A PICTORIAL VIEW SHOWS AN OBJECT'S THREE DIMENSIONS IN A SINGLE DRAWING. The classification is by what the projectors do: PROJECTION ├── PARALLEL (projectors parallel; no convergence) │ ├── ORTHOGRAPHIC (projectors ⊥ to the plane) │ │ ├── MULTIVIEW — the front/top/side set; NOT pictorial │ │ └── AXONOMETRIC — object tilted; pictorial │ │ ├── ISOMETRIC — 3 equal angles, 1 scale │ │ ├── DIMETRIC — 2 equal, 2 scales │ │ └── TRIMETRIC — none equal, 3 scales │ └── OBLIQUE (projectors at an ANGLE to the plane) │ ├── CAVALIER — depth at FULL scale │ └── CABINET — depth at HALF scale └── PERSPECTIVE (projectors CONVERGE at the eye) ├── ONE-POINT — 1 vanishing point ├── TWO-POINT — 2 vanishing points └── THREE-POINT — 3 vanishing points THE ORGANISING QUESTION: WHAT IS SACRIFICED? MULTIVIEW sacrifices immediate comprehension and keeps every true size — for manufacturing. AXONOMETRIC sacrifices true shape on all faces and keeps parallelism and measurability along axes — for assembly. OBLIQUE sacrifices realism and keeps ONE face in true shape — for objects dominated by one face. PERSPECTIVE sacrifices measurability entirely and keeps realism — for presentation. ── OBLIQUE PROJECTION ────────────────────────────────────── THE PROJECTORS ARE PARALLEL BUT STRIKE THE PLANE AT AN ANGLE. The distinctive result: ONE FACE — the front — IS PLACED PARALLEL TO THE PLANE AND THEREFORE APPEARS IN ITS TRUE SIZE AND TRUE SHAPE. That is what oblique offers and axonometric cannot: circles on the front face STAY CIRCLES and can be drawn with a compass, and angles on it are TRUE. For an object whose interest is concentrated on one face — a flange, a dial, a plate with holes — this is a large practical saving. THE RECEDING AXIS is drawn at 30°, 45° or 60° to the horizontal (45° is usual), and the two variants differ only in the scale used along it: CAVALIER — depth drawn at FULL SCALE (1.0). Geometrically consistent, and every edge is true length. BUT IT LOOKS BADLY DISTORTED: the object appears far too deep, because the eye expects distant edges to shorten and they do not. CABINET — depth drawn at HALF SCALE (0.5). Not geometrically "correct", but IT LOOKS RIGHT. The name comes from the furniture industry, which drew cabinets this way. THE CHOICE IS AN HONEST ADMISSION THAT A DRAWING IS FOR A HUMAN EYE: cabinet oblique deliberately introduces an error to cancel a perceptual one. RULES: put the face with the most detail, the most curves, or the greatest irregularity ON THE FRONT — that is the whole advantage of the method, and placing a plain face there wastes it. Put the longest dimension along the front too. ── PERSPECTIVE PROJECTION ────────────────────────────────── PROJECTORS CONVERGE AT THE STATION POINT (the eye), so PARALLEL EDGES CONVERGE TO VANISHING POINTS ON THE HORIZON. THIS IS HOW THE EYE AND THE CAMERA ACTUALLY SEE. ONE-POINT PERSPECTIVE — one face parallel to the picture plane; edges going into the distance meet at a SINGLE vanishing point. The classic view down a corridor, a railway, or a street. Used for interiors. TWO-POINT — the object rotated so no face is parallel to the picture plane; vertical edges stay vertical, and the two sets of horizontal edges converge to TWO vanishing points on the horizon. THE MOST USED IN ARCHITECTURE, because it looks like standing at the corner of a building. THREE-POINT — the object also tilted, so VERTICALS CONVERGE too, to a third vanishing point above or below. Used for tall buildings viewed from the ground or from the air — it produces the "looking up at a skyscraper" effect. THE VOCABULARY: PICTURE PLANE (the paper), STATION POINT (the eye), HORIZON LINE (at eye level), GROUND LINE, VANISHING POINT. THE HORIZON IS ALWAYS AT THE VIEWER'S EYE LEVEL, which is why raising the horizon in a drawing makes the viewer feel they are looking down from above. THE FATAL LIMITATION FOR ENGINEERING: NO DIMENSION IN A PERSPECTIVE VIEW IS TRUE, AND TWO EQUAL EDGES DRAW AT DIFFERENT LENGTHS DEPENDING ON DISTANCE. IT CANNOT BE MEASURED, SO IT CANNOT BE MANUFACTURED FROM.

THE COMPLETE COMPARISON — the table this topic exists to produce: MULTIVIEW ISOMETRIC OBLIQUE PERSPECTIVE (ortho) (axono.) (cabinet) ───────────────────────────────────────────────────────────────── projectors parallel, parallel, PARALLEL, CONVERGE ⊥ to plane ⊥, object at an tilted ANGLE faces in true shape EACH view NONE THE FRONT NONE shows one FACE parallel edges parallel parallel parallel CONVERGE circles circles in ellipses CIRCLES on ellipses their view everywhere the front measurable? FULLY along axes front face NO fully realism none moderate low HIGHEST ease of drawing easy easy EASIEST hardest primary use MANUFACTURE assembly, single-face PRESENTATION, instruction objects architecture ───────────────────────────────────────────────────────────────── HOW TO CHOOSE, stated as decisions: NEED TRUE DIMENSIONS FOR MANUFACTURE? → orthographic multiview. Nothing else will do. NEED SOMEONE TO UNDERSTAND THE SHAPE FAST? → isometric. IS THE OBJECT DOMINATED BY ONE FACE, especially with circles on it? → oblique (cabinet). SHOWING A BUILDING TO A CLIENT? → perspective. THE PRACTICE THAT MOST DRAWINGS FOLLOW: ORTHOGRAPHIC VIEWS CARRY THE SPECIFICATION, AND A SMALL PICTORIAL VIEW IN THE CORNER CARRIES THE UNDERSTANDING. They are complementary rather than competing, and a good drawing sheet uses both. A NOTE ON CAD, which has changed the economics of this topic: Historically, choosing a pictorial method was a decision about DRAWING LABOUR — perspective was avoided because constructing it by hand is slow. In a 3D CAD system the model exists once and ANY projection is generated by changing a setting, so the cost argument has vanished. WHAT HAS NOT CHANGED IS THE GEOMETRY AND THEREFORE THE MEANING: a perspective view produced by CAD is still unmeasurable, and an isometric one is still 22.5% oversize if drawn at full scale. The engineer must still know which view can be trusted for what — which is precisely why the topic is still examined.