Geometric and Engineering Drawing is an established text suitable for GCSE and basic engineering courses. This book aims to cover the whole range of subject. K. Morling. Graduate of the Institution of Mechanical Engineers. About ScienceDirect · Remote access · Shopping cart · Advertise. The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed.
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For all students and lecturers of basic engineering and technical drawing The new edition of this successful text describes all the geometric instructions and. GEOMETRICAL AND MECHANICAL ENGINEERING DRAWING. 35 Pages·· ENGINEERING MECHANICS AND DRAWING - Text Books Online. These understandings can come through studying and using this book. . 4 Geometric and Engineering Drawing Plain Scales There are two types of scale.
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Geothermal Reservoir Engineering, Second Edition. Solid Waste Engineering , Second Edition. If the oblique length has been scaled down, then the ordinates on the oblique lengths must be scaled down in the same proportions. Ordinate spacing reduced by oblique scale Figure 6.
The normal 6 mm ordinates are reduced to 3 mm on the oblique faces and the 3 mm ordi- nates are reduced to 1.
This must always be done in oblique projection in order to scale the distances between the ordi- nates on the oblique view to half those on the plane view.
The advantage of oblique projection over other pictorial projections is that circles drawn on the front face are not distorted. Unfortunately, examiners usually insist that circles are drawn on the oblique faces, as in Fig. However, if you are free of the influence of an examiner and wish to draw a component in oblique projection, it is obviously good sense to ensure that the face with the most circles or curves is the front face.
It is obvious that the drawing on the left is easier to draw than the one on the right. Oblique Projection 71 Exercise 6 All questions originally set in imperial units. Figure 1 shows two views of a small casting. Draw, full size, an oblique projection of the casting with face A towards you.
Figure 2 shows two views of a cast iron hinge block. Make an oblique drawing of this object, with face A towards you, omitting hidden detail. Figure 3 shows the outline of the body of a depth gauge. Make an oblique drawing, twice full size, of the body with corner A towards you. Draw, full size, an oblique projection of the car brake light switch shown in Fig.
It should be positioned so that it is resting on surface A, with the cylinder B towards you. Figure 5 shows two views of a holding-down clamp.
Draw the clamp, full size, in oblique projection with corner A towards you. Two views of a casting are shown in Fig. Two views of a machined block are shown in Fig. Use half-size measurements along the oblique lines. The curve CD is parabolic and D is the vertex of the curve.
Hidden detail need not be shown. Oxford Local Examinations see Chapter 11 for information not in Chapter 6. A special link for a mechanism has dimensions as shown in Fig. Radius curves may be sketched in and hidden details are to be omitted. Constructions To construct a figure, similar to another figure, having sides 75 the length of the given figure.
Three examples, using the same basic method, are shown in Fig. From P draw lines through all the corners of the figure. Extend the length of one of the lines from P to a corner, say PQ, in the ratio 7: The new length is PR. Beginning at R, draw the sides of the larger figure parallel to the sides of the orig- inal smaller figure.
This construction works equally well for reducing the size of a plane figure. Figure 7. These constructions are practical only if the figure which has to be enlarged or reduced has straight sides. If the outline is irregular, a different approach is needed. The change in size is determined by the two grids.
A grid of known size is drawn over the first face and then another grid, similar to the first and at the required scale, is drawn alongside. Both grids are marked off, from A to J and from 1 to 5 in this case, and the points where the irregular outlines cross the lines of the grid are transferred from one grid to the other. The closer together the lines of the grid, the greater the accuracy of the scaled copy.
It is sometimes necessary to enlarge or reduce a plane figure in one direction only. In this case, although the dimensions are changed, the proportions remain the same.
First produce CA and BA. Mark off the new dimensions along CA and BA pro- duced. Although this figure is more complicated than Fig. There is very little practical application of this type of construction these days. When plasterers produced flamboyant ceilings with complicated cornices, and car- penters had to make complex architraves and mouldings, this type of construction was often employed.
However, it is still a good exercise in plane geometry and does occasionally find an application. The enlarged or reduced figures produced in Figs. Usually this does not matter, particularly if the figure is for a template; it just has to be turned over. However, if it does matter, a construction simi- lar to that used in Fig. The curved part of the figure is divided into as many parts as is necessary to produce an accurate copy.
