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Linear Algebra for Computer Scientists. 14. 3D Transformation Matrices

Most real time animated computer games are based on 3 dimensional models composed of thousands of tiny primitive shapes such as triangles, and each vertex in a model is encoded as a vector. In this computer science video you will learn how matrices are used to transform these vectors in three dimensional space. You will meet some new types of transformation matrix, the translation matrix, the scaling matrix and three variations of the rotation matrix. You will learn how a single transformation matrix can be composed from several transformation matrices by calculating their dot product, to create a single transformation matrix that encodes multiple 3D transformations at once. Chapters: 00:00 Recap 2D computer models 00:54 2D Transformation Matrices 01:53 Apply a 2D Transformation Matrix to a 2D Vector 02:22 Transformations in Three Dimensions 03:12 3D Transformation Matrices 05:34 Apply a 3D Transformation Matrix to a 3D Vector 07:12 Composing 3D Transformation Matrices 07:53 Transform a 3D Model 08:13 Local and Global Coordinate Systems in a 3D world