![]() To find the enlarged shape you need to follow these instructions:ġ) Draw and measure a line from the centre of enlargement to a vertex of the original shape.Ģ) Multiply this length by the scale factor.ģ) Draw a new vertex this distance from the centre of enlargement in the same direction as the original line.Ĥ) Repeat for each vertex and then join up all the new vertices to create a new enlarged shape. To carry out an enlargement we need:īelow is an example of an enlargement with a scale factor of 2 and the dot as the centre of enlargement. As well as this we need the ‘centre of enlargement’ so that we know where the enlargement is done in relation to. The lengths of each side are multiplied by what is called a ‘scale factor’ to get the new shape. The new object will therefore be similar (this means that they have the same angles and sides but are just different sizes). EnlargementĪn enlargement is where we need to change the size of a shape by a certain amount. ![]() To do this we must simply reverse the signs of the vector to give us the inverse which is. So, to find the inverse of any column vectors we must simply change the positives to negatives and vice versa. Therefore, we must simply reverse the signs for the numbers in the column vector so that the shape will be moved back to where it started. Its inverse can also be found this is the column vector which would take the shape back to its original position. The column vector for this translation isĪny movement of an object can be put as a column vector. Here is a picture of a square that has been moved 6 squares to the right and 3 down. The number at the bottom ( y) tells the number an object is moved up or down by, with a positive moving the object up and a negative moving it down. The number on the top ( x) is the left and right movement, with a positive move to the right and negative to the left. This can obviously be up, down, left or right, and a translation written mathematically is as a column vector. TranslationĪ translation is a movement of an object in a straight line. Here we will give a brief description of the main types of transformations. ![]() There are many different kinds of transformations and more than one of these can be used on the same object. Let S 11 and S 12are matrix to be multiplied.A transformation is a change in the size or position of an object in relation to something, usually a square background. The P 1 and P 2are represented using Homogeneous matrices and P will be the final transformation matrix obtained after multiplication.Ībove resultant matrix show that two successive translations are additive.Ĭomposition of two Rotations: Two Rotations are also additiveĬomposition of two Scaling: The composition of two scaling is multiplicative. Let t 1 t 2 t 3 t 4are translation vectors. Rules used for defining transformation in form of equations are complex as compared to matrix.The number of operations will be reduced.Advantage of composition or concatenation of matrix: It will position the object at the origin location.Ībove transformation can be represented as T V.ST V -1 Note: Two types of rotations are used for representing matrices one is column method. This second translation is called a reverse translation. Step3: Scaling of an object by keeping the object at origin is done in fig (c) Step2: The object is translated so that its center coincides with the origin as in fig (b) Step1: The object is kept at its position as in fig (a) For this following sequence of transformations will be performed and all will be combined to a single one The enlargement is with respect to center. Example showing composite transformations: The output obtained from the previous matrix is multiplied with the new coming matrix. If a matrix is represented in column form, then the composite transformation is performed by multiplying matrix in order from right to left side. ![]() The ordering sequence of these numbers of transformations must not be changed. Suppose we want to perform rotation about an arbitrary point, then we can perform it by the sequence of three transformations The process of combining is called as concatenation. The resulting matrix is called as composite matrix. A number of transformations or sequence of transformations can be combined into single one called as composition.
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