Oblique Projection

8402 /www/nrich/html/content/id/8402/ 1 0000-00-00T00:00:00 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <ul id="stemLinks"> <li><a href="http://nrich.maths.org/8396">Warm-up</a></li> <li><a href="http://nrich.maths.org/894">Try this next</a></li> <li><a href="http://nrich.maths.org/6903">Think higher</a></li> <li><a href="http://en.wikipedia.org/wiki/Oblique_projection">Read: mathematics</a></li> <li><a href="http://plus.maths.org/content/maths-goes-movies">Read: science</a></li> <li><a href="http://www.significant-bits.com/a-laymans-guide-to-projection-in-videogames">Explore further</a></li> </ul> <div class="framework">If you are not familiar with Oblique Projection, start by reading our article <a href="http://nrich.maths.org/8396">3D Drawing</a>.</div> <mdo:image alt="multilink structure" src="multilink4.png" style="margin: 10px; float: right; width: 232px; height: 250px;"></mdo:image>Here is another view of the multilink structure discussed in <a href="http://nrich.maths.org/8396">3D Drawing</a>. Draw it in <a href="https://nrich.maths.org/8396?part=index#oblique">Oblique Projection</a> - you may find using squared paper helpful. Now try drawing it again, this time with a different face as the front. Which properties of the original structure are preserved in your drawings, which are not? You should think about: <ul> <li>the relationship between the lengths of the edges of the cubes</li> <li>the angles between them</li> <li>parallel and perpendicular lines</li> </ul> What do you think the advantages of Oblique Projection are? What disadvantages are there with this method of representing 3D objects in 2D?</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><h3>Why do this problem?</h3> Representing 3D objects in two dimensions on paper is a vital skill in the Design Technology curriculum, as well as an aspect of Shape and Space in the Maths curriculum. <a href="http://nrich.maths.org/8402">This problem</a> is part of a set of problems which will help students to understand why there are different ways to represent a 3D object in two dimensions, and what maths lies behind each method. The article <a href="https://nrich.maths.org/8396">3D Drawing</a> was written to support these problems. <h3>Key questions</h3> What are the advantages of this method of 3D drawing? What are the disadvantages? What features of the object are retained in the drawing, which are not? <h3>Possible extension</h3> Oblique Projection is probably the easiest for students to understand. Those who find it straight-forward should be encouraged to tackle the other problems in this set (linked from <a href="http://nrich.maths.org/8396">3D Drawing</a>) and to compare the various methods. <h3>Possible support</h3> Students who find it difficult to draw the multi-link structure shown in the problem could be given simpler multi-link structures to draw, helping them to build up to drawing more complex ones.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image alt="drawing in oblique perspective" src="obliquedrawing.png" style="width: 193px; height: 225px; margin: 10px 30px; float: left;"></mdo:image>The drawing preserves: <ul> <li>parallel lines</li> </ul> The drawing does not preserve: <ul> <li>the relationship between the lengths of the edges of the cubes - all edges are equal in reality, but not on the drawing</li> <li>the angles between them - all edges are right angles in reality, but some are 45 degrees on the drawing</li> <li>perpendicular lines - because not all right angles are preserved</li> </ul> Advantages of oblique projection include that it is straight-forward to draw, and the relationship of each cube to the others is clear. Disadvantages include the number of features of the original structure which are not preserved. </mdoxml> 2 3 0 0 1 0 0 Oblique Projection Explore the properties of oblique projection. Applications Design Applications Maths Supporting SET 3D Geometry, Shape and Space 2D representations of 3D shapes Applications STEM - design technology