Projections of straight lines pdf

Other projections show great circle routes as straight lines, making it easy to figure out the shortest distance between two places. Pseudoconic projections are projections with parallels which are circular arcs with common central points. 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 line measures 80mm long and inclined at 30 to h. The projections of the images under of intersecting segments are straight lines through the. Assume the line to be located in each of the four quadrants by turns. Mar 14, 2020 projections of straight lines ppt, engineering drawing, semester mechanical engineering notes edurev is made by best teachers of mechanical engineering. The end a is 12 mm in front of the vp and 15 mm above hp. An analytical introduction to descriptive geometry mechanical. Hence, in monges projection, a straight line is represented by a pair of projections p,p.

Projection property of chromaticity coordinates fact. Find tho true lengths of the lines, the true angle between them and the distance between a and c. 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. Projections of straight lines pdf book manual free download. The times projection was developed by moir in 1965 for bartholomew. Engineering graphics projections of a straight line.

The projections of a line measures 80mmin the top viewand 70 mminthe front view. The straight lines crossing at right angles of this map projection make it useful for navigation, but it distorts the size of areas away from the equator. A line ab 25mm is parallel to the vp and perpendicular to the hp. Projections of straight line when inclined to both hp and vp. Parallels are straight lines increasing in separation with distance from the. 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. Since the projection is from the centre of the sphere, a gnomonic map can represent less.

Projection of straight lines and planes first angle brainkart. Visible lines, hidden lines, and centerlines often coincide on a drawing and you have to decide which lines to show. Oct 06, 2014 projections of straight line when inclined to both hp and vp example3. Lambert azimuthal equalarea equal area polar aspect. Projections by presentation of a metric property would include equidistant, conformal, gnomonic, equal area, and compromise projections. Distances are true only along the great circle the line of tangency for this projection, or along two lines parallel to it. Thus projection of a straight line is the foundation of engineering drawing. 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. Projection of straight lines free download as pdf file. Sometimes used with gnomonic map on which any straight line is on a great circle and shows shortest path between two points. 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. 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.

Some projections, like the mercator above, show loxodromes as straight lines. Engineering graphics 1st yr projection of points and lines. A trajectory when moving along a straight line for some time t. 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. Draw the projections of the following straight lines. Planisphaerium by ptolemy is the oldest surviving document that describes it. These projections account for area, shape, direction, bearing, distance, and scale. A thick continuous line is used for visible edges and outlines.

All books are in clear copy here, and all files are secure so dont worry about it. To draw the projections of a straight line located at different positions with respect to the vp and the hp. A straight line may have different orientations in space well be positioning this line in different ways. Examples of pseudoconic projections include bonne, which is an equalarea map projection. Make a straight line prediction of future demand 4.

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. However, it is easy to see that the line in the xyplane corresponding to the. Projections of straight linesdefinition of straight line. Associated examining board the plan and elevation of two straight lines are given in fig 7. In standard presentation, these map the central meridian and parallels as straight lines.

Read online projections of straight lines book pdf free download link book now. Distances, directions, areas, and shapes are fairly accurate within 15. It is a modified galls stereographic, except times has curved meridians. Then decide the view which will give us the true length of the line and true inclination. Projection of straight lines ii free download as powerpoint presentation. Front views of the two end points of a straight line, when joined, give the front view of the straight line. Page 4 engo 421 map projections lecture notes on map projections engo 421. Revolving or moving straight lines in different ways obtains these surfaces and planes. The maps are not constrained to rectangles or discs. Lines and planes in r3 a line in r3 is determined by a point a. We know that the equation of a line which cuts the yaxis i. 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. The mid point of theline is 45 mmin front ofvpand 35 mm above hp. This is the reason the mercator projection was invented.

Now the straight line is the great circle, and the curved one is the loxodrome. Pdf the determination and projection of an oblique line by means of the cartesian coordinates x, y, z of its ends, without the straight line. Great circles transform to straight lines via the gnomonic projection. A straight line is the shortest distancebetween two points. Scribd is the worlds largest social reading and publishing site. The general recommendation are that thick lines are twice as thick as thin lines.

The end a is 12 mm in front of the vp and 15 mm above. 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 that is it may be parallel or inclined to. Linear regression nds a line of best t based on minimizing the sum of squared errors.

The projection of the line segment joining points px 1, y 1, z 1 and qx 2, y 2, z 2. Straight line locus of a point, which moves linearly the shortest distance between any two given points. The gnomonic projection is illustrated in figure 4. Engineering graphics projection of points and lines. Projection of straight lines, situated in first quadrant only, inclined to both horizontal and vertical planes location of traces only. Successfully representing a plane on your stereonet will therefore require you to draw a line. Parallel to one plane and perpendicular to the other. Other meridians are curves or possibly straight from pole to equator, regularly spaced along parallels.

