UNIT 2 PROJECTION OF LINES. 1. End A of a line AB is 15mm above HP & 20mm in front of VP while its end B is 50mm above HP and 75mm in front of VP. Projections of a Point – in 1st quadrant. 6. Lines – Objective & Types. 7. Simple Cases of Lines. 8. Lines inclined to one plane. 9. Lines inclined to both planes. Lecture 7. Projection of Lines and. 2. Projection of Lines and. Projection of Planes. Indian Institute of Technology Guwahati. Guwahati –
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PROJECTIONS OF STRAIGHT. LINES. STRAIGHT LINE. It is the shortest distance between two given points. Thus, the two ends of a straight line are points. Projection of points and straight lines located in the first quadrant – examples. 1. Orthographic projection-when the projectors are perpendicular to the plane of. Ans) As per rule, just draw lines parallel to x- y above and below at given distances from HP and VP. b) (i) ┴ to HP, 20 In front of VP, one end 15 above HP .
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Gnomonic projection pdf All parallels are ellipses, parabolas or hyperbolas, except for the Equator and the poles.
This kind of projection is made as if a sheet of paper had been laid on a point on Earth s surface, often one of the poles. Orthographic Projection is a way of drawing an 3D object from different. The gnomonic projection is the most commonly used map projection system for long-range strategic direction finding plotting and analysis.
The concept of gnomonic projection requires some explanation. An extensive list is given at the end of the Introduction C hapter in Snyder.
Scale increases perpendicular to the radii toward the periphery. The significant property of this projection is that all great circles are straight lines. No truncations.
Mercator Projection vs. These projections can also be equal area, conformal or equidistant. AssmA,cr A single, direct, and self-contained demonstration is given of the important self-indexing characteristic of the gnomonic projection. Every projection has its own set of advantages and disadvantages. Adam Taylor The most common way of getting around this problem is to use a Mercator projection.
The centre of projectiou is always designated by C, the foot of the bqplot. For these reasons, gnomonic projections are not used for day to day navigation and plotting, and should be regarded as an aid in voyage planning.
That is, the plane is normally placed above the north or south pole. This projection is often used by navigators to gauge The Gnomonic projection is a planar perspective projection viewed from the center of the globe. Hamilton Preface These notes are laid out with the Intention that this booklet will serve as a notebook for the student as well as providing him with most The Techniques of Astral Projection By Dr.
Cylindrical projection preserves area Mercator Projection vs. Here just a few will be given. Every map projection distorts some aspect of the spatial information when it is placed on a piece of paper.
Before you do either proof, you may want to clarify in your own mind what a circle on the surface of a sphere is. Chapter 7: Map projections 79 An ideal map projection retains all these graticule characteristics through the translation to the map.
What Is the Planar Projection? Home Math Calculus A planar projection is simply a map projection that hypothetically projects the Earth onto a tangent or secant plane; while any point on the planet can be used, a planar projection will generally take one of the poles as the point from which its projection is done.
This page was last edited on 28 November , at The following table lists a representative sample of the map projections supported by the IBM Informix spatial data types. See how the ellipses plotted on the gnomonic projection shown above vary in both size and shape, but are all oriented toward the center of the projection.
By default, the projection pole is placed at the center of the map data set that is to be projections, and other lines, on the vertical plane are represented by lines of dots. Douglas M. It maps points on a great circle to a straight line. Much has been written about map projections, yet people still find this subject to be one of the most bewildering aspects of map use. A great circle is the most direct path between two locations across the surface of the globe.
The following algorithm for an ellipsoidal gnomonic is a direct perspective from the geocenter through the ellipsoid onto the tangential plane via ECEF, topocentric coordinates and a little matrix algebra.
Such projections are necessary to create maps.
In this paper,the gnomonic formula from the earth ellipsoid to the surface of projection is derived by double projection method,the three important characterictics and application of the Ellipsoidal Gnomonic Projection are described.
We will outline two proofs of the fact that stereographic projection preserves circles, one algebraic and one geometric. A cylindrical projection does a fairly decent job of representing the entire globe, especially when you compare with conic projections which are good for representing continents.
They appear below. Its origin goes back to the old Greeks who used it for star maps almost years ago. The gnomonic chart became popular with the publication by Hugh Godfray in of two polar gnomonic charts covering the greater part of the world, one for the northern and the other for the southern hemisphere.
Hradllek and A. Gnomonic charts are usually used for the Polar Regions, while Mercator charts are usually used for the remaining areas on earth. Many people readily admit that they don't under-stand map projections.
The gnomonic map projection in the image is centered on the North Pole with meridians radiating out as straight lines This is a perspective projection from the center of the globe on a plane tangent at the center point, which is a pole in the common polar aspect, but can be any point.
The projection is neither equal-area nor conformal. Such projection looking at a solid from its center is called a gnomonic projection. We project the cuboctahedron from its center to a two-dimensional picture plane Figure 1c. Gnomonic Projection An explanation of the gnomonic projection of the sphere; and of such points of astronomy as are most necessary in the use of astronomical maps: being a description of the construction and use of the larger and smaller maps of the stars; as also of the six maps of the earth script plots this projection.
