tailieunhanh - Lecture Computer graphics: Lecture 15 - Fasih ur Rehman

This chapter discuss the purpose of the components required for successful communications; describe these uses of computer communications: wireless messaging services, wireless Internet access points, cybercafés, global positioning systems, collaboration, groupware, voice mail, and Web services; | Computer Graphics Lecture 15 Fasih ur Rehman Last Class Combining Transformations Affine versus Rigid body Transformations Homogenous Transformations Today’s Agenda Homogeneous transformations Types of Transformations Linear Transformations Affine Transformations Projective Transformations Homogenous Coordinate System Basic 2D transformations in 3D are Translation Scaling as 3x3 Rotation as 3x3 Shear as 3x3 Linear Transformations Combination of Scaling, rotation and shear are linear transformations Linear Transformations satisfy following Origin maps origin Lines maps lines Parallelism is preserved Ratios remain the same Affine Transformations Affine transformations are combinations of linear transformations and Translation Affine transformations obey the following Origin does not necessarily map the origin Lines maps lines Parallelism is preserved Ratios remain the same Projective Transformations Affine Transformations and projective warps form projective transformation Projective . | Computer Graphics Lecture 15 Fasih ur Rehman Last Class Combining Transformations Affine versus Rigid body Transformations Homogenous Transformations Today’s Agenda Homogeneous transformations Types of Transformations Linear Transformations Affine Transformations Projective Transformations Homogenous Coordinate System Basic 2D transformations in 3D are Translation Scaling as 3x3 Rotation as 3x3 Shear as 3x3 Linear Transformations Combination of Scaling, rotation and shear are linear transformations Linear Transformations satisfy following Origin maps origin Lines maps lines Parallelism is preserved Ratios remain the same Affine Transformations Affine transformations are combinations of linear transformations and Translation Affine transformations obey the following Origin does not necessarily map the origin Lines maps lines Parallelism is preserved Ratios remain the same Projective Transformations Affine Transformations and projective warps form projective transformation Projective Transformations obey the following Origin does not necessarily map the origin Lines maps lines Parallelism is not preserved Ratios remain are not the same Closed under composition Matrix Composition Homogenous transformations can also be combined by Matrix multiplication Example Example Multiplication Order Scaling, Rotation and then translation Summary Homogeneous transformations Types of Transformations Linear Transformations Affine Transformations Projective Transformations References Fundamentals of Computer Graphics Third Edition by Peter Shirley and Steve Marschner Interactive Computer Graphics, A Top-down Approach with OpenGL (Sixth Edition) by Edward .