Orthographic projection
form of parallel projection in which all the projection lines are orthogonal to the projection plane
Orthographic projection, or orthogonal projection (also analemma), is a means of representing three-dimensional objects in two dimensions. Orthographic projection is a form of parallel projection in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the projection plane.
The term orthographic sometimes means a technique in multiview projection in which principal axes or the planes of the subject are also parallel with the projection plane to create the primary views. If the principal planes or axes of an object in an orthographic projection are not parallel with the projection plane, the depiction is called axonometric or an auxiliary views. (Axonometric projection is synonymous with parallel projection.) Sub-types of primary views include plans, elevations, and sections; sub-types of auxiliary views include isometric, dimetric, and trimetric projections.
A lens that provides an orthographic projection is an object-space telecentric lens.
Geometry
A simple orthographic projection onto the plane z = 0 can be defined by the following matrix:
P
=
[
1
0
0
0
1
0
0
0
0
]
{\displaystyle P={\begin{bmatrix}1&0&0\\0&1&0\\0&0&0\\\end{bmatrix}}}
For each point v = (vx, vy, vz), the transformed point Pv would be
P
v
=
[
1
0
0
0
1
0
0
0
0
]
[
v
x
v
y
v
z
]
=
[
v
x
v
y
0
]
{\displaystyle Pv={\begin{bmatrix}1&0&0\\0&1&0\\0&0&0\\\end{bmatrix}}{\begin{bmatrix}v_{x}\\v_{y}\\v_{z}\end{bmatrix}}={\begin{bmatrix}v_{x}\\v_{y}\\0\end{bmatrix}}}
Often, it is more useful to use homogeneous coordinates. The transformation above can be represented for homogeneous coordinates as
P
=
[
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
]
{\displaystyle P={\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&0\\0&0&0&1\end{bmatrix}}}
For each homogeneous vector v = (vx, vy, vz, 1), the transformed vector Pv would be
P
v
=
[
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
]
[
v
x
v
y
v
z
1
]
=
[
v
x
v
y
0
1
]
{\displaystyle Pv={\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&0\\0&0&0&1\end{bmatrix}}{\begin{bmatrix}v_{x}\\v_{y}\\v_{z}\\1\end{bmatrix}}={\begin{bmatrix}v_{x}\\v_{y}\\0\\1\end{bmatrix}}}
In computer graphics, one of the most common matrices used for orthographic projection can be defined by a 6-tuple, (left, right, bottom, top, near, far), which defines the clipping planes. These planes form a box with the minimum corner at (left, bottom, -near) and the maximum corner at (right, top, -far).
“Orthographic projection” enters the record as form of parallel projection in which all the projection lines are orthogonal to the projection plane. Crown Archives preserves that source wording while asking what Orthographic, projection and form can confirm, complicate or overturn.
Why this record matters
“Orthographic projection” is worth following because a concise public description often conceals a longer documentary argument. Here, Orthographic, projection and form provides the most credible route into that argument.
The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Sep 25, 2026. The linked authority identifier is Q980329. None of the 0 selected statements returned an explicit reference.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Orthographic projection”, its source revision and the description used here.
- Expand the search: follow Orthographic projection primary sources, Orthographic projection archive and Orthographic research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Orthographic projection”?
- What terminology or title could unlock a more precise catalogue search?
- Which institution is responsible for the underlying evidence?
Search terms from this dossier
This entry incorporates text from “Orthographic projection” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.