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. As a result, landmasses such as Greenland, Antarctica, Canada and Russia appear far larger than they actually are relative to landmasses near the equator, such as Central Africa. History There is some controversy over the origins of the Mercator. German polymath Erhard Etzlaub engraved miniature "compass maps" (about 10×8 cm) of Europe and parts of Africa that spanned latitudes 0°–67° to allow adjustment of hi

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Fast Projection Onto Convex Smooth Constraints

Andreas Krause, Ilnura Usmanova

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on projection problems where the constraints are smooth and the number of constraints is significantly smaller than the dimension. The runtime of existing approaches to solving such problems is either cubic in the dimension or polynomial in the inverse of the target accuracy. Conversely, we propose a simple and efficient primal-dual approach, with a runtime that scales only linearly with the dimension, and only logarithmically in the inverse of the target accuracy. We empirically demonstrate its performance, and compare it with standard baselines.

PMLR2021

6. MEMS based color-VGA micro-projector system

Nicolas Abelé, Thierry Barras, Laurent Fabre, Maher Kayal, Fabrizio Lo Conte, Didier Raboud

This paper presents a complete portable laser-based projection system using twofold of one dimensional magnetic actuated MEMS linear scanning micro-mirrors. Dedicated high speed electronics was developed to drive the MEMS, detect the mirror scanning position at any time and synchronize the two mirrors and the laser pulsation. The achieved projection system head is 4.5 cm3 and is able to project colorful static images and videos (50 fps) with projection size of 50 cm diagonal at 50 cm distance with VGA (640×480 px) resolution.

Elsevier Science, Reg Sales Off, Customer Support Dept, 655 Ave Of The Americas, New York, Ny 10010 Usa2010

Micro-beamer based on MEMS micro-mirrors and laser light source

Nicolas Abelé, Laurent Fabre, Maher Kayal, Fabrizio Lo Conte, Christophe Winter

This paper presents a complete portable laser-based projection system using two one-dimensional magnetic actuated MEMS linear scanning micro-mirrors. Dedicated high speed electronics was developed to drive the MEMS, detect the mirror scanning position at any time and synchronize the two mirrors and the laser pulsation. The achieved projection system head is 3 cm3 and is able to project static images and videos with projection size of 50 cm diagonal at 50 cm distance with 32x32 px resolution, the resolution is only limited by current optical setup. The circuit building blocks itself can project image with resolution up to QVGA (320x240 px), suitable for information display applications. © 2009.

Elsevier Science, Reg Sales Off, Customer Support Dept, 655 Ave Of The Americas, New York, Ny 10010 Usa2009

CIVIL-308: Rock mechanics

Les étudiants comprennent le comportement mécanique de la roche intacte, des joints et des massifs rocheux et savent déterminer les facteurs influençant un projet. Ils savent utiliser les méthodes appropriées pour analyser et dimensionner l'excavation et le soutènement des ouvrages souterrains.

ENV-340: Fundamentals of satellite positioning

Bases des références géodésiques, principe de mesure utilisé en localisation par satellites et de l'estimation de la qualité de positions GNSS (Global Navigation Satellites Systems).

ENV-140: Fundamentals of geomatics

Bases de la géomatique pour les ingénieurs civil et en environnement. Présentation des méthodes d'acquisition, de gestion et de représentation des géodonnées. Apprentissage pratique avec des méthodes topométriques et d'imagerie du territoire.

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 expr

Latitude

In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° a

Circle of latitude

A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line. Circles of l