Gönderen Konu: 2B/3B problemlere Matematik çözümler  (Okunma sayısı 7448 defa)

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Çevrimdışı Gokhan Sonmez (LW3D)

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2B/3B problemlere Matematik çözümler
« : Haziran 14, 2005, 17:22:39 ÖS »
Geometric Tools sitesinde, çeşitli matematik problemlere çözümler yer almaktadır. İlgilenen arkadaşlara faydalı olabileceğini düşünüyorum..

http://www.geometrictools.com/Documentation/Documentation.html

Alıntı

Applications:
Command Line Parsing  
Key Frame Interpolation via Splines and Quaternions  
Polyline Reduction  

Approximation:
Approximating an Ellipse by Circular Arcs  
Fitting 3D Data with a Cylinder  
Fitting 3D Data with a Helix  
Least Squares Fitting of Data  

Containment:
Centers of a Simplex (circumscribed/inscribed balls)  
Largest Fixed-Aspect, Axis-Aligned Rectangle Inscribed in a Convex Quadrilateral  
Minimum Area Rectangle Containing a Convex Polygon  

Curves:
Least-Squares Reduction of B-Spline Curves  
Calculation of Curvatures and Torsions  
Kochanek-Bartels Cubic Splines  
Moving At Constant Speed (parameterize by arc length)  
Representing a Circle or Sphere with NURBS  
Subdivision of a Parabolic Segment by Arc Length  

Distance:
Distance Between Two Circles in 3D  
Distance Between a Circle and a Disk in 3D  
Distance Between Ellipses in 2D  
Distance Between Two Ellipses in 3D  
Distance Between Line and Circle or Disk in 3D  
Distance Between Two Line Segments in 3D  
Distance from Linear Component to Tetrahedron  
Distance Between Point and Circle or Disk in 3D  
Distance Between Point and Triangle in 3D  
Distance Between Point and Line, Ray, or Line Segment  
Distance from a Point to an Ellipse in 2D  
Distance from a Point to an Ellipsoid  
Distance from Point to Orthogonal Frustum  
Distance from Point to a General Quadratic Curve or a General Quadric Surface  
Geodesics on a Parameterized Surface  

Foundation:
Estimating a Tangent Vector for Bump Mapping  
Clipping a Mesh Against a Plane  
A Collinearity Test Independent of Point Order  
Euler Angle Formulas  
Information About Ellipses  
Conversion of Left-Handed Coordinates to Right-Handed Coordinates  
A Linear Algebraic Approach to Quaternions  
Low-Degree Polynomial Roots  
Perspective Mapping Between Quadrilaterals  
Perspective Mapping Between Cuboids  
Perspective Mapping Between Two Convex Quadrilaterals  
Perspective Projection of an Ellipsoid  
Platonic Solids (parameters, vertices, mesh connectivity)  
Solving Systems of Polynomial Equations  
Polysolids and Boolean Operations  
Quaternion Algebra and Calculus  
Rotation Representations and Performance Issues  
Triangulation by Ear Clipping  

Image Analysis:
Extraction of Level Sets from 2D Images  
Extraction of Level Sets from 3D Images  
Fast Gaussian Blurring  
Level Set Extraction from Gridded 2D and 3D Data  
Theory of Ridges  
Skeletonization of 2D Binary Images  

Interpolation:
B-Spline Interpolation on Lattices  
C1 Quadratic Interpolation of Meshes  
Thin Plate Splines  

Intersection:
Dynamic Collision Detection using Oriented Bounding Boxes  
Intersection of Orthogonal View Frustum and Oriented Bounding Box using Separation Axis Testing  
Intersection of Linear and Circular Components in 2D  
Intersection of a Line and a Cone  
Intersection of Cylinders  
Intersection of Ellipses  
Intersection of Ellipsoids  
Intersection of Objects with Linear and Angular Velocities using Oriented Bounding Boxes  
Intersection of a Sphere and a Cone  
Intersection of a Triangle and a Cone  
Intersection of Convex Objects: The Method of Separating Axes  

Miscellaneous:
Geometric Invariance (vector fields, Lie algebra, prolongations)  
Integer-based Ellipse Drawing  
Medial-Based Morphing for 2D Binary Objects (medial axes, differential geometry)  
Spherical Harmonics  


Numerical Analysis:
Bisection in 1D, 2D, and 3D  
CORDIC Methods  
Eigensystems for 3x3 Symmetric Matrices  
Eigensystem Solvers for Symmetric Matrices  
Fast Inverse Sqrt  
Derivative Approximation by Finite Differences  
Systems of Linear Equations  
Numerical Integration  
Numerical Methods for Ordinary Differential Equations  
Numerical Methods for Partial Differential Equations  
Special Functions  

Physics:
Extremal Queries using BSP Trees  
Particle Motion on a Height Field  
Polyhedral Mass Properties (Revisited)  
Rough Plane Analysis  
Stability Analysis for Systems of Differential Equations  

Surfaces:
Classifying Quadrics using Exact Arithmetic  
Mesh Differential Geometry  
Principal Curvatures of Surfaces  

Tessellation:
Tessellation of a Unit Sphere Starting with an Inscribed Convex Triangular Mesh  


  • 3D Generalist