Amogh N P
✦ In loving memory of Amogh N P — Architect · Designer · Visionary ✦
An Indian student drafting plan, front and side elevation views.
Lesson III25ARS123 · Architectural Graphics I

Orthographic Projection & Solids

How plan, elevation and section are really made.

≈ 40 min

Every plan, section and elevation is an orthographic projection — and there is a precise geometry beneath it, worked out by Gaspard Monge over two centuries ago. Learn that geometry and the drawings stop being conventions to memorise and become something you can reason about.

Learning objectives

By the end of this lesson, you will be able to — mapped to the course outcomes for Building Materials & Construction I:

1
CO3 · Understand

Explain orthographic projection and why three views fix an object.

2
CO3 · Understand

Distinguish first-angle from third-angle and place the views correctly.

3
CO3 · Apply

Project simple solids and find the true shape of a section.

4
CO3 · Apply

Develop the surface of a cone or prism into a flat pattern.

Multiview projection

The principle, and first vs third angle

This is the constructed theory beneath the freehand plans and sections you draw in Design Drawing. Select a topic.

Multiview projection

Parallel projectors strike the plane of projection at 90°, so faces parallel to the plane appear true. The three principal planes (horizontal, vertical, profile) give plan, front elevation and side elevation. One view fixes only two dimensions — you need three to be unambiguous.[1]

Three views describe one object the object front plan side Parallel projectors hit each plane at 90°. One view fixes two dimensions — you need three views to remove all ambiguity.
DiagramOne object projected into plan, front elevation and side elevation
Where the views land First-angle (India) frontL sideplan plan BELOW · left side on the RIGHT Third-angle (USA) frontL sideplan plan ABOVE · left side on the LEFT The most-muddled point in the course: in FIRST-angle the plan drops BELOW the front view; in third-angle it sits above.
DiagramView placement in first-angle versus third-angle projection — the point most people get backwards
Cutting and unfolding

Sections & development

A cutting plane reveals the interior and a true shape; unfolding a surface gives a flat pattern to cut and fold. Cones and cylinders develop exactly — a sphere never can.[2, 3]

Cut it open — the true shape of section AA true shape (hatched at 45°) Project the cut onto a plane parallel to the cutting plane to recover its true shape. Fill the cut with even 45° hatching.
DiagramA cutting plane through a solid and the true shape of the section, hatched at 45 degrees
Unrolling a surface (development) cone flat sector (radial-line method) Cones and cylinders are single-curved — they unroll without distortion. A sphere is double-curved: it cannot be flattened (only approximated), which is why every flat map distorts.
DiagramDeveloping a cone into a flat sector; a sphere cannot be developed without distortion
White geometric solid models — cube, prism, cone, pyramid, cylinder.
PhotoWhite geometric solid models — cube, prism, cone, pyramid, cylinder.
A sectional drawing with the cut hatched at 45°.
PhotoA sectional drawing with the cut hatched at 45°.
Flat development patterns of a cone and a pyramid, part-folded.
PhotoFlat development patterns of a cone and a pyramid, part-folded.
An Indian student drafting plan, front and side elevation views.
PhotoAn Indian student drafting plan, front and side elevation views.
Descriptive geometry

The geometry beneath it all

All of this rests on descriptive geometry, devised by Gaspard Monge (kept a French military secret, published 1799) to represent 3-D objects in 2-D by systematic projection. Its two core problems — the true length of a line and the true shape of a plane — are exactly what auxiliary views and sections recover. CAD did not replace it; it automated it.[4]

Check your understanding

Self-assessment

1. In FIRST-angle projection, the plan (top view) is placed:

2. The 'true shape' of a section is found by:

3. Which surface CANNOT be developed (flattened) without distortion?

In a nutshell

Recap

Orthographic projection: parallel projectors at 90°; three views remove ambiguity.
First-angle (India) puts the plan BELOW the front view; third-angle above.
Project solids by the axis position; get a section's true shape on a parallel plane.
Cones/cylinders develop exactly; spheres can't — it all rests on Monge's descriptive geometry.
The evidence

References & further reading

  1. [1]Multiview orthographic projection — principle, the four quadrants, first vs third angle, the symbol. https://en.wikipedia.org/wiki/Multiview_orthographic_projection
  2. [2]Projection and sections of solids; true shape of section; hatching. Brainkart. https://www.brainkart.com/article/Projection-of-Solids-and-Section-of-Solids_6520/
  3. [3]Developable surfaces — cylinders/cones develop; spheres cannot (Gaussian curvature). https://en.wikipedia.org/wiki/Developable_surface
  4. [4]Gaspard Monge and the origin of descriptive geometry (Géométrie descriptive, 1799). Britannica. https://www.britannica.com/biography/Gaspard-Monge-comte-de-Peluse

Further reading

  • Bhatt, N.D. (2014). Engineering Drawing — Plane and Solid Geometry (53rd ed.). Anand: Charotar — Orthographic Projection, Projection of Solids, Sections, Development.
  • Paré, E.G., Loving, R.O. & Hill, I.L. Descriptive Geometry. New York: Macmillan / Prentice Hall.
  • Monge, G. (1799). Géométrie descriptive. Paris — the founding text of the discipline.

Sources gathered and fact-checked June 2026. Published values vary by source, sample and method — treat as indicative and confirm against the cited standard before structural use.

Design Drawing — Sections, Elevations & Site PlansThe same views, drawn freehand for design communication.