The rest of the construction should be self-explanatory. All the changes of shape so far have been dependent upon a known change of length of one or more of the sides. No consideration has been made of a specific change of area.
The ability to enlarge or reduce a given shape in terms of area has applications. If, for instance, fluid flowing in a pipe is divided into two smaller pipes of equal area, then the area of the larger pipe will be twice that of the two smaller ones. This does not mean, of course, that the dimensions of the larger pipe are twice that of the smaller ones.
Select a point P. This may be on a corner, or within the outline of the pentagon, or outside the outline although this is not shown because the construction is very large. Let A be a corner of the given pentagon. Join PA and produce it. Draw a semi-circle, centre P, radius PA. From P, drop a perpendicular to PA to meet the semi-circle in S. Mark off PR: PQ in the required ratio, in this case 2: Although Fig.
The construction is identi- cal to that used for Fig. PQ is 4: Note that if there is a circle or part circle in the outline, the position of its centre is plotted. From B, the apex of the triangle, drop a perpendicular to meet the base in F. Bisect FB. From A and C erect perpendiculars to meet the bisected line in D and E.
ADEC is the required rectangle. It should be obvious from the shading that the part of the triangle that is outside the rectangle is equal in area to that part of the rectangle that overlaps the triangle. Produce DC to meet the semi-circle in G. DG is one side of the square. For the construction of a square, given one of the sides, see Chapter 2.
This construction can be adapted to find the square root of a number. To construct a square equal in area to a given triangle Fig. First change the triangle into a rectangle of equivalent area and then change the rectangle into a square of equivalent area. Join CF.
Join CG. The quadrilateral ABCF now has the same area as the triangle GCF and the original five-sided figure has been reduced to a three-sided figure of the same area. GCF is the required triangle.
When this theorem is shown pictorially, it is usually illustrated by a triangle with squares drawn on the sides. This tends to be a little misleading since the theorem is valid for any similar plane figures Fig. This construction is particularly useful when you wish to find the size of a circle that has the equivalent area of two or more smaller circles added together.
To find the diameter of a circle that has the same area as two circles, 30 mm and 50 mm diameter Fig. Draw a line 30 mm long. From one end erect a perpendicular, 50 mm long. The hypotenuse of the triangle thus formed is the required diameter If you have to find the single equivalent diameter of more than two circles, reduce them in pairs until you have two, and then finally one left. BC Fig. To divide a polygon into a number of equal areas e.
This construction is very similar to that used for Fig. Proceed as for the triangle and complete as shown in Fig. Exercise 7 All questions originally set in imperial units. Figure 2 shows a sail for a model boat. Draw the figure, full size, and construct a similar shape with the side corresponding to AB 67 mm long. Also construct a similar but larger polygon so that the side corresponding with AB becomes Measure and state the lengths of the sides of the enlarged polygon.
Oxford Local Examinations 4. Make a copy of the plane figure shown in Fig. Enlarge your figure proportionally so that the base AB measures 88 mm. Oxford and Cambridge Schools Examinations Board 6. Cambridge Local Examinations 7. Construct, full size, the figure illustrated in Fig. Figure 5 shows a section through a length of moulding.
Draw an enlarged section so that the mm dimension becomes mm. Oxford Local Examinations see Chapter 11 for information not in Chapter 7. Figure 6 shows a shaped plate, of which DE is a quarter of an ellipse.
The shape is shown in Fig. Construct a regular hexagon having a distance between opposite sides of mm. Reduce this hexagon to a square of equal area. Measure and state the length of side of this square. Joint Matriculation Board A water main is supplied by two pipes of 75 mm and mm diameter.
It is required to replace the two pipes with one pipe which is large enough to carry the same volume of water. Part 1. Draw the two pipes and then, using a geometrical construction, draw the third pipe. Part 2. Draw a pipe equal in area to the sum of the three pipes. Southern Regional Examinations Board Three squares have side lengths of 25, Construct, without resorting to calculations, a single square equal in area to the three squares, and measure and state the length of its side. The inclusion of curves within the outline of a com- ponent may be for several reasons: This last reason applies particularly to those industries that manufac- ture articles to sell to the general public.
