Dissertation > Excellent graduate degree dissertation topics show

Matrix Representation and Conversion Matrix for Two Bases of the Algebraic Hyperbolic Trigonometric Space

Author: XuHui
Tutor: WangGuoZhao
School: Zhejiang University
Course: Applied Mathematics
Keywords: Matrix representation Uniform hyperbolic trigonometric polynomial B-Spline basis Algebraic trigonometric hyperbolic Bézier basis Conversion matrix Representation of curves and surfaces
CLC: TP391.72
Type: Master's thesis
Year: 2008
Downloads: 22
Quote: 0
Read: Download Dissertation


The limitations caused by the rational model in NURBS(Non-Uniform Rational B-Spline) curves and surfaces motivate the broad research of new representation of curves and surfaces.Among that research,the uniform hyperbolic trigonometric polynomial(UAHT) B-Spline basis and the algebraic trigonometric hyperbolic(AHT) Bézier basis which are both defined in the algebraic trigonometric hyperbolic spaceΓ=span{sint,cost,sinht,cosht,tn-5,…t,1}(n≥5) have been largely studied for their similar properties to the uniform B-spline basis and the Bernstein basis respectively.This paper presents the matrix representation for the UAHT B-Spline basis in a recursive way,which is generated over the algebraic trigonometric hyperbolic spaceΓ.This definition of the matrix form is more straightforward and legible than the definition in the recursive and integral approach.As examples,the specific expressions of the matrix representation for UAHT B-Spline basis of order 6 are given by the recursive method.Similarly,the matrix representation for the AHT Bézier basis overΓis derived in the recursive approach too.At the same time,this paper also gets the specific expressions of the matrix representation for AHT Bézier basis of order 6 by employing the recursive results.At last,the conversion matrix from the AHT Bézier basis to the UAHT B-Spline basis of the same order is also given by a recursive approach.The conversion matrix between both bases not only has the practical value,but also proposes a new tool for the theoretic research about the two bases.We also construct the conversion matrix between the two bases of order 6 by the method proposed in this paper.These results constitute the primary contents of this paper.As we know,it is both convenient and practical to describe curves and surfaces by matrix representation in CAGD,such as facilitating the evaluation and conversion of the curves and surfaces.The matrix forms for curves and surfaces are largely promoted in CAD.So we expect the results concerning the matrix form of the UAHT B-Spline basis and the AHT Bézier basis on the algebraic spaceΓFn can be employed in future CAD/CAM systems.

Related Dissertations

  1. The quaternion M ( ? ) Bius transform classification and dimensional Clifford algebra equation,O151.21
  2. Research on CLEAR Algorithm for Solving the Navier-Stokes Equations and Its Application to the Numerical Simulation of Water-Sediment Flow,O241
  3. Clustering Based on Improved Minimum Spanning Tree Algorithm,TP311.13
  4. Automorphism Group of Direct Product of Finite Groups,O152.1
  5. Graph and matrix -based association rule mining algorithm,TP311.13
  6. Subdivision of NURBS Curves and Surfaces Based on Matrix Representation,TP391.7
  7. Research on Optimal Allocation of Land Use Spatial Structure,F224
  8. Research of Manifold Learning in Data Dimension Reduction and Classification,TP311.13
  9. Evaluation, Degree Reduction and Offset Approximation of Curves and Surfaces,TP391.41
  10. Analysis and Application of the Complex Normal Form Method,O175
  11. Some Researches on Completely 0-Simple Semigroups,O152.7
  12. Matrix Representation and Conversion Matrix for Two Bases of the Algebraic Hyperbolic Space,TP391.7
  13. Research on Properties of Polynomial Bezoutian Matrix and Toeplitz-Bezout Matrix,O151.21
  14. Development of dual - passband filter,TN713
  15. Symmetry, Subgroups and Supergroups of Quasicrystallographic Point Groups,P57
  16. Group Theory Analysis of 3D Braided Structural Composites,TB332
  17. Studies on Key Technologies of Optical Packet-Switched Networks,TN929.11
  18. Geometric Approximation and Graphics Transformation in Shape Modeling,TP391.72
  19. Approximating Curves and Surfaces with Constraints,TP391.72
  20. The Research of Vector CAD Electronic Drawing Protection System,TP391.72
  21. Based on Pro/E Reconstruct Sprinkler Structure and Investigations on Internal Flow Characteristic of the Sprinkler by Numerical Simulation and Experiment Methods,TP391.72

CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Machine-assisted technology > Machine -aided design (CAD), aided drawing
© 2012 www.DissertationTopic.Net  Mobile