Projections of straight lines pdf

It was originally known as the planisphere projection. The shortest distance between any two points is called a straight line. Projection of straight lines and planes first angle. These projections also have radial symmetry in the scales and hence in the distortions. A thick continuous line is used for visible edges and outlines.

Great circle on a spherical earth, a great circle is the shortest distance between two locations. Projection of straight lines in engineering graphics pdf. The line measures 80mm long and inclined at 30 to h. A map projection is transverse or in transverse aspect if the appearance of the graticule image is.

A straight line is the shortest distance between two points. Engineering graphics projections of a straight line. Projection of straight lines ii line geometry angle. Nov 12, 2016 in this tutorial, the object is a straight line. The end a is 12 mm in front of the vp and 15 mm above. Pseudoconic projections are projections with parallels which are circular arcs with common central points. A great circle is a straight line on a gnomonic projection. Point a is 35mm above the hp and 20mm in front of the vp. However, it is easy to see that the line in the xyplane corresponding to the. The simplest position a straight line occupies in a space is, it is parallel to both v.

Up to the late 18th century the mercator and stereographic projections were treated as completely unrelated. Show that the geodesics on a sphere are exactly the great circles by looking at straight lines on better and. Projections of straight line when inclined to both hp and vp. Linear regression nds a line of best t based on minimizing the sum of squared errors.

Chart projections a chart projection is a way to project the earths surface, which is spherical, onto paper, which is flat. From tj the midpoint of a straight line ab is 60mm above h. Graphics projection of straight lines free download as pdf file. Lines and planes in r3 a line in r3 is determined by a point a. The stereographic projection was known to hipparchus, ptolemy and probably earlier to the egyptians. Straight line depreciation is the most commonly used and easiest method for allocating depreciation of an asset. The sphere and the plane touch at the tangent point. Projection of straight lines in engineering graphics pdf in engineering drawing practice two principal planes are used to get the. Oct 06, 2014 projections of straight line when inclined to both hp and vp example3. These projections account for area, shape, direction, bearing, distance, and scale. Lambert azimuthal equalarea equal area polar aspect.

Line projections by projection of the points specifying the line ab, a. Light paths in three different categories orthographic, stereographic, and gnomonic can also be used. The projections of a straight line in various positions in the first quadrant are grouped based on its orientation with reference to the vertical and horizontal planes. A straight line is the shortest distancebetween two points. All books are in clear copy here, and all files are secure so dont worry about it. Distances are true only along the great circle the line of tangency for this projection, or along two lines parallel to it. Projections of straight lines pdf book manual free download. Straight line locus of a point, which moves linearly the shortest distance between any two given points. Engineering graphics 1st yr projection of points and lines.

One of its most important uses was the representation of celestial charts. Line ab 75mm long makes 45 0 inclination with vp while its fv makes 55. When informally fitting a line, you want to find a line for. Projection of straight lines, situated in first quadrant only, inclined to both horizontal and vertical planes location of traces only. Kotsakis objectives in these noteswe develop a body of theory to understand and analyse the distortion properties of maps that underlie different map projection algorithms. Planisphaerium by ptolemy is the oldest surviving document that describes it. The end a is 12 mm in front of the vp and 15 mm above hp. The mercator and stereographic projections, and many in between. A straight line may have different orientations in space well be positioning this line in different ways. These lines are the same as in the mercator above, but the projection changes their. A line ab 25mm is parallel to the vp and perpendicular to the hp. We know that the equation of a line which cuts the yaxis i. Page 3 projections of straight lines projections of straight lines definition of straight line. They make air and ship navigation easy, because you just have to draw a straight line, point your ship in that direction, and start sailing.

The projections of a line measures 80mmin the top viewand 70 mminthe front view. Other meridians are curves or possibly straight from pole to equator, regularly spaced along parallels. Now the straight line is the great circle, and the curved one is the loxodrome. Associated examining board the plan and elevation of two straight lines are given in fig 7.