It is not enough these days to make vacuum cleaners, food mixers or ball-point pens functional and reliable. The designer uses circles and curves to smooth out and soften an outline. Blending is a topic that students often have difficulty in understanding and yet there are only a few ways in which lines and curves can be blended.
When construct- ing an outline that contains curves blending, do not worry about the point of contact of the curves; rather, be concerned with the positions of the centres of the curves. A curve will not blend properly with another curve or line unless the centre of the curve is correctly found. If the centre is found exactly, the curve is bound to blend exactly. To find the centre of an arc, radius r, which blends with two straight lines meeting at right angles Fig.
With centres B and C, radius r, draw two arcs to intersect in O. O is the required centre. This construction applies only if the angle is a right angle. To find the centre of an arc, radius r, which blends with two straight lines meeting at any angle Fig. Construct lines, parallel with the lines of the angle and distance r away, to inter- sect in O. To find the centre of an arc, radius r, which passes through a point P and blends with a straight line Fig.
Construct a line, parallel with the given line, distance r away. The centre must lie some- where along this line. With centre P, radius r, draw an arc to cut the parallel line in O. There are two possible centres, shown in Figs. Construct a line, parallel with the given line, distance R away.
With centre A, radius R — r1, draw an arc. With centre B, radius R — r2, draw an arc to intersect the first arc in O. These seven constructions will enable you to blend radii in all the conditions that you are likely to meet Figure 8.
The construction lines have been left off each successive stage for clarity but if you are answering a similar question during an examination, leave all the construc- tion lines showing. If you do not, the examiner may assume that you found the cen- tres by trial and error and you will lose the majority of the marks.
There are three more constructions that are included in the blending of lines and curves and these are shown below. Draw the centre line between the parallel lines. From a point A, drop a perpendicular to meet the centre line in O1.
With centre O1, radius O1A, draw an arc to meet the centre line in B. Produce AB to meet the other parallel line in C. From C erect a perpendicular to meet the centre line in O2.
With centre O1, radius r, draw an arc to meet the centre line in B. With centre O2, radius r, draw the arc BC. Join AB and divide into the required ratio, AC: Perpendicularly bisect AC to meet the perpendicular from A in O1. Perpendicularly bisect CB to meet the perpendicular from B in O2. Figure 1 shows an exhaust pipe gasket.
Draw the given view full size and show any con- structions used in making your drawing. Do not dimension your drawing. Figure 2 is an elevation of the turning handle of a can opener. Draw this view, twice full size, showing clearly the method of establishing the centres of the arcs. Figure 3 shows the outline of an electric lamp. Important — Construction lines must be visible, showing clearly how you obtained the cen- tres of the arcs and the exact positions of the junctions between arcs and straight lines.
Draw the shape, full size. Line AB is to be increased to 28 mm. Construct a scale and using this scale draw the left half or right half of the shape, increasing all other dimensions proportionally. Figure 4 shows a garden hoe. Draw this given view, full size, and show any construction lines used in making the drawing. Do not dimension the drawing. Figure 5 shows one half of a pair of pliers.
Draw, full size, a front elevation looking from A. Your constructions for finding the centres of the arcs must be shown. Figure 6 shows the design for the profile of a sea wall. Measure in metres the dimensions A, B, C and D and insert these on your drawing. Constructions for obtaining the centres of the radii must be clearly shown. Details of a spanner for a hexagonal nut are shown in Fig.
Draw this outline showing clearly all constructions. The end of the lever for a safety valve is shown in Fig. Draw this view, showing clearly all construction lines. Draw, to a scale of 2: Oxford Local Examinations 57 35 6. You may not have been aware of it, but you have met loci many times before. One of the most common loci is that of a point that moves so that its distance from another fixed point remains constant: Another locus that you know is that of a point that moves so that its distance from a line remains constant: Problems on loci can take several different forms.
One important practical appli- cation is finding the path traced out by points on mechanisms. This may be done simply to see if there is sufficient clearance around a mechanism or, with further knowledge beyond the scope of this book, to determine the velocity and hence the forces acting upon a component. There are very few rules to learn about loci; it is mainly a subject for common sense. Take, for instance, the case of the man who was too lazy to put wedges under his ladder.
The inevitable happened and the ladder slipped. The path that the feet of the man took is shown in Fig. The top of the ladder slips from T to T9.
