Visual Plane
every picture states the point it is correct from
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The thread: One machine used twice

A shadow is a projection from the lamp. A reflection is the view from a camera on the far side of the mirror. A parallel drawing is a photograph from infinitely far away. Three subjects usually taught as three recipes are one operation with the centre moved.
correct from 26 cm, at 160 mm wide34° across Light and mirrors

A shadow is a second projection

The construction that puts a shadow on the ground is the construction that puts the scene on the picture plane, with the lamp where the eye was. Shadow drawing is taught as a separate set of recipes and it is one operation with the centre moved, which is why the same code draws both.

 elevationx 1.000y 1.000z 0.000cavalierx 1.000y 1.000z 1.000cabinetx 1.000y 1.000z 0.500isometricx 0.816y 0.816z 0.816dimetricx 0.943y 0.943z 0.471axis scales measured from the drawingall five preserve midpoints The other systems

Parallel projection is not primitive perspective

Isometric and oblique drawing are not what people used before they worked perspective out. They are a different answer to a different question, and the difference is one measurable quantity — a parallel projection preserves the ratio in which a point divides a segment, and a perspective projection destroys it by up to a quarter of the segment's length.

 horizonshadows meet at x = -58, off the frameon the horizon, as it must be Light and mirrors

Where shadows vanish

The shadows of parallel posts under the sun meet at a point, and that point must lie on the horizon. Under a lamp they meet at the lamp's foot instead. Both are checkable in any photograph, and a picture whose shadows fail the check was not lit by anything.

 eye, 74° offgrey: the word before the projectionblack: the same word, projected Where to stand

Anamorphosis is only a viewpoint

A smear on a wall that resolves into a skull when the viewer stands in one particular place off to the side. It is not a trick added to perspective — it is perspective, with the centre of projection put somewhere nobody would naturally stand, and it is the clearest demonstration there is that every picture has such a point.

 isometric — the limit2.5 m6 m20 m200 msame box, same drawn sizethe eye recedes The other systems

The eye taken to infinity

A parallel projection is a photograph from infinitely far away with the lens lengthened to match. That is not an analogy — it is the limit, it can be watched happening, and it explains why a long lens flattens a scene and why an isometric drawing has no viewing distance to state.

 grey: the reflectiontwo routes, agreeing to 0e+0 px after one flip Light and mirrors

A mirror is a second camera

Reflect the scene and photograph it, or reflect the camera and photograph the scene. The two routes disagree by 906 px and agree to 6 × 10⁻¹⁴ once one axis of the image is reversed — which is the whole of why a mirror is said to swap left and right, written down.

 flat picture plane — straight lines stay straightcylindrical picture surface — even stretch, bowed linesone scene, two picture surfacesneither is the distorted one Where to stand

When the picture surface is not flat

A flat picture plane keeps straight lines straight and stretches the edges without bound. A cylindrical one spreads the stretch evenly and bends every straight line that is not through the axis. Neither is the distorted one — they are answers to different questions, and the choice decides what a wide view can be.

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