Linear Geometry with Computer GraphicsCRC Press, 16 Δεκ 1992 - 458 σελίδες Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups. |
Περιεχόμενα
Preface | 1 |
Symmetric Bilinear Forms | 43 |
Plane Geometries | 95 |
Homogeneous Spaces in | 173 |
7 | 241 |
A Equivalence Relations | 397 |
GraphLib Documentation | 405 |
| 439 | |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
affine plane algebra angle basis begin belongs Bezier bijective called computer graphics congruent consider converges coordinates cosets curve deCasteljau define Definition denote determined dimensional edge eigenvalues element EQUATION Euclidean group example EXERCISE face field F FIGURE finite follows function geometry given gives GL(V GraphLib guide points homeomorphism homogeneous space hyperbolic identify implies inner product plane inner product space integer intersect isometric isomorphism isotropic Koch system LEMMA line segment linear transformation matrix representation metric space neighborhood nonsingular nonzero open set orthogonal parallel pedge pixels polynomial POSTULATE procedure projective plane PROOF properties Prove PtList quadric real projective plane Recall result Riemann sphere rotation satisfies scalar sequence sphere subgroup subset subspace Suppose symmetric bilinear form texture mapping THEOREM topological group topological space translation triangle U₁ V₁ vector space verify vert vertex vertices wing-edge