The motion of the top of the ladder has been stopped at T1, T2, T3, etc. The points are joined together with a smooth curve. It is interesting to note that the man hits the ground at right angles assuming that he remains on the ladder. The resulting jar often causes serious injury and is one of the reasons for using chocks.
Another simple example is the locus of the end of a bureau door stay Fig. This type of stay is also often used on wardrobe doors. Its function is to allow the door to open to a certain point, and then to support the door in that position.
The stay, of course, has two ends and the locus on one end is easily found: The other end of the stay is allowed to slide through the pin but it is not allowed to move off it. As the end of the stay moves along the arc, its movement is stopped several times and the position of the other end of the stay is marked.
These points are joined together with a smooth curve. Obviously the designer of such a bureau would have to plot this locus before deciding the depth of the bureau. Pin Stay Hinge Bureau door Figure 9. Loci Loci of Mechanisms The bureau door stay is a very simple mechanism.
We now look at some of the loci that can be found on the moving parts of some machines. Definitions Velocity is speed in a given direction. It is a term usually reserved for inanimate objects; we talk about the muzzle velocity of a rifle or the escape velocity of a space probe.
When we use the word speed we refer only to the rate of motion. When we use the word velocity we refer to the rate of motion and the direction of the motion.
Linear velocity is velocity along a straight line a linear graph is a straight line. Angular velocity is movement through a certain angle in a certain time. It makes no allowance for distance travelled.
If, as in Fig. The velocity, as distinct from the angular velocity, will be much greater of course. P Q Figure 9. The piston travels in a straight line; the crank rotates. The connecting rod, which links these two, follows a path that is somewhere in between these two, the exact shape being dependent on the point of the rod being considered.
Figure 9. The movement of the piston is also continuous between the top and bottom of its travel. As with most machines that have cranks, the best policy is to plot the position of the crank in 12 equally spaced positions. The piston must always lie on the centre line and, of course, the connecting rod cannot change its length.
It is therefore a simple matter to plot the position of the connecting rod for the 12 positions of the crank. This is best done with compasses or dividers. The mid-point of the connecting rod can then be marked with dividers and the points joined together with a smooth curve. Loci The direction of rotation of the crank is usually given in problems of this nature.
It may make no difference to plotting any of the loci, but it could make a tremen- dous difference to the functioning of the real machine: Trammels A trammel can consist of a piece of paper or a piece of card or even the edge of a set square. It must have a straight edge and you must be able to mark it with a pencil.
A trammel enables you to plot a locus more quickly than the method shown above. However, if you are intending to sit for examinations check that the examination rules allow you to use trammels. The length of the rod and the point are marked on a piece of paper. One end of the rod is constrained to travel around the crank circle and the other slides up and down the centre line of the slider. Move the trammel so that one end is always on the circle while the other end is always on the slider centre line, marking the required point as many times as necessary.
Join the points with a smooth curve. It is required to plot the locus of P, a point on the lower end of the link CD. This can only be done by plotting the locus of C, ignoring the link CD. Once this has been done, we can find the position of CD at any given moment, and hence the locus of point P. No construction lines are shown in Fig. This, in turn, would enable you to find 12 positions for C, and then 12 positions of the rod CD. Finally, this would lead to the 12 required positions of P.
Alternatively, the locus of C could have been plotted with a trammel that had the length of the link AB, and the position of C marked on it. Another trammel, with the length of the rod CD and the position of P marked on it, would have given the locus of P.
Loci Some Other Problems in Loci A locus is defined as the path traced out by a point that moves under given definite conditions. Three examples of loci are shown below where a point moves relative to another point or to lines. To plot the locus of a point P that moves so that its distance from a point S and a line XY is always the same Fig.
The first point to plot is the one that lies between S and the line. Since S is 20 mm from the line, and P is equidistant from both, this first point is 10 mm from both. If we now let the point P be 20 mm from S, it will lie somewhere on the circum- ference of a circle, centre S, radius 20 mm. Since the point is equidistant from the line, it must also lie on a line drawn parallel to XY and 20 mm away. The second point, then, is the intersection of the 20 mm radius arc and the parallel line.
The third point is at the intersection of an arc, radius 30 mm and centre S, and a line drawn parallel to XY and 30 mm away. The fourth point is 40 mm from both the line and the point S.