Parallel to one plane and perpendicular to the other. A straight line 55 mm long makes an angle of 30 deg to the hp and 45 deg to the vp. Skew lines two straight lines in space are said to be skew lines, if they are neither parallel nor intersecting. Projection of straight lines ii free download as powerpoint presentation.

Page 4 engo 421 map projections lecture notes on map projections engo 421. Adjust straight line projection for seasonality to get a seasonalized forecast unfortunately, as we will see, we cant just throw all the data into linear regression and see what comes out. Some projections, like the mercator above, show loxodromes as straight lines. Examples of pseudoconic projections include bonne, which is an equalarea map projection. A thin line is used for hatching, leader lines, short centre lines, dimensions and projections.

Thus projection of a straight line is the foundation of engineering drawing. Hence, when a line is parallel to a plane, its projection on the plane is equal to its true. Projection of straight lines and planes first angle brainkart. Map projections tn 6 a map is a representation of all or part of the earth drawn on a flat surface at a specific scale. Maps were devised because they are much easier to use, store, and transport than globes, and they facilitated the development of much larger scaled representations than was the case with a globe. Assume the line to be located in each of the four quadrants by turns. The projection of the line segment joining points px 1, y 1, z 1 and qx 2, y 2, z 2. To draw the projections of a straight line located at different positions with respect to the vp and the hp. Great circles transform to straight lines via the gnomonic projection. Many map projections can then be grouped by a particular developable surface. The maps are not constrained to rectangles or discs. Parallels are straight lines increasing in separation with distance from the. Nov 03, 2014 top views of two end points of a straight line, when joined, give the top view of the straight line.

Other projections show great circle routes as straight lines, making it easy to figure out the shortest distance between two places. Determination of true length and true inclinations of straight lines from the projections not involving traces projection of plane surfaces like rectangle, square, pentagon, hexagon, circle surfaces inclined to one reference plane. The mid point of theline is 45 mmin front ofvpand 35 mm above hp. In standard presentation, these map the central meridian and parallels as straight lines. The projections of a straight line are obtained by joining the top and front views of. A straight line ab of 40 mm length has one of its ends a, at 10 mm from the hp and 15 mm from the vp.

Projection property of chromaticity coordinates fact. Read online projections of straight lines book pdf free download link book now. The straight line connecting red and blue is referred to as line of purples. Draw the projections of the following straight lines.

This document is highly rated by mechanical engineering students and has been viewed 3270 times. Location of a line the location of a line in projection quadrants is described by specifying the distances of its end points from the vp, hp and pp. A point t lies on a line p if its horizontal projection lies on the horizontal projection of the. Projection of straight lines pdf projecting the image of an object to the plane of projection is known as. Projections of a straight line introduction the shortest distance between any two points is called a straight line.

Aug 06, 2019 the main features of azimuthal map projections are straight meridian lines, radiating out from a central point, parallels that are circular around the central point, and equidistant parallel spacing. The navigator must know the different types of chart projections and the principles of their constructions, so that the chart projection. The projections of the images under of intersecting segments are straight lines through the. Projection of straight lines free download as pdf file. Since there are only two straight lines on the stereonet, its likely that the line representing your plane will be a curve as well. Download projections of straight lines book pdf free download link or read online here in pdf. Projections of straight lines ppt, engineering drawing, semester mechanical engineering notes edurev notes for mechanical engineering is made by best teachers who have written some of the best books of mechanical engineering.

The stereographic projection is a marvellous tool to understand the pencils of coaxial circles and many aspects of the relation between the spherical geometry, the euclidean af. Hence, the projections of a straight line may be drawn by joining the. Projection of lines a straight line is the shortest distance between two points. An analytical introduction to descriptive geometry mechanical. Projections of straight lines ppt, engineering drawing. Revolving or moving straight lines in different ways obtains these surfaces and planes. The times projection was developed by moir in 1965 for bartholomew. The gnomonic projection is illustrated in figure 4.

