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Focus On Curves and Surfaces (Focus on Game Development)

ISBN: 159200007X
EAN: 2147483647

Year: 2003
Pages: 104

Authors: Kelly Dempski

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• LRN
• Table of Contents
• Focus on Curves and Surfaces
• Higher-Degree Polynomials
• In Conclusion
• Chapter 4: B-Splines
• The Effects of Weighting Factors
• Part Three: Focus on Surfaces
• From B-Spline Curves to Surfaces
• Chapter 10: More NURBS Surfaces
• Drawing a Bezier Patch with DirectX
• What Is Differential Calculus?
• What Is a Vector?
• Web Sites
• Rhino 2.0 (Evaluation Version)
• Introduction
• Joining Curves and Continuity
• Part Two: Focus on Curves
• The Building Blocks of a B-Spline
• Conic Sections and NURBS Curves
• Chapter 7: Basic Surface Concepts and Bezier Surfaces
• Implementing B-Spline Surfaces
• Ruled Surfaces
• In Conclusion
• What Is a Derivative?
• Normalizing Vectors
• Xfrog (Evaluation Version)
• How Should This Book Be Read?
• Introducing the Curve Application
• Chapter 3: Parametric Equations and Bezier Curves
• Knot Vectors
• Finding the Derivative of NURBS Curves
• Extending Curves to Patch Surfaces
• In Conclusion
• Surfaces of Revolution
• Part Four: Appendixes
• Derivatives of Polynomial Functions
• Vector Cross Product
• What s Included
• In Conclusion
• What Is a Parametric Equation?
• Controlling the B-Spline
• Implementing NURBS in Code
• Finding Surface Normal Vectors
• Chapter 9: NURBS Surfaces
• Swept Surfaces
• The Quotient Rule
• In Conclusion
• Who Am I?
• Chapter 2: Trigonometric Functions
• Derivatives of Parametric Equations
• Generating Closed Shapes with B-Splines
• In Conclusion
• Lighting a Surface
• Advantages of NURBS Surfaces over B-Spline Surfaces
• Skinned Surfaces
• Derivatives of Trigonometric Functions
• Part One: Focus on Basics
• Defining Sine, Cosine, and Tangent
• Bezier Curves Defined in Parametric Terms
• Finding Derivatives of B-Spline Curves
• Chapter 6: Subdivision of Curves
• Extending the Basic Application to 3D
• From NURBS Curves to Surfaces
• Generalizing Swept and Skinned Shapes
• Partial Derivatives of Multivariable Functions
• Chapter 1: Polynomial Curves
• Properties of Waves
• Joining Bezier Curves
• Implementing B-Spline Code
• Simple Adaptive Subdivision
• Setting Up Buffers for a Generic Surface
• Implementing NURBS Surfaces
• In Conclusion
• Caveats and Conclusions
• What Is a Curve?
• Some Simple Uses for Trigonometric Functions
• Finding Derivatives of Bezier Curves
• In Conclusion
• The Source Code
• In Conclusion
• Moving Beyond Fluttering Sheets
• Chapter 11: Higher-Order Surfaces in DirectX
• What Is a Polynomial?
• Computing Trigonometric Functions with Taylor Series Approximations
• Putting It All Together
• Chapter 5: NURBS
• Performance Considerations
• Chapter 8: B-Spline Surfaces
• Advantages of NURBS Surfaces
• DirectX versus Doing It Yourself
• Lines and Slopes
• Higher-Degree Polynomials
• Joining Curves and Continuity
• Introducing the Curve Application
• In Conclusion
• Chapter 2: Trigonometric 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
• Web Sites
• Appendix D: What s on the CD
• Rhino 2.0 (Evaluation Version)