Exam Structure for DCG
Section A: 4 short questions on the Core topics, 20 marks per question, marked out of your best 3. Attempt all four.
Section B: 3 long questions on the Core topics. 45 marks per question, marked out of your best two. Read all three, do the two you are most confident on, if you have time at the end of the exam then attempt the third.
Section C: This section has 5 optional areas on Applied Graphics but you will only be marked on two of these. The areas covered are Structural Forms and Geological Geometry. Do not waste time attempting another question in this section.
The exam is 3 hours long which allows for around 35 minutes for each of the long questions and another 35 minutes for all of the short questions in Section A.
Make sure your sets are fully equiped before the exam.
Core Topics
Orthographic and Auxiliary Projection
Most questions on the course are given in an orthographic (ele, plan and end ele). A lot of questions will need to have auxiliaries to solve them. Know how to do first and second auxiliaries. Auxiliaries will be used to get true lengths, dihedral angles, point views, etc
Solids in Contact
Know how to find points of contact in plan and elevation
How to rotate spheres, cones, cylinders to the side of an object, bring them down and find them in their correct position in plan.
Tracery - Given two solids that the new object touchs off but not the size of the new object. Use tracery to find the centrepoint.
Tangent Planes - You will be asked to get the traces of the tangent plane. This is solves by cones. If the plane is lying against the cone (tangential to it) then the plane has to have the same angle as the side of the cone. But the same angled cone over the other solid, get the projections in plan to get the Horizontal Trace and then find the Vertical Trace in elevation
Axonometric, Dimetric and Trimetric
Set up the axes as given in the question. Draw a level line, project and get the semi circle to allow you to set up the plan. Do similar for elevation or end elevation. Look at the 3D view given in the question to decide which elevation to draw and the direction the plan is drawn. If you get this wrong the object could end up facing in the wrong direction. Circles and curves are got by dividing up 60/30 and projecting the individual points to the middle to get the freehand curve
Perspective
Gettiing the plan drawn, finding the spectator, picture plane, ground line, horizon line and vanishing points will get you nearly half the marks in this question.
Join outer parts of plan to the spectator, bisect this angle to get the line of vision, go 90° to this through whatever point given in the question to get the picture plane.
Go parallel to the edges of the plan from the spectator till it hits the picture plane and project up 90° to the picture plane to the horizon line to give the vanishing points.
Heights can only be marked off when its touching off the piture plane. If it doesn't touch the picture plane then you need to continue the line/edge on till it does hit the PP, bring it up and mark the height off on that line, vanish it back to collect the point you were looking for.
Remember that all points have to go be joined from the plan to the spectator and brought up from where that its off the picture plane.
To get curves in perspective you need to divide up the circle/curve 60/30 and find the points individually
Auxiliary Vanishing Points are used for sloping surfaces in perspective (like a roof). The angle is set from the line going from the spectator parrallel to the edge of the plan that was used to get the vanishing points. This will give a height that is used for marking above or below the vanishing point (depending what is needed).
Conic Sections
Parabola - Eccentricity is equal to one which means the line of ecc. is always 45°.
Ellipse - Eccentricity is less than one so the line of ecc. is any angle less that 45°
Hyperbola - Eccentricity is greater than one so the line of ecc. is any angle greater than 45°
Eccentricity method is done the same way on all three sections. Ecc = PF/PD (See page 191)
Remember that 45° line from focus to the line of ecc. and straight down from there will give the vertex.
Know how to draw a tangent to a point on the curve and a point outside the curve for all threeDouble Hyberbola is drawn using a different method The transverse axis goes from vertex to vertex. Remember the rule PF1-PF2 = transverse axis.
Learn the properties common to all conics
Know how to get the centre of curvature for a point.
Solids cut by Oblique Plane
Set up the ele and plan. Draw the traces. Project up along the horizontal trace to get an auxiliary view showing the cutting plane. Use this view to find the points needed to finish the plan.
