**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Parallel projection

Summary

In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane, known as the projection plane or , where the rays, known as lines of sight or projection lines, are parallel to each other. It is a basic tool in descriptive geometry. The projection is called orthographic if the rays are perpendicular (orthogonal) to the image plane, and oblique or skew if they are not.
A parallel projection is a particular case of projection in mathematics and graphical projection in technical drawing. Parallel projections can be seen as the limit of a central or perspective projection, in which the rays pass through a fixed point called the center or viewpoint, as this point is moved towards infinity. Put differently, a parallel projection corresponds to a perspective projection with an infinite focal length (the distance between the lens and the focal point in photography) or "zoom". Further, in parallel projections, lines that are parallel in three-dimensional space remain parallel in the two-dimensionally projected image.
A perspective projection of an object is often considered more realistic than a parallel projection, since it more closely resembles human vision and photography. However, parallel projections are popular in technical applications, since the parallelism of an object's lines and faces is preserved, and direct measurements can be taken from the image. Among parallel projections, orthographic projections are seen as the most realistic, and are commonly used by engineers. On the other hand, certain types of oblique projections (for instance cavalier projection, military projection) are very simple to implement, and are used to create quick and informal pictorials of objects.
The term parallel projection is used in the literature to describe both the procedure itself (a mathematical mapping function) as well as the resulting image produced by the procedure.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (33)

Related people (7)

Related concepts (5)

Related courses (17)

Related MOOCs (9)

Related units (1)

Related lectures (45)

Architectural drawing

An architectural drawing or architect's drawing is a technical drawing of a building (or building project) that falls within the definition of architecture. Architectural drawings are used by architects and others for a number of purposes: to develop a design idea into a coherent proposal, to communicate ideas and concepts, to convince clients of the merits of a design, to assist a building contractor to construct it based on design intent, as a record of the design and planned development, or to make a record of a building that already exists.

Axonometric projection

Axonometric projection is a type of orthographic projection used for creating a pictorial drawing of an object, where the object is rotated around one or more of its axes to reveal multiple sides. "Axonometry" means "to measure along the axes". In German literature, axonometry is based on Pohlke's theorem, such that the scope of axonometric projection could encompass every type of parallel projection, including not only orthographic projection (and multiview projection), but also oblique projection.

Descriptive geometry

Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. The theoretical basis for descriptive geometry is provided by planar geometric projections. The earliest known publication on the technique was "Underweysung der Messung mit dem Zirckel und Richtscheyt", published in Linien, Nuremberg: 1525, by Albrecht Dürer.

AR-211: Stereotomy

En histoire de l'architecture, la stéréotomie est l'art de concevoir et fabriquer des volumes complexes en pierre et des assemblages en bois.
Ce cours propose une réinterprétation de la stéréotomie

ME-107: Mechanical construction II (for MT)

Le cours de ME-107 vise à l'acquisition d'une solide culture technique de base en vue d'être capable de traiter des cas concrets de construction mécanique, via une revue des concepts, composants, et m

ME-102: Mechanical construction II (for ME)

Le cours de ME-102 vise à l'acquisition d'une solide culture technique de base en vue d'être capable de traiter des cas concrets de construction mécanique, via une revue des concepts, composants, et m

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 1)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Algebra (part 2)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Orthogonal Projection: Vector Decomposition

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

Orthogonal Families and Linear Combinations

Explores orthogonal families, vector orthogonality, and linear combinations in vector spaces.

Jérôme Baudry, Ion-Gabriel Mihailescu

Our contribution will propose a new approach for engaging with scientific instruments inspired by a recent exhibition which we have designed and organized. Inverting the current trope of presenting history through many objects, the exhibition weaved togeth ...

2023Stephan Brunner, Justin Richard Ball

Non-adiabatic electron response leads to significant changes in ion temperature gradient (ITG) eigenmodes, leading, in particular, to fine-structures that are significantly extended along the magnetic field lines at corresponding mode rational surfaces (MR ...

We have developed a pictorial multi-item scale, called P-SUS (Pictorial System Usability Scale), which aims to measure the perceived usability of mobile devices. The scale is based on the established verbal usability questionnaire SUS (System Usability Sca ...