7.7 The four shapes — Throwcast Manual

A lens is one of four castings. Two of them are the same part hung different ways round, so picking those cards reveals a segment for the handedness — a card each would have been four cards for one lens.

The lens-shape cards with Front picked — Figure 7.7a **Front** — a straight barrel off the front panel, the light leaving at its tip. Every ordinary zoom and prime, and the shape to pick when nothing about the machine turns the beam. It is asked for a distance column, a Tele column if the lens zooms, and optionally where the image can sit.

The cards with L-shaped picked, showing the side segment — Figure 7.7b **L-shaped** — two sections at 90°: forward off the panel, then out to a side. Picking it reveals Light leaves by, four ways to hang one part: the left, the right, up or down. Its two legs are typed, and they are the authority for the geometry — the fit contributes the throw ratio and a cross-check. It is the one shape asked nothing about the vertical, its vertical being its own arm.

The cards with Rear fold picked, showing the folds segment — Figure 7.7c **Rear fold** — three sections at 90°: forward, up past the lid, then back over the cabinet, so the light leaves the far end and flies back over the machine it came out of. Folds chooses up over the lid or down under the base. All three legs are typed; the glass sits at leg 1 minus leg 3 from the front face, which is why this family is not *also* asked where its lens is.

The cards with Ultra-short-throw picked — Figure 7.7d **Ultra-short-throw** — a mirror inside throws from a point no drawing carries, which is exactly the point the wizard exists to solve. Whether it is welded into the body or bolted onto a lens mount is read from the machine, not asked: the two are printed from different conventions, and they get different columns.

What each is asked for follows from the sheets it is transcribed from — and a column a family could never fill is one it is never shown:

Table 7.2 What the third step offers, by shape.
Shape	Typed sections	Columns it gets
Front	None — the barrel is what the fit solves.	Distance, Tele, and the image-position pair.
L-shaped	Leg 1 mount → elbow, leg 2 elbow → glass, with its own datum.	Distance and Tele, measured to the near face, the lens tip or the far face.
Rear fold	Three legs — forward, up past the lid, back over the cabinet.	Distance, Tele, image position.
Ultra-short-throw, welded in	The barrel that gets drawn.	Distance, Tele, Drop and Plate → datum.
Ultra-short-throw, bolted on	Barrel (front face → throw point) and Head (past it to the end).	Distance and image position. No Tele — every lens of this kind is a prime — and no Drop.

Where sections are typed they are the authority, not a hint: the casting is what you typed, the beam is derived from it, and the rows contribute the throw ratio, the zoom walk and a cross-check. Where the rows put the throw point somewhere the legs do not, the disagreement is reported in millimetres rather than resolved silently in either direction.

Why a fixed-lens machine is offered only two

A machine whose lens is welded in gets Front and Ultra-short-throw — no elbow, no rear fold. Those are lenses, not bodies: parts that bolt to a lens mount, which is why they come off by construction. Both bundled catalogues agree — 98 bodies carry a welded-in lens and not one of them turns its light, while all 17 right-angle entries are separate lenses. Offering the card there would offer a machine nobody builds, and picking it would silently yaw the beam 90° into a wall. A layout the four cards cannot express is still typed by hand into the Mounting rows.