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Lecture Computer graphics: Lecture 14 - 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 14 Fasih ur Rehman Last Class Translation Shear Reflection Today’s Agenda Combining Transformations Affine versus Rigid body Transformations Homogenous Transformations Combining Transforms General transformation of a point: P' = N • P + A Scaling or rotation, Translate, we set A, and N is the multiplicative identity. Example Rigid Body Transforms The transforms in which angles and lengths are preserved are called rigid body transforms. The body or object is not distorted after the application of transformation. Rotation and Translation are examples Affine Transformations Parallelism of lines are preserved but angles between the lines are not preserved in affine transformations An arbitrary sequence of rotation, translation and scaling can cause affine transformation Shear is another example A Dangerous Representation Point and vectors are two distinct geometric types but a confusion may arise Homogeneous Coordinates How a 2D vector is represented by 3 x 3 . | Computer Graphics Lecture 14 Fasih ur Rehman Last Class Translation Shear Reflection Today’s Agenda Combining Transformations Affine versus Rigid body Transformations Homogenous Transformations Combining Transforms General transformation of a point: P' = N • P + A Scaling or rotation, Translate, we set A, and N is the multiplicative identity. Example Rigid Body Transforms The transforms in which angles and lengths are preserved are called rigid body transforms. The body or object is not distorted after the application of transformation. Rotation and Translation are examples Affine Transformations Parallelism of lines are preserved but angles between the lines are not preserved in affine transformations An arbitrary sequence of rotation, translation and scaling can cause affine transformation Shear is another example A Dangerous Representation Point and vectors are two distinct geometric types but a confusion may arise Homogeneous Coordinates How a 2D vector is represented by 3 x 3 matrix x’ = x + a y’ = y + b Homogenous Coordinate System A 3rd Coordinate is added to every 2D point (x, y, t) represents (x/t, y/t) (x, y, 0) represents infinity (0, 0, 0) is not allowed Summary Combining Transformations Affine versus Rigid body Transformations Homogenous 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 .