This may be contin- ued for as long as is required. The curve produced is a parabola. Since it is twice as far away from R as it is from S, this is done by propor- tional division of the line RS. If we now let P be 40 mm from R it must be 20 mm from S. Thus, the second posi- tion of P is at the intersection of an arc, centre R, radius 40 mm and another arc, centre S and radius 20 mm.
The third position of P is the intersection of arcs, radii 50 and 25 mm, centres R and S, respectively. This is continued for as long as necessary. In this case, at a point mm from R and 50 mm from S, the locus meets itself to form a circle. Loci To plot the locus of a point P that moves so that its distance from the circum- ference of two circles, centres O1 and O2 and radii 20 and 15 mm, respectively, is always in the ratio 2: Thus, divide the space between the two circumferences in the ratio 3: If we now let P be 10 mm from the circumference of the circle, centre O1, it will lie somewhere on a circle, centre O1, and radius 30 mm.
Thus, the second position of P is the intersection of two arcs, radii 30 and 30 mm, centres O1 and O2, respectively. The third position of P is the intersection of two arcs, radii 35 and The fourth position is at the intersection of arcs of 40 and 45 mm radii. This is continued for as long as is required. Exercise 9 All questions originally set in imperial units. Figure 1A shows a door stay as used on a wardrobe door. The door is shown in the fully open position. Draw, full size, the locus of end A of the stay as the door closes to the fully closed position.
The stay need only be shown diagrammatically as in Fig. Figure 2 shows a sketch of the working parts, and the working parts represented by lines, of a moped engine. Using the line diagram only, and drawing in single lines only, plot, full size, the locus of the point P for one full turn of the crank BC. Do not attempt to draw the detail shown in the sketch.
Show all construction. The trammel method must not be used. In Fig. The rod PB is connected to the crank at B and slides through the pivot D. Plot, to a scale 1 21 full size, the locus of P for one revolution of the crank. Roller 1 slides along slot AB while roller 2 slides along CD and back. Draw, full size, the locus of P, the end of the rod, for the complete movement of roller 1 from A to B.
As an experiment a very low gear has been fitted to a bicycle. This gear allows the bicycle to move forward 50 mm for every 15 degrees rotation of the crank and pedal. These details are shown in Fig. The first forward position has been shown on the drawing.
Figure 7 is a line diagram of a slotted link and crank of a shaping machine mechanism. The link AC is attached to a fixed point A about which it is free to move about the fixed point on the disc. The disc rotates about centre O. D is also free to slide along DE. When the disc rotates in the direction of the arrow, plot the locus of C, the locus of P on the link CD, and clearly show the full travel of B on AC. The guide A is allowed to rotate about its fixed point.
This locus is part of a recognised curve. Name the curve and the parts used in its construction. In the mechanism shown in Fig. BCDE is a rigid link. Plot the complete locus of E.
A rod AB 70 mm long rotates at a uniform rate about end A. Plot the path of a slider S, initially coincident with A, which slides along the rod, at a uniform rate, from A to B and back to A during one complete revolution of the rod. With a permanent base of mm, draw the locus of the vertices of all the triangles with a constant perimeter of mm.
Oxford and Cambridge Schools Examination Board Three circles lie in a plane in the positions shown in Fig. Draw the given figure and plot the locus of a point which moves so that it is always equidistant from the circumferences of circles A and B.
Plot also the locus of a point which moves in like manner between circles A and C. The drawing must show quite clearly the detailed outlines of all the faces and these outlines must be fully dimensioned.
If the object is very simple, this may be achieved with a freehand sketch. A less simple object could be drawn in either isomet- ric or oblique projections, although both these systems have their disadvantages.
Circles and curves are difficult to draw in either system and neither shows more than three sides of an object in any one view. Orthographic projection, because of its flexibility in allow- ing any number of views of the same object, has none of these drawbacks. Orthographic projection has two forms: Traditionally, British industry has used first angle while the United States of America and, more recently, the continental countries used the third angle system.
There is no doubt that British industry is rapidly changing to the third angle system and, although this will take some years to complete, third angle will eventually be the national and international standard of orthographic projection. Figure A plane is a perfectly flat surface. In this case one of the planes is horizontal and the other is vertical. The view looking on the top of the block is drawn directly above the block on the horizontal plane HP.
