Focus on Curves and Surfaces 1st Edition by Kelly Dempski, Andre LaMothe ISBN 159200007X 9781592000074

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Product details:
ISBN 10: 159200007X
ISBN 13: 9781592000074
Author: Kelly Dempski, Andre LaMothe

Focus on Curves and Surfaces 1st Edition Table of contents:

Chapter 1: The Fundamentals of Curves and Surfaces

• Defining Curves and Surfaces in 3D Space
• Overview of Mathematical Concepts in Computer Graphics
• Coordinates, Vectors, and Matrices in Geometry
• The Role of Curves and Surfaces in 3D Models
• Applications in Game Development and Animation

Chapter 2: Mathematical Foundations for Curves

• Parametric Equations for Curves
• Tangent, Normal, and Binormal Vectors
• Bézier Curves: Linear, Quadratic, and Cubic
• Hermite Curves and Interpolation
• B-Splines and Their Properties
• Example: Drawing a Bézier Curve in 2D and 3D

Chapter 3: Curves in 3D Space

• The Geometry of Curves in Three Dimensions
• 3D Parametric Curves
• Computing Tangents, Normals, and Curvature
• Application of 3D Curves in Animation and Pathfinding
• Example: Creating a 3D Path for Animation

Chapter 4: Surfaces: The Basics

• Introduction to Parametric Surfaces
• Mathematical Representation of Surfaces
• Types of Surfaces: Planes, Spheres, and More Complex Forms
• Surface Normal and Tangent Vectors
• Surface Curvature and Continuity
• Example: Modeling a Simple 3D Surface

Chapter 5: Bézier Surfaces and Their Applications

• Defining Bézier Surfaces Using Control Points
• Linear, Quadratic, and Cubic Bézier Surfaces
• De Casteljau’s Algorithm for Surface Construction
• Interpolation Techniques for Surface Design
• Using Bézier Surfaces in Game Development
• Example: Creating a Complex 3D Surface Using Bézier Curves

Chapter 6: B-Splines: Basics and Beyond

• Introduction to B-Splines and Their Advantages
• Uniform and Non-Uniform B-Splines
• Knot Vectors and Basis Functions
• B-Splines vs. Bézier Surfaces
• Application of B-Splines in Modeling
• Example: Creating Smooth Surfaces with B-Splines

Chapter 7: NURBS (Non-Uniform Rational B-Splines)

• Understanding NURBS Surfaces
• Control Points, Weights, and Knots in NURBS
• Evaluating and Manipulating NURBS Surfaces
• NURBS vs. Bézier and B-Splines
• Application of NURBS in CAD and Game Development
• Example: Modeling a Car Body with NURBS

Chapter 8: Surface and Curve Intersections

• Finding Intersections Between Curves and Surfaces
• Mathematical Methods for Curve-Surface Intersections
• Applications in Collision Detection and Ray Tracing
• Implementing Intersection Algorithms in Game Engines
• Example: Calculating Ray-Surface Intersections in 3D Graphics

Chapter 9: Rendering Curves and Surfaces

• Algorithms for Rendering Curves and Surfaces in 3D Graphics
• Mesh Generation from Curves and Surfaces
• Using Tessellation for Complex Surfaces
• Rendering Curves with OpenGL and DirectX
• Shading and Texturing Curves and Surfaces
• Example: Rendering a Smooth Curve in a 3D Environment

Chapter 10: Advanced Topics in Curves and Surfaces

• Subdivision Surfaces and Their Applications
• Implicit Surfaces and Their Use in Modeling
• Advanced Rendering Techniques for Curves and Surfaces
• Computational Methods for Large-Scale Surface Modeling
• Real-Time Curves and Surfaces in Game Engines
• Example: Creating Advanced 3D Terrain Using Subdivision Surfaces

Chapter 11: Optimizing Curve and Surface Calculations

• Performance Considerations in Curve and Surface Rendering
• Efficient Storage of Control Points and Knots
• Optimizing Tessellation for Real-Time Applications
• Parallel Processing and Hardware Acceleration for Curves
• Techniques for Reducing the Complexity of Surfaces
• Example: Optimizing a Real-Time 3D Character Model

Chapter 12: Practical Applications of Curves and Surfaces

• Using Curves and Surfaces in Game Design and Animation
• Modeling Terrain, Characters, and Objects in 3D Games
• Animation Curves: Controlling Movement, Rotation, and Scaling
• Modeling Complex Environments with Curves and Surfaces
• The Role of Curves and Surfaces in Simulation and VR
• Example: Building a Game World with Curves and Surfaces

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