Lecture

Perspective: Introduction and Definitions

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 introduction and definitions related to perspective in descriptive geometry. It explains the representation of shadows, projections, and the essential role of the observer's position. The lecture delves into methods like axonometry and Honge's method, emphasizing the concept of parallel and orthogonal projections. It also discusses the construction of images using radial methods and the importance of the principal point in orthogonal projections. The instructor demonstrates how to project objects onto a plane and the significance of the observer's eye as the center of projection. Various techniques, such as central projection and perspective, are explored to achieve a representation closer to human vision.

Official source

Related concepts (16)

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.

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.

Mercator projection

The Mercator projection (mərˈkeɪtər) is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles.

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.

Related lectures (49)

Shape from Texture

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

True Sizes: Folding Method in Descriptive Geometry

Explains the folding method in descriptive geometry to determine true sizes of segments and distances between points.

Geometric Projections: Orthogonal and Monge Projections

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

Physics 1: Harmonic Oscillator and Spherical Coordinates

Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.

Mechanical Construction I: Views and Projections