Mathematical Optics

11	Dihedral Polynomials
Marlos Viana

CONTENTS

11.1    Introduction

11.2    Dihedral Groups

11.3    Canonical Projections

11.4    Dihedral Polynomials

11.4.1  D_4,1 Dihedral Polynomials

11.4.2  D_4,2 Dihedral Polynomials

11.4.3  D_4,3 Dihedral Polynomials

11.4.4  D_4,4 Dihedral Polynomials

11.5    Between-Class Relations

11.6    Applications

11.6.1  Refraction Power Contours

11.6.2  Curvature Contours

11.6.3  Baker’s Asphericity Model

11.7    Additional Comments

11.A   Appendix A: Selected Mathematica© Command Lines

11.A.1  Dihedral D₄ Orbits

11.A.2  Ring Plots

References

11.1    INTRODUCTION

Dihedral polynomials p(x, y) are families of real orthogonal polynomials that reduce according to certain representations of the dihedral groups. They ...