Lecture

General Axonometry: Descriptive Geometry

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the fundamentals of axonometry in descriptive geometry, including the representation of objects in 3D space on a 2D plane. Topics include different types of projections, such as isometric and oblique, as well as the principles of orthographic projection. The instructor explains how to represent objects with different magnitudes and angles, emphasizing the importance of accurate measurements and precise calculations. Additionally, the lecture delves into the concept of image transformation and the relationship between pre-images and images in geometric transformations.

Official source

Related concepts (14)

3D projection

A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. 3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element.

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.

Orthographic projection

Orthographic projection (also orthogonal projection and 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.

Map projection

In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent.

Parallel projection

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.

Related lectures (63)

Shape from Texture

Explores recovering surface orientation from image texture under different projections and the use of deep learning for normal prediction.

Geometric Projections: Orthogonal and Monge Projections

Covers orthogonal and Monge projections in descriptive geometry, focusing on geometric properties and visualization techniques.

Technical Drawing: Fundamentals and Applications

Covers the basics of technical drawing, including projections, standardized norms, and challenges in incomplete drawings.

Descriptive Geometry: Concepts and Exercises

Covers fundamental concepts and exercises in Descriptive Geometry, focusing on spatial problem-solving techniques and relative line positions.

True Sizes: Folding Method in Descriptive Geometry