CAD-Lecture 2 Dr. Salih Akour

Background Material Geometries Revision of Vector Algebra

Geometry  Ancient branch of mathematics  Euclidean geometry deals with (measurement of) distance angle, area and volume  Geometry is the study of Manifolds (spaces) - Riemann Geometry  “Geometry is the study of those properties that are invariant when the elements (points) are subjected to the transformation of a given transformation group” Klein’s geometry.

Geometry  Affine geometry deals with points, lines etc Affine space is a set acted on by vector space.  Projective geometry includes all the above and in addition a line at infinity.

Geometry  Vector and Position Vector A vector is an ordered triple (a,b,c) where a, b, c are real numbers. Also, ai+bj+ck in component form where i,j,k are unit vectors  A position vector P(x,y,z) implies a vector from the origin (0,0,0) to the point (x,y,z)  Magnitude or Norm of

Unit vector and Component form  The vector P(x,y,z) = xi+yj+zk can be pictorial represented with respect to the Cartesian coordinate system as follows

GKS, is the production and manipulation of pictures (in a way that does not depend on the computer or graphical device being used).