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. Projection of straight lines in engineering graphics pdf in engineering drawing practice two principal planes are used to get the. Unlike conic projections, the meridian is not constrained to be a straight line. A map projection is transverse or in transverse aspect if the appearance of the graticule image is. 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. You can get this from a straight line on a mercator projection. Line projections by projection of the points specifying the line ab, a. Projection of straight lines ii line geometry angle. Projections of straight lines straight line it is the shortest distance between two given points. Projections of straight lines ppt, engineering drawing. Hence, the projections of a straight line may be drawn by joining the.

When informally fitting a line, you want to find a line for. Page 3 projections of straight lines projections of straight lines definition of straight line. Draw the projections of the line if it is parallel to the vp and inclined at 30 to the hp. Different surfaces and planes form the configuration or shape of any object. Conic in standard presentation, conic or conical projections map meridians as straight lines, and parallels as arcs of circles. 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. Up to the late 18th century the mercator and stereographic projections were treated as completely unrelated. Line ab 75mm long makes 45 0 inclination with vp while its fv makes 55. 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. Projection of lines free download as powerpoint presentation. 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. Projections of straight lines pdf book manual free. The navigator must know the different types of chart projections and the principles of their constructions, so that the chart projection.

Hence, when a line is parallel to a plane, its projection on the plane is equal to its true. Nov 03, 2014 top views of two end points of a straight line, when joined, give the top view of the straight line. Top views of two end points of a straight line, when joined, give the top view of the straight line. These projections also have radial symmetry in the scales and hence in the distortions. Projection of straight lines pdf projecting the image of an object to the plane of projection is known as. Straight line depreciation is the most commonly used and easiest method for allocating depreciation of an asset. A straight line is the shortest distance between two points. Projection of straight lines and planes first angle.

Skew lines two straight lines in space are said to be skew lines, if they are neither parallel nor intersecting. Other projections show great circle routes as straight lines, making it easy to figure out the shortest distance between two. Point a is 35mm above the hp and 20mm in front of the vp. Since there are only two straight lines on the stereonet, its likely that the line representing your plane will be a curve as well. Nov 12, 2016 in this tutorial, the object is a straight line. Many map projections can then be grouped by a particular developable surface. The simplest position a straight line occupies in a space is, it is parallel to both v. The sphere and the plane touch at the tangent point. Remember how the strike and dip of a plane are simply the trend of the. The term planisphere is still used to refer to such charts. The straight line connecting red and blue is referred to as line of purples.

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. Projection of straight lines line geometry angle scribd. Since meridians lines of longitude and the equator are great circles, they are always shown as straight lines on a gnomonic map. The above position resulting in straight line as a top view and front view. If line is in 1 st quadrant draw its projections and find its inclination with hp. 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.

Graphics projection of straight lines free download as pdf file. Tips for projection of straight linesiiinclined to both. On other projections straight lines are not rhumb lines. There are two models for creating different map projections. Projections of a straight line introduction the shortest distance between any two points is called a straight line. This document is highly rated by mechanical engineering students and has been viewed 3270 times. Great circle on a spherical earth, a great circle is the shortest distance between two locations. Download projections of straight lines book pdf free download link or read online here in pdf.

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. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Sep 11, 2007 tips for projection of straight lines iiinclined to both planes. Projections of straight line when inclined to both hp and. Projection of lines a straight line is the shortest distance between two points. These lines are the same as in the mercator above, but the projection changes their. 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. Here is an example problem for drawing the orthographic views for a straight line when inclined to both principal planes. The projections of a straight line are obtained by joining the top and front views of. The midpoint of a straight line ab 90mm long is 60mm above hp and 50mm in front of vp. Proof given a straight line, either it cuts the yaxis, or is parallel to or coincident with it. The stereographic projection was known to hipparchus, ptolemy and probably earlier to the egyptians.

A straight line 55 mm long makes an angle of 30 deg to the hp and 45 deg to the vp. For any other position first assume the given line parallel to both the planes. Thus a straight line is the basic conceptual figure using which any object like a machine component or a structural element is represented. A point t lies on a line p if its horizontal projection lies on the horizontal projection of the. Straight lines in x,y,zspace project to straight lines in x,ychromaticity space. The shortest distance between any two points is called a straight line. It was originally known as the planisphere projection.

Light paths in three different categories orthographic, stereographic, and gnomonic can also be used. In engineering drawing practice two principal planes are used to get the. 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. A thin line is used for hatching, leader lines, short centre lines, dimensions and projections.

A great circle is a straight line on a gnomonic projection. Point in the first quadrant point p is 40 mm in front of vp, 50 mm above hp, 30 mm in front of left profile. Any straight line on the map is a rhumb line line of constant direction. 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.

Projection of straight lines in engineering graphics pdf. 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. Show that the geodesics on a sphere are exactly the great circles by looking at straight lines on better and. One of its most important uses was the representation of celestial charts.