BlenderDev/ComputingGeometry
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CS3621 Introduction to Computing with Geometry Notes
Dr. C.-K. Shene
Associate Professor Department of Computer Science Michigan Technological University
© 1997-2003 C.-K. Shene
http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/
翻译进行中,教程时间比较久远,很多新的技术在出现,所以翻译不会只按部就班的做,也会添加最新的一些东西.最终为大家保留一个知识库.欢迎共同编写.
Select the topics you wish to review:
Unit 1: Course Overview
Why Is Computing with Geometry Important? The Theme of this Course The Complexity of Geometric Problems Computing with Floating Point Numbers Problems References
Unit 2: Geometric Concepts
Coordinate Systems, Points, Lines and Planes Simple Curves and Surfaces Homogeneous Coordinates Geometric Transformations Problems References
Unit 3: Solid Models
Solid Representations: An Introduction Wireframe Models Boundary Representations Manifolds The Winged-Edge Data Structure The Euler-Poincaré Formula Euler Operators Constructive Solid Geometry Interior, Exterior and Closure Regularized Boolean Operators A CSG Design Example Problems References
Unit 4: Parametric Curves
Parametric Curves: A Review Tangent Vector and Tangent Line Normal Vector and Curvature Continuity Issues Rational Curves Problems References
Unit 5: Bézier Curves
An Introduction Construction Moving Control Points De Casteljau's Algorithm Why Is de Casteljau's Algorithm Correct? Derivatives of a Bézier Curve Subdividing a Bézier Curve Why Is the Subdivision Algorithm Correct? Degree Elevation of a Bézier Curve Why Is the Degree Elevation Algorithm Correct? Problems References
Unit 6: B-spline Curves
Motivation B-spline Basis Functions Definition Important Properties Computation Examples B-spline Curves Definition Open Curves Closed Curves Important Properties Computing the Coefficients A Special Case Moving Control Points Modifying Knots Derivatives of a B-spline Curve Important Algorithms for B-spline Curves Knot Insertion Single Insertion Inserting a Knot Multiple Times De Boor's Algorithm De Casteljau's and de Boor's Algorithms Subdividing a B-spline Curve Problems References
Unit 7: NURBS Curves
Motivation Definition Important Properties Modifying Weights Important Algorithms for B-spline and NURBS Curves Knot Insertion: Single Insertion De Boor's Algorithm Rational Bézier Curves Rational Bézier Curves: Conic Sections Circular Arcs and Circles Problems References
Unit 8: Surfaces
Basic Concepts Bézier Surfaces Construction Important Properties De Casteljau's Algorithm B-spline Surfaces Construction Important Properties De Boor's Algorithm
Unit 9: Interpolation and Approximation
Parameter Selection and Knot Vector Generation Overview The Uniformly Spaced Method The Chord Length Method The Centripetal Method Knot Vector Generation The Universal Method Parameters and Knot Vectors for Surfaces Solving Systems of Linear Equations Curve Interpolation Global Interpolation Curve Approximation Global Approximation Surface Interpolation Global Interpolation Surface Approximation Global Approximation