Proof given a straight line, either it cuts the yaxis, or is parallel to or coincident with it. This kind of map can be made to show as a straight line the shortest distance between any two preselected points along the selected great circle. The above position resulting in straight line as a top view and front view. Here is an example problem for drawing the orthographic views for a straight line when inclined to both principal planes. Conic in standard presentation, conic or conical projections map meridians as straight lines, and parallels as arcs of circles. A visible line always takes precedence and covers up a centerline or hidden line when they fall over on top of each other in a view. There are two models for creating different map projections. Unlike conic projections, the meridian is not constrained to be a straight line. Top views of two end points of a straight line, when joined, give the top view of the straight line. You can get this from a straight line on a mercator projection. Tips for projection of straight linesiiinclined to both. Sometimes used with gnomonic map on which any straight line is on a great circle and shows shortest path between two points. Since meridians lines of longitude and the equator are great circles, they are always shown as straight lines on a gnomonic map. Sep 11, 2007 tips for projection of straight lines iiinclined to both planes.

Projections of straight lines pdf book manual free. The term planisphere is still used to refer to such charts. Different surfaces and planes form the configuration or shape of any object. Any straight line on the map is a rhumb line line of constant direction. Orthogonal projection of a straight line if a straight line p is not a ray of projection not perpendicular to either projection plane, then its horizontal and vertical projections are lines p and p. The midpoint of a straight line ab 90mm long is 60mm above hp and 50mm in front of vp.

Successfully representing a plane on your stereonet will therefore require you to draw a line. Projection of lines free download as powerpoint presentation. Engineering graphics projection of points and lines. Draw the projections of the line if it is parallel to the vp and inclined at 30 to the hp. Make a straight line prediction of future demand 4. Projections of straight line when inclined to both hp and. This is the reason the mercator projection was invented. Since the projection is from the centre of the sphere, a gnomonic map can represent less. Projection of straight lines line geometry angle scribd. The general recommendation are that thick lines are twice as thick as thin lines. Visible lines, hidden lines, and centerlines often coincide on a drawing and you have to decide which lines to show.

A line that describes the relationship between a dependent variable and an independent variable can be used to make predictions of the value of the dependent variable given a value of the independent variable. Then decide the view which will give us the true length of the line and true inclination. Projections by presentation of a metric property would include equidistant, conformal, gnomonic, equal area, and compromise projections. It is a modified galls stereographic, except times has curved meridians. Projections of straight lines straight line it is the shortest distance between two given points. If line is in 1 st quadrant draw its projections and find its inclination with hp. Equal areasa map projection is equal area if every part, as well as the whole, has the same area as the corresponding part on the earth, at the same reduced scale. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Thus a straight line is the basic conceptual figure using which any object like a machine component or a structural element is represented. Front views of the two end points of a straight line, when joined, give the front view of the straight line. Projections of straight linesdefinition of straight line. Remember how the strike and dip of a plane are simply the trend of the. In engineering drawing practice two principal planes are used to get the.

Azimuthal projections have the property that directions from a central point are preserved and therefore great circles through the central point are represented by straight lines on the map. Straight lines in x,y,zspace project to straight lines in x,ychromaticity space. Directions along a rhumb line are true between any two points on map, but a rhumb line is usually not the shortest distance between points. A trajectory when moving along a straight line for some time t. The image of a point on the sphere is the intersection of the line through the point and the center of the sphere with the image plane. Scribd is the worlds largest social reading and publishing site. Hence, in monges projection, a straight line is represented by a pair of projections p,p. Other projections show great circle routes as straight lines, making it easy to figure out the shortest distance between two. For any other position first assume the given line parallel to both the planes. Find tho true lengths of the lines, the true angle between them and the distance between a and c. A straight line may have different orientations in space well be positioning this line in different ways that is it may be parallel or inclined to.