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Linear Algebra for Computer Scientists. 13. Transformation Matrices

Animated computer graphics are based on models composed of thousands of tiny primitive shapes such as triangles, and each vertex in a model is encoded as a vector. This computer science video demonstrates how matrices are used to transform these vector. In particular you will learn how to derive a two dimensional rotation matrix using trigonometric identities, and how to transform a model in two dimensional space with a scaling matrix, a translation matrix and a rotation matrix. You will also learn how several transformation matrices can be combined using matrix multiplication to create a single transformation matrix that encodes multiple transformations at once. Chapters: 00:00 Introduction to 3D computer models 00:50 Scale a vector with a vector 02:10 Translate a vector with a vector 02:40 Derive a rotation matrix using trigonometric identities 07:42 Rotate a vector with a matrix 08:48 Scale a vector with a matrix 09:32 Scale and rotate a vector with a single matrix 10:42 2D translation matrices 13:06 Translation, rotation and scaling combined 15:05 The role of a graphics processing unit (GPU)