Trang 4 Transformation Definition■ What is a transformation?□ P′=TP□Transform the coordinates / normal vectors of objects■ Uses□Moving the objects to the desired location in the environm
Lesson Modeling Transformation Trinh Thanh Trung School of ICT, HUST Content Transformation 2D modeling transformation Homogenous transformation 3D modeling transformation Transformation Transformation Definition ■ What is a transformation? □ P′=T(P) □ Transform the coordinates / normal vectors of objects ■ Uses □ Moving the objects to the desired location in the environment □ Multiple instances of a prototype shape □ Kinematics of linkages/skeletons – character animation □ Viewing □ Virtual camera: parallel and perspective projections Types of transformation ■ Object Transformation alters the coordinates of each point according to some rule, leaving the underlying coordinate system unchanged ■ Coordinate Transformation produces a different coordinate system, and then represents all original points in this new system Stages of transformation Model MODELING World VIEW Display Coordinate TRANSFORMS Coordinate TRANSFORMS Coordinate System System System PROJECTION Projection Coordinate TRANSFORMS System Modeling Transformation View Transformation Projection Transformation Affine transformation ■ Whole collections of points may be transformed by the same transformation T, e.g lines or circles ■ The image of a line, L, under T, is the set of all images of the individual points of L ■ For most mappings of interest, this image is still a connected curve of some shape ■ For some mappings, the result of transforming a line may no longer be a line ■ Affine Transformations, however, preserve lines, and are the most commonly-used transformations in computer graphics