Perspective Drawing

8399 /www/nrich/html/content/id/8399/ 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/8402">Warm-up</a></li> <li><a href="http://nrich.maths.org/696">Try this next</a></li> <li><a href="http://nrich.maths.org/7484">Think higher</a></li> <li><a href="http://plus.maths.org/content/putting-it-perspective">Read: mathematics</a></li> <li><a href="http://www.instructables.com/id/How-to-Draw---Basic-Linear-Perspective/">Read: design technology</a></li> <li><a href="http://nrich.maths.org/7023">Explore further</a></li> </ul> <div class="framework">If you are not familiar with perspective drawing, read our <a href="https://nrich.maths.org/8396">article on 3d drawing</a> first.</div> <mdo:image alt="multilink structure" src="multilink6.png" style="margin: 10px; float: right; width: 229px; height: 225px;"></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="http://nrich.maths.org/8396#linear">two-point linear perspective</a>. 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 linear perspective drawing 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. This problem 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> Challenge students to do a perspective drawing of the structure from a different perspective! (They should do a sketch first to ensure they know which cubes will be visible). <h3>Possible support</h3> Perspective drawing is much more difficult to do accurately than either oblique projection or isometric. 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">You may find it helps to do your drawing on plain paper, with squared paper beneath it to make it easier to draw a horizontal line and vertical lines. All vertical lines remain vertical, other lines are oblique - you are trying to construct what you actually see in the photo. Start by drawing a horizontal line and putting the two vanishing points on it, one near each end of the line. Draw a vertical line representing the central vertical edge of the front green cube. Draw construction lines from both vanishing points to both ends of this vertical line. Considering the relative apparent proportions of the vertical edge and the bottom left and right hand edges of the green cube, and draw in the left and right hand vertical edges of the front green cube, and then the extreme right and left hand edges of the rear green and blue cubes. Continue adding construction lines from both vanishing points to all cube vertices, using intersections of the construction lines to locate further vertices. When you have constructed the bottom layer of cubes, think about where you want the right hand edge of the yellow cube to appear to meet the vertical/right hand edge of the red cube, and what the apparent height of the red cube should be relative to the green cubes. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div style="text-align: center;"><mdo:image alt="perspective drawing" src="perspectivedrawing-solution.png" style="width: 650px; height: 356px;"></mdo:image></div> <div>All cube edges which are vertical in the photo are vertical in the drawing. The line connecting the two vanishing points is horizontal. The vertical edge of the central cube was drawn first - the height is an estimate. Then the construction lines from both vanishing points to both ends of this edge were drawn in. The left and right bottom edges were then drawn in along the construction lines, again the lengths were estimated to give the impression of perspective. From these edges, the remaining vertical edges for the bottom layer of cubes can be drawn in. Further construction lines are added between both vanishing points and all vertices. Finally the upper layer cube was added, starting from the back right vertical, to ensure that the top rear edge of the lower layer of cubes would meet it appropriately. The only property of the original construction preserved in this drawing are the vertical lines - and even they are not all the same length. An advantage of this type of drawing is that it is possible to draw what you actually see. A disadvantage is that it is difficult to do well, and can take several attempts. Given the hit and miss nature of this construction (the image above is my third attempt), you will not be surprised to learn that there is a mathematical way to calculate where all the vertices should be - this is called Projective Geometry.</div></mdoxml> 5 4 0 0 1 1 0 Perspective Drawing What geometric properties does perspective drawing preserve, what is distorted? Applications Design Applications Maths Supporting SET 3D Geometry, Shape and Space 2D representations of 3D shapes Applications STEM - design technology