![]() ![]() ![]() To produce a tessellation, you can find the midpoint between two points, rotate a shape around a point, and translate a shape by a given vector. You can click and drag the corners of the quadrilateral to change its shape. You might find the interactivity below useful for this: If your answer is yes, can you explain why all quadrilaterals tessellate, and can you give an algorithm which will produce a tessellation of any quadrilateral? A tessellation of squares is named by choosing a vertex and then counting the number of sides of each shape touching the vertex. n 4 180 1 2 n 180 1 2 4 180 90 2 Each angle in a square is 90 degrees. Image Source: OpenGL Wiki The abstract patch space spans its dimensions within the range 0, 1.Each intermediate point is represented by a fractional coordinate (u, v) that corresponds to its location within the patch. Each angle of an n-sided polygon equals Each angle of an n-sided polygon equals Examples. Once the inner rings have been generated, the outer ring was its final intermediate points generated based on each outer tessellation level. ![]() Can you explain why it doesn't tessellate? 180 1 2 3 180 60 3 Each angle in an equilateral triangle is 60 degrees. If your answer is no, give an example of a quadrilateral which doesn't tessellate. What do you notice about your tessellations? Escher Tessellation Properties and Transformations A regular tessellation means that the pattern is made up of congruent regular polygons, same size and shape, including some type of movement that is, some type of transformation or symmetry. Make an Escher-style tessellation online. Click here to make a square tessellation online. Squares - rather obvious By colouring them, you can build up more complicated patterns. For example, can you find a way to tessellate any parallellogram? What about a kite? Or a trapezium? More examples of triangle tessellations Large grid of triangles to print or save Design a triangle mosaic online - which you can use to make tessellations. You might want to think about different types of quadrilaterals. Ask me for more details if you choose this pattern for your artwork. Instead of sliding a cutout to an opposite side - you rotate it. This is an example of a more complex tessellation pattern - 'rotation' template. For example, equilateral triangles tessellate like this: Lets think about other triangles which tessellate: You can print off some square dotty paper, or some isometric dotty paper, and try drawing different triangles on it. Another example of a square-based tessellation. Have a go at drawing some quadrilaterals, and finding ways to make them tessellate (you can print off some square dotty paper, or some isometric dotty paper, and try drawing different quadrilaterals on it. You could also draw some quadrilaterals using this interactive). We say that a shape tessellates if we can use lots of copies of it to cover a flat surface without leaving any gaps. What about other types of quadrilaterals? It's quite easy to see how squares tessellate: In this problem we're going to be thinking about tessellating different quadrilaterals. You may not have thought about it, but you will ahve seen titlings by squares before. This problem follows on from some of the ideas in Tessellating Triangles. The most common and simplest tessellation uses a square. ![]()
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