Visual Plane — every picture states the point it is correct from Illustrated essays on perspective and drawing systems with the projection computed rather than constructed by hand: every figure is projected from a stated camera, states the viewing distance it is correct from, and the camera is recovered from the picture it drew. https://www.visualplane.xyz/ 2026-08-05T21:50:13.401Z What a projection destroys https://www.visualplane.xyz/essays/what-a-projection-destroys/ 2026-08-05T21:50:13.401Z A projection loses length, angle, area and the ratio in which a point divides a segment. Exactly one quantity comes through untouched, and almost everything that can be checked about a picture is checked with it — including, as it turns out, some things it cannot check at all. One, two and three point are one construction https://www.visualplane.xyz/essays/one-two-and-three-point/ 2026-08-05T21:50:13.401Z The names count how many vanishing points sit at a finite place in the picture, and the count is a fact about how the object is turned and the camera is aimed. Nothing about the method changes between them, and a vanishing point does not appear — it arrives from infinity. The point you have to stand at https://www.visualplane.xyz/essays/the-point-to-stand-at/ 2026-08-05T21:50:13.401Z A perspective picture is a projection through a centre, and scaling that centre's distance to the width the picture is actually shown at gives a distance in centimetres. Shown 160 mm wide, a 40° picture is correct from 22 cm and a 90° one from 8 cm. Nobody stands there, and that single fact explains most of what gets called distortion. A shadow is a second projection https://www.visualplane.xyz/essays/a-shadow-is-a-second-projection/ 2026-08-05T21:50:13.401Z 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. The cube that is a box https://www.visualplane.xyz/essays/the-cube-that-is-a-box/ 2026-08-05T21:50:13.401Z The two-point cube every book teaches has a step it supplies no construction for. Place the two far edges symmetrically and the drawing depicts a cube for free; place them eight points apart — a difference invisible on the page — and it depicts a box 1.4 times shallower than it is wide. Parallel projection is not primitive perspective https://www.visualplane.xyz/essays/parallel-projection-is-not-primitive/ 2026-08-05T21:50:13.401Z 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. Where parallel lines meet https://www.visualplane.xyz/essays/where-parallel-lines-meet/ 2026-08-05T21:50:13.401Z They meet at a point that is not in the plane, and the horizon is the line made of all such points. Treating that as bookkeeping misses what it buys — a vanishing point becomes an ordinary point of the picture, findable from the drawn lines, checkable, and enterable into any calculation the others are. The measuring point, and the step the method leaves out https://www.visualplane.xyz/essays/the-measuring-point/ 2026-08-05T21:50:13.401Z Laying out equal depths correctly needs a second vanishing point that most treatments never introduce — the one belonging to the diagonals. With it the construction lands on the projected divisions to eighty femtopixels. Without it, depth is placed by judgement and the drawing depicts something nobody chose. Wide angle is not distortion https://www.visualplane.xyz/essays/wide-angle-is-not-distortion/ 2026-08-05T21:50:13.401Z A wide lens stretches shapes at the edge of the frame by exactly 1/cos θ — 3% at 28° across, 41% at 90°. Every bit of that is what a correct rectilinear projection must do, and every bit of it disappears if the picture is viewed from the point it was made for. Nobody views it from there. What isometric actually means https://www.visualplane.xyz/essays/what-isometric-actually-means/ 2026-08-05T21:50:13.401Z The three axis scales are equal to each other. They are not equal to one. Every unit along every axis is drawn at 0.8165 of its true length, which is √(2/3), and a great deal of confusion about isometric drawing comes from the word promising something it does not deliver. Where shadows vanish https://www.visualplane.xyz/essays/where-shadows-vanish/ 2026-08-05T21:50:13.401Z 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. Dividing depth by eye https://www.visualplane.xyz/essays/dividing-depth-by-eye/ 2026-08-05T21:50:13.401Z Three methods for spacing a receding row, all of them taught, all of them wrong. Read back as distances, the best misplaces a post by 3.5 metres in a row that is supposed to be spaced 1.4. And the obvious way of checking them gives one of the three a perfect score. Recovering the camera from the picture it drew https://www.visualplane.xyz/essays/recovering-the-camera/ 2026-08-05T21:50:13.401Z Draw a box from a known camera, forget the camera, and get it back from the twelve drawn edges alone. Agreement to one part in 10¹⁵ is a statement about the geometry, because the only thing that crossed between the two halves was a list of line segments. The horizon is at eye level — if the picture plane is vertical https://www.visualplane.xyz/essays/the-horizon-at-eye-level/ 2026-08-05T21:50:13.401Z The horizon cuts every standing figure at the same fraction of its height however far away it is, which is the most immediately usable fact in the subject. It holds when the camera is level, and a twelve-degree tilt is enough to spread the fractions by more than a percentage point. Anamorphosis is only a viewpoint https://www.visualplane.xyz/essays/anamorphosis-is-only-a-viewpoint/ 2026-08-05T21:50:13.401Z 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. The eye taken to infinity https://www.visualplane.xyz/essays/the-eye-taken-to-infinity/ 2026-08-05T21:50:13.401Z 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. A mirror is a second camera https://www.visualplane.xyz/essays/a-mirror-is-a-second-camera/ 2026-08-05T21:50:13.401Z 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. The circle whose centre moves https://www.visualplane.xyz/essays/the-circle-whose-centre-moves/ 2026-08-05T21:50:13.401Z The image of a circle is an ellipse, and the image of the circle's centre is not the centre of that ellipse. The gap is 3 or 4% of the ellipse's width in an ordinary view — large enough to see, small enough to be dismissed as a slip by anyone not expecting it, and the reason drawn wheels look wrong. When the picture surface is not flat https://www.visualplane.xyz/essays/when-the-picture-surface-curves/ 2026-08-05T21:50:13.401Z 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.