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Lecture Computer graphics: Lecture 10 - Fasih ur Rehman

This chapter explains various storage media and storage devices. Students discover how memory is different from storage. Floppy disks are introduced, and characteristics of a floppy disk, floppy disk drives, care of floppy disks, and high-capacity floppy disks are presented. Hard disks are explained, and students find out about characteristics of a hard disk, how a hard disk works, removable hard disks, hard disk controllers, RAID, and maintaining data on a hard disk. | Computer Graphics Lecture 10 Fasih ur Rehman Last Class Viewing Perspectives Projections Today’s Agenda Geometric Objects Vector Space Affine Space Scalars, Points and Vectors Geometry is a subject that relates objects in n – dimensional space (In computer graphics we deal with 3 dimensional space) Scalars, vectors and points form minimum set of primitives and are used to build sophisticated objects. A point is a location in space that neither has size nor shape. Real numbers (magnitudes) such as distance between two points are a scalars Vectors are also required to work with directions. Scalars Scalars are members of sets which can be combined by addition and multiplication and obey associativity, commutivity and inverses axioms Scalars don’t possess any geometric properties Real and Complex numbers Vectors A quantity defined by magnitude and direction Velocity, Force etc. For computer graphics, a directed line segment (can be used for any vector) is most significant example Vector . | Computer Graphics Lecture 10 Fasih ur Rehman Last Class Viewing Perspectives Projections Today’s Agenda Geometric Objects Vector Space Affine Space Scalars, Points and Vectors Geometry is a subject that relates objects in n – dimensional space (In computer graphics we deal with 3 dimensional space) Scalars, vectors and points form minimum set of primitives and are used to build sophisticated objects. A point is a location in space that neither has size nor shape. Real numbers (magnitudes) such as distance between two points are a scalars Vectors are also required to work with directions. Scalars Scalars are members of sets which can be combined by addition and multiplication and obey associativity, commutivity and inverses axioms Scalars don’t possess any geometric properties Real and Complex numbers Vectors A quantity defined by magnitude and direction Velocity, Force etc. For computer graphics, a directed line segment (can be used for any vector) is most significant example Vector Operations Vectors have following properties Inverses: Equal in magnitude but opposite in direction Scalar Multiplication: A vector can be multiplied by a scalar (magnitude changes only not the direction) Zero vector is also defined with zero magnitude and undefined direction Head to Tail Rule is used to add vectors Head to Tail Rule Linear Vector Space Extensions Linear Vector Space may not have ways to measure a scalar quantity. A Euclidean space is an extension of a vector space that adds a measure of size or distance and allows us to define such things as the length of a line segment. An affine space is an extension of the vector space that includes an additional type of object: the point. Operations between vectors and points are allowed Example Affine Space Combines point and vector space Allows following operations Vector-vector addition Scalar-vector multiplication Point-vector addition Scalar-scalar operations Summary Geometric Objects Vector Space Affine Space References .