Baker B. It is particularly useful when plotting across great expanses The Gnomonic projection is a planar perspective projection viewed from the A geographic transformations pdf file which contains lists of supported geographic and PDF A gnomonic projection is one of the oldest mappings of a sphere to a plane.
The gnomonic projection Bridges Conference Proceedings Gnomonic Projection A gnomonic projection of the earth is derived by projecting the surface of the globe, from its center, upon a planar surface. We have left the text as it was printed, including Map Projections Part I One of the most important aspects of mapping is the map projection A map projection is any method of representing the surface of a sphere or other shape on a flat surface The 3-D earth is transformed to a 2-D flat surface by use of a geometric form, such as a: o Plane o Cylinder o Cone It can also be derived mathematically An explanation of the gnomonic projection of the sphere: and of such points of astronomy as are most necessary in the use of astronomical maps: being a description of the construction and use of the larger and smaller maps of the stars; as also of the six maps of the earth.
But the ideal map projection can never be achieved and if a projection is designed to guarantee a particular characteristic as true, others on it necessarily will be distorted.
No approximations. A mercator projection is defined as a projection of a map of the world onto a cylinder in such a way that all the parallels of Projected coordinate systems, map projections, parameters, and linear units of measure Current as of ArcGIS version 9. Directions from a central point to all other points are maintained accurately in azimuthal projections also known as zenithal or true-direction projections.
You can also see Project Templates.
Clynch I. The Gnomonic map projection displays all great circles as straight lines. Gnomonic Chart. The gnomonic, stereographic, and orthographic are perspective Cylindrical Projection Advantages and Disadvantages. Files are available under licenses specified on their description page.
Projection Of Lines: Department of Mechanical Engineering
A plane, projected onto which is the same as intersecting another plane will be a straight line, so great circles are straight lines on gnomonic projections. It is neither equal-area or conformal. The gnomonic projection is a nonconformal map projection obtained by projecting points or on the surface of sphere from a sphere's center to point in a plane that is tangent to a point Coxeter , p. All dimensions less than 1 should have a leading zero.
Such projections display all great circles as straight lines, resulting in any line segment on a gnomonic map showing the shortest route between the segment's two endpoints. The mapmaker must select the one best suited to the needs, reducing distortion of the most important The main disadvantages of the gnomomic projection are that courses, direction and distance can not be readily measured. Figure 8. Many different CRS are used to describe geographic data.
Its base is on the HP.
Now your simple diagram is over. So apex should not touch the XY line. Draw the corresponding Top view of that elevation by projection lines.
Draw the projection of a hexagonal prism whose one rectangular faces size is 25mm x 65mm resting on HP on one of its base corners. Such that the other extreme corner is 30mm above HP with the axis parallel to VP.
Hint: draw a hexagonal prism of side 25mm and axis 65mm long, it rests on HP on one of its base corners. Draw a simple diagram with two base edges are parallel to VP. Next redraw that front view with one base corner on HP.
Then the other top corner in that edge is 30mm above HP, take distance 30mm above HP and maark that point. Now the axis is parallel to VP and inclined to HP. Draw the plan top view with the projection lines. An equilateral triangular prism 20mm side of base and 50mm long rests with one of its shorter edges on HP such that the rectangular face containing the edge on which the prism rests is inclined at 30 degree to HP.
The shorter edge resting on HP is perpendicular to VP. Hint: draw a simple diagram with one base edge is perpendicular to VP in your right side , i.
A square prism of base side 35mm and axis length 60mm lies on the HP on one of its longer edge with its faces equally inclined to the HP. Draw its projections when its axis is inclined at 30 degree to VP. Hint: draw the simple diagram that its longer edge is rest on HP and its rectangular faces equally inclined to HP, i. Next redraw the plan top view that its axis is inclined at 30 degree to VP.
A pentagonal pyramid of base of side 30mm and axis 65mm has one of its slant faces on VP and the edge of the base contained by that face is inclined at 45 degree to HP.
Hint: draw the simple position that one slant face is on the VP, i. Next redraw the front view, now the edge of the base contained face in VP is inclined at 45 degree to HP. Draw the top view plan by projection lines. A pentagonal prism side of base 30mm and altitude 60mm is resting on one of the corners of its base on the HP.
The longer edge containing that corner is inclined at an angle of 45 degree to the HP and the vertical plane containing that edge and the axis are inclined at an angle of 30 degree to the VP.
Draw the projections.A thick continuous line is used for visible edges and outlines.
Embed Size px. Consider suitable scale..
Department of Mechanical Engineering
Start on. Next redraw the plan top view that its axis is inclined at 30 degree to VP. Like this presentation? A pentagonal pyramid of base of side 30mm and axis 65mm has one of its slant faces on VP and the edge of the base contained by that face is inclined at 45 degree to HP.
Then the other top corner in that edge is 30mm above HP, take distance 30mm above HP and maark that point. Eren Tutar. This is also VT of line.
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