIN

The scene

Both accuracies feed the bands below, so understating them is how a page comes to promise a precision it has not got. A stain read to a tenth of a millimetre is careful work with a scale in the photograph; half a millimetre is a quick measurement in the field, and it costs more than most people expect.

Walls

A wall is the vertical plane standing on the line between two corners, given as plan coordinates. Walk from the first corner to the second and the room is on your left. The heading printed beside each wall is the way a drop must have been going to strike it — if it points into the room rather than out of it, the corners are the wrong way round and the button puts it right. The floor is always there and needs no defining.

Stains

Seven numbers each: a name, which surface it is on, two coordinates, the width and the length of the ellipse in millimetres, and the direction of its long axis in degrees. On the floor the two coordinates are x and y and the direction is measured round from the x axis. On a wall they are the distance along from the first corner and the height above the floor, and the direction is measured from “along the wall” towards “up” — so a drop on its way down reads as a negative angle. In both cases the direction is the way the drop was going, which is the tail end of the stain pointing away from you.

What it comes to

The scene in plan: each stain as a dot with its long axis run backwards, the walls as heavy lines, the shaded box the spread of positions your stated reading accuracy allows, and the cross where they converge. The cross is a real answer. The height printed above it is a ceiling.

Stain by stain

The last column is the bound each stain gives on its own, and how far that bound moves when everything it depends on moves to the ends of its stated accuracy. Three separate things push it. A nearly round stain has an impact angle that is barely knowable, because the arcsin runs away as the width approaches the length. A steeply descending drop has a bound the tangent stretches out of usefulness. And the distance out is measured from the convergence, so the spread of the convergence moves every bound at once — which on a floor stain is the only way the long-axis reading reaches the height at all, since turning a floor stain’s axis changes neither its position nor the angle it was descending at. A stain can suffer from one of the three and not the others, which is why this is computed by moving the readings rather than read off a formula.

The working