Area: Group Project (Group 18)

Introduction Monte Carlo method List of Useful Functions
Property of Polygon Identify Method 1 Identify Method 2
Classify Vertex 1 Point in Polygon 1 Monte Carlo Method 1 Classify Vertex 2 Monte Carlo Method 2
Point in Polygon 2 Ray-casting Algorithm Winding Number algorithm Monte Carlo Method 3
Monte Carlo Integration Variance Reduction: Antithetic Monte Carlo Method 4 Variance Reduction: Control Variates
Pick's Theorem Determinants Convex Hull and Random Polygon
Bibliography

Bibliography:

  1. Weisstein, Eric W. "Perp Dot Product." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PerpDotProduct.html
  2. De Loera, Jesus; Rambau, Joerg; Santos, Francisco (2010). Triangulations: Structures and Algorithms. Springer Science & Business Media. p. 103. ISBN 9783642129711.
  3. Internal and external angles. (n.d.). In Wikipedia, The Free Encyclopedia. Retrieved 13:40, April 13, 2019, from https://en.wikipedia.org/w/index.php?title=Internal_and_external_angles
  4. F. S. Hill, Jr.. (1994). The pleasures of “perp dot” products. In Graphics Gems IV, Paul S. Heckbert (Ed.). Academic Press Professional, Inc., San Diego, CA, USA p. 138-148.
  5. Weisstein, Eric W. "Convex Polygon." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConvexPolygon.html
  6. Jing, Lanru; Stephansson, Ove (2007). Fundamentals of Discrete Element Methods for Rock Engineering: Theory and Applications. Elsevier Science. p. 145-197 ISBN 9780444829375.
  7. Haines E. (1991). Fast Ray-convex Polyhedron Intersection. In Graphics Gems II, Arvo. J. (Ed.). Academic Press Professional, Inc., San Diego, CA, USA p. 246-250.
  8. Krantz, S. G. "Closed Curves." §2.1.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 19-20, 1999.
  9. Weisstein, Eric W. "Closed Curve." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ClosedCurve.html
  10. Braden, Bart. The Surveyor's Area Formula. In The College Mathematics Journal, vol. 17, no. 4, 1986, pp. 326–337. JSTOR, www.jstor.org/stable/2686282.
  11. Matthews, Paul C. (1998). Vector Calculus. Springer-Verlag London. p. 93-96 ISBN 9783540761808.
  12. T. Lidebrandt. “Variance reduction: Three approches to control variates,” Master Thesis, Mathematical statistics, Stockholm University, 2007.
  13. Weisstein, Eric W. "Simpson's Rule." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SimpsonsRule.html
  14. D. P. Kroese, T. Taimre, and Z. I. Botev. Handbook of Monte Carlo Methods. John Wiley & Sons, New York, 2011.
  15. Boyle, P. (1977) Options: a Monte Carlo approach, Journal of Finan- cial Economics 4: 323-338.
  16. Weisstein, Eric W. "Pick's Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PicksTheorem.html
  17. Kreyszig E. (2011). "CHAP. 9.3 Vector Product (Cross Product)". Advanced Engineering Mathematics (10th ed.). John Wiley & Sons. p. 368-374. ISBN 9780470913611.
  18. Convex hull. (n.d.). In Wikipedia, The Free Encyclopedia. Retrieved 18:33, April 16, 2019, from https://en.wikipedia.org/wiki/Convex_hull
  19. M. H. Kalos; P. A. Whitlock. (1986). Monte Carlo Methods. Vol. 1: Basics. Wiley- Interscience. p. 31-34. p. 107-111. ISBN 0471898392.
  20. Haines E. (1994). Point in polygon strategies. In Graphics Gems IV, Paul S. Heckbert (Ed.). Academic Press Professional, Inc., San Diego, CA, USA p. 24–46.