CONTENTS -- LETTER FROM THE SERIES EDITOR -- INTRODUCTION -- Part One: Focus on Basics -- CHAPTER 1 POLYNOMIAL CURVES -- What Is a Curve? -- What Is a Polynomial? -- Lines and Slopes -- Higher-Degree Polynomials -- Joining Curves and Continuity -- Introducing the Curve Application -- In Conclusion -- CHAPTER 2 TRIGNOMETRIC FUNCTIONS -- Defining Sine, Cosine, and Tangent -- Properties of Waves -- Some Simple Uses for Trigonometric Functions -- Computing Trigonometric Functions with Taylor Series Approximations -- Aliasing -- In Conclusion -- Part Two: Focus on Curves -- CHAPTER 3 PARAMETRIC EQUATIONS AND BEZIER CURVES -- What Is a Parametric Equation? -- Derivatives of Parametric Equations -- Bezier Curves Defined in Parametric Terms -- Joining Bezier Curves -- Finding Derivatives of Bezier Curves -- Putting It All Together -- In Conclusion -- CHAPTER 4 B-SPLINES -- The Building Blocks of a B-Spline -- Knot Vectors -- Controlling the B-Spline -- Generating Closed Shapes with B-Splines -- Finding Derivatives of B-Spline Curves -- Implementing B-Spline Code -- In Conclusion -- CHAPTER 5 NURBS -- NURBS: Rational Splines -- The Effects of Weighting Factors -- Conic Sections and NURBS Curves -- Finding the Derivative of NURBS Curves -- Implementing NURBS in Code -- In Conclusion -- CHAPTER 6 SUBDIVISION OF CURVES -- Simple Adaptive Subdivision -- The Source Code -- Performance Considerations -- In Conclusion -- Part Three: Focus on Surfaces -- CHAPTER 7 BASIC SURFACE CONCEPTS AND BEZIER SURFACES -- Extending Curves to Patch Surfaces -- Finding Surface Normal Vectors -- Lighting a Surface -- Extending the Basic Application to 3D -- Setting Up Buffers for a Generic Surface -- In Conclusion -- CHAPTER 8 B-SPLINE SURFACES -- Advantages of B-Spline Surfaces over Bezier Surfaces -- From B-Spline Curves to Surfaces -- Implementing B-Spline Surfaces.

In Conclusion -- CHAPTER 9 NURBS SURFACES -- Advantages of NURBS Surfaces over B-Spline Surfaces -- From NURBS Curves to Surfaces -- Implementing NURBS Surfaces -- Moving Beyond Fluttering Sheets -- Advantages of NURBS Surfaces -- In Conclusion -- CHAPTER 10 MORE NURBS SURFACES -- Ruled Surfaces -- Surfaces of Revolution -- Swept Surfaces -- Skinned Surfaces -- Generalizing Swept and Skinned Shapes -- In Conclusion -- CHAPTER 11 HIGHER-ORDER SURFACES IN DIRECTX -- DirectX versus Doing It Yourself -- Higher-Order Surfaces in DirectX -- Drawing a Bezier Patch with DirectX -- In Conclusion -- Part Four: Appendixes -- APPENDIX A: DERIVATIVE CALCULUS -- What Is Differential Calculus? -- What Is a Derivative? -- Derivatives of Polynomial Functions -- The Quotient Rule -- Derivatives of Trigonometric Functions -- Partial Derivatives of Multivariable Functions -- Caveats and Conclusions -- APPENDIX B: A QUICK LOOK AT VECTORS -- What Is a Vector? -- Normalizing Vectors -- Vector Cross Product -- In Conclusion -- APPENDIX C: BIBLIOGRAPHY -- Books -- Web Sites -- APPENDIX D: WHAT'S ON THE CD -- The DirectX 8.1 SDK -- Rhino 2.0 (Evaluation Version) -- Xfrog (Evaluation Version) -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Z.