The view looking on the side of the block is drawn directly in line with the block on the vertical plane VP. If you now take away the stepped block and, imagining that the two planes are hinged, fold back the HP so that it lines up with the VP, you are left with two drawings of the block.
One is a view looking on the top of the block and this is directly above another view looking on the side of the block.
The same block is drawn in Fig. You still have a VP and a HP but they are arranged differently. The block is suspended between the two planes and the view of the top of the block is drawn on the HP and the view of the side is drawn on the VP.
Again, imagining that the planes are hinged, the HP is folded down so that the planes are in line. This results in the drawing of the side of the block being directly above the drawing of the top of the block compare this with the third angle drawings.
Standardization and disambiguation[ edit ] Engineering drawings specify requirements of a component or assembly which can be complicated. Standards provide rules for their specification and interpretation. Standardization also aids internationalization , because people from different countries who speak different languages can read the same engineering drawing, and interpret it the same way.
Media[ edit ] For centuries, until the post-World War II era, all engineering drawing was done manually by using pencil and pen on paper or other substrate e. Since the advent of computer-aided design CAD , engineering drawing has been done more and more in the electronic medium with each passing decade. Today most engineering drawing is done with CAD, but pencil and paper have not entirely disappeared. Some of the tools of manual drafting include pencils, pens and their ink, straightedges , T-squares , French curves , triangles, rulers , protractors , dividers , compasses , scales, erasers, and tacks or push pins.
Slide rules used to number among the supplies, too, but nowadays even manual drafting, when it occurs, benefits from a pocket calculator or its onscreen equivalent.
And of course the tools also include drawing boards drafting boards or tables. The English idiom "to go back to the drawing board", which is a figurative phrase meaning to rethink something altogether, was inspired by the literal act of discovering design errors during production and returning to a drawing board to revise the engineering drawing.
Drafting machines are devices that aid manual drafting by combining drawing boards, straightedges, pantographs , and other tools into one integrated drawing environment. CAD provides their virtual equivalents. Producing drawings usually involves creating an original that is then reproduced, generating multiple copies to be distributed to the shop floor, vendors, company archives, and so on. The classic reproduction methods involved blue and white appearances whether white-on-blue or blue-on-white , which is why engineering drawings were long called, and even today are still often called, " blueprints " or " bluelines ", even though those terms are anachronistic from a literal perspective, since most copies of engineering drawings today are made by more modern methods often inkjet or laser printing that yield black or multicolour lines on white paper.
The more generic term "print" is now in common usage in the U. In MBD, the information captured by the CAD software app is fed automatically into a CAM app computer-aided manufacturing , which with or without postprocessing apps creates code in other languages such as G-code to be executed by a CNC machine tool computer numerical control , 3D printer , or increasingly a hybrid machine tool that uses both.
Thus today it is often the case that the information travels from the mind of the designer into the manufactured component without having ever been codified by an engineering drawing. In MBD, the dataset , not a drawing, is the legal instrument. The term "technical data package" TDP is now used to refer to the complete package of information in one medium or another that communicates information from design to production such as 3D-model datasets, engineering drawings, engineering change orders ECOs , spec revisions and addenda, and so on.
However, even in the MBD era, where theoretically production could happen without any drawings or humans at all, it is still the case that drawings and humans are involved. These workers often use drawings in the course of their work that have been produced by rendering and plotting printing from the MBD dataset.
In these cases, the drawing is still a useful document, although legally it is classified as "for reference only", meaning that if any controversies or discrepancies arise, it is the MBD dataset, not the drawing, that governs. Systems of dimensioning and tolerancing[ edit ] Almost all engineering drawings except perhaps reference-only views or initial sketches communicate not only geometry shape and location but also dimensions and tolerances for those characteristics.
Several systems of dimensioning and tolerancing have evolved. The simplest dimensioning system just specifies distances between points such as an object's length or width, or hole center locations. Since the advent of well-developed interchangeable manufacture , these distances have been accompanied by tolerances of the plus-or-minus or min-and-max-limit types. Coordinate dimensioning involves defining all points, lines, planes, and profiles in terms of Cartesian coordinates, with a common origin.
Common features[ edit ] Drawings convey the following critical information: Geometry — the shape of the object; represented as views; how the object will look when it is viewed from various angles, such as front, top, side, etc.