Rotate the points from the auxiliary to get the true shap of the cut surface out 90° from the plan
Get the traces of a plane by continuing on the edges in both plan and ele to find the traces.
Intersecting Planes
The coordinates are given in the sequence in, up, down.
To get the dihedral angle you first need the line of intersection, then look 90° to that to get its true length. Then look along the true length to get the dihedral angle.
To get the line of intersection you may have to take either one or two level lines to get points on that line of intersection. Take the level line in ele so that it goes across the two planes. Where it intersects the planes, drop the points down and find them in plan. Join them up according to the planes they are on and this will give two lines crossing in plan to give one point on the line of intersection.
Skew Lines
This is a follow on from intersecting planes but it only deals with two lines.
To get the line parallel to each other, you take a level line in ele, go parallel to the other line to give a point, drop that down and do the same in plan to give the strike line. This line is the angle of the auxiliary for getting the two lines parallel.
At this point a few different things can be asked, shortest horizontal distance, shortest perpendicular distance, etc.
Interpentration
On basic questions, intersection points can be got by using method like Limits, Radial Elements, Horizontal and Vertical sections.Questions like these generally tend to come up in the short questions.
Long questions tend to be in the form of auxiliary plan method. Draw what you can of the ele and plan. Project the auxiliary plan by taking distance from the xy line down to points in the plan. Label all the points in all three view. Remember there will be a set of points where the object starts to go into the other and also a set where the object comes out the other side. Take one of these at a time. Point that are not found on the edges may need to have a generator drawn for them in the auxiliary, find that generator in ele and then find the point on that generator.
Developments
Developments are the opening out of an 3D object to a flat 2D shape.
An envelopment is the opposite of a development, given the flat shape and you have to draw the 3D shape.
Applied Graphics
Structural Forms
This has three main parts, the hyperboloid of revolution, the hyperbolic paraboloid and the surface of translation piece.
Hyperboloid of Revolution - Know how to draw the curve in elevation by drawing the asymptote in plan and ele and finding the points from that , Know how to draw it if the top has some part cut off it and also if you are asked to get a true shape
Hyperbolic Paraboloid - Divide up the edges to get the elements needed. Project these elements to all view and they will produce the curves needed. Know how to take a section view along a line. Get the plane director by using the level line method as in intersecting planes. This will give an auxiliary showing the plane director which is when all the elements are parallel to each other. This will also be the angle of the horizontal trace of the plane director if asked that.
Surface of Translation - This is where a parabola slides down another parabola. It gives a shape that can be called a saddle roof. You need to know how to draw a parabola in a rectangle. Then it is a case of taking heights from the ele, dropping them down from the top of the parabola in end ele to give a width and using that width to give the points in plan.
Additions to this is where parts of the piece are cut off or you have to work in reverse to get the curve in ele after taking the width from the plan to get the height needed in end ele.
Geological Geometry
There are two main topics in this section, road geometry and mining geometry.
Road Geometry - You will have to know how to get cut and fill for a level and sloping road.
If you are cutting then the level of the road is below the contours on the map. If you are filling then the level of the road is above the contours on the map.
For a level road you come out parallel to the side of the road. The distances you come out is determined on wheither you are cutting or filling and what ratios there are for them. The ratio given is always multiplied by the intervals of the ground contours (normally 5m).
For a sloping road you will have to set up a cone (semi-circle) at the edge of the road. It will depend on if you are cutting or filling which part of the road this cone will be placed.
If you are cutting the cone will be on the low side of the road
If you are filling the cone will be on the high side of the road
Mining Geometry - Know how to get the dip, strike and thickness the traditional method by using the elevation and the level line method
These can also be found just in the plan by dividing the line between the highest and lowest of the three points. It is divided into the number of intervals there are between these two points. (eg. 80 and 55 have 5 intervals of 5m between them so the line would be divided into 5 parts). The other point is then joined to its corresponding height on the divided line to give the strike line. The dip and thickness are found by looking along this strike line and taking an auxiliary
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