Publications, talks and more.

Research Interests: Constructive Algebraic Geometry, Symbolic Computation, Curves and Surfaces, Mathematical Methods in CAGD.

Publications (inverse chronological order): 

1. Alcázar J.G., Quintero E. (2021), “Exact and approximate similarities of non-necessarily rational planar, parametrized curves, using centers of gravity and inertia tensors”, International Journal of Algebra and Computation Vol. 31, No 4, pp. 581-603.

2. Alcázar J.G., Pérez-Díaz S. (2021), “Computing the form of highest degree of the implicit equation of a rational surface ”, Advances in Applied Mathematics Vol. 123, pp. 102-128.

3. Alcázar J.G. (2020), “On the affine image of a rational surface of revolution”, Mathematics 8(11), 2061

4. Alcázar J.G., Quintero E. (2020), "Affine equivalences of trigonometric curves", Acta Applicandae Mathematicae Vol. 170, pp. 691-708

5. Knez M., Peternell M., Alcázar J.G. (2020), “Editorial: From Theoretical to Applied Geometry – Recent Developments”, Computer Aided Geometric Design, Special issue on the CGTA 2019 Congress, Vol. 81, 101192.

6. Alcázar J.G., Goldman R. (2020), “Recognizing algebraic affine rotation surfaces”, Computed Aided Geometric Design Vol. 81, 101905..

7. Alcázar J.G., Caravantes J., Díaz-Toca G., Tsigaridas E. (2020), “Computing the topology of a planar or space hyperelliptic curve”, Computer Aided Geometric Design Vol. 78, 101830.

8. Alcázar J.G., Quintero E. (2020), "Affine equivalences, isometries and symmetries of ruled rational surfaces", Journal of Computational and Applied Mathematics, Vol. 364.

9. Alcázar J.G., Goldman R. (2019), “Algebraic affine rotation surfaces of parabolic type”, Journal of Geometry Vol. 110 (3)

10. Nieto J.C., Alcázar J.G., Orden D., Marazuela S., Rodríguez G. (2019), "Estimation of spatio-temporal grouping properties using Delaunay triangulation and spline techniques", Ocean Engineering Vol. 187.

11. Alcázar J.G., Lavicka M., Vrsek J. (2019), "Symmetries and similarities of planar algebraic curves using harmonic polynomials", Journal of Computational and Applied Mathematics Vol. 357, pp. 302--318.

12. Alcázar J.G., Díaz Toca G.M., Hermoso C. (2019), "On the problem of detecting when two implicit plane algebraic curves are similar", International Journal of Algebra and Computation, Vol. 29, No. 5, pp. 775–793.

13. Alcázar J.G., Caravantes J., Díaz Toca G.M. (2018), "On the square-freeness of the offset equation to a rational plane curve", International Journal of Algebra and Computation, Vol. 28, No. 3, pp. 395–409

14. Alcázar J.G., Dahl H., Muntingh G. (2018), "Symmetries of canal surfaces and Dupin cyclides", Computer Aided Geometric Design Vol. 59, pp. 68-85. 

15. Alcázar J.G., Hermoso C., Muntingh G. (2018), "Similarity detection of rational space curves", Journal of Symbolic Computation 85, pp- 4-24.

16. Alcázar J.G., Goldman R. (2017), "Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution", IEEE Transactions on Visualization and Computer Graphics Vol. 23, Issue 12, pp. 2550-59.

17. Alcázar J.G., Goldman R., Hermoso C.,(2016), "Algebraic surfaces invariant under scissor shears", Graphical Models vol. 87, pp. 23-34.

18. Alcázar J.G., Hermoso C. (2016), "Recognizing projections of algebraic curves", Graphical Models vol. 87, pp. 1-10.

19. Alcázar J.G., Hermoso C., Muntingh G. (2016), "Detecting similarities of rational space curves", Proceedings ISSAC 2016 (Waterloo, Canadá, July 2016).

20. Alcázar J.G., Goldman R., (2016), "Finding the axis of revolution of a surface of revolution", IEEE Transactions on Visualization and Computer Graphics, Vol. 22 (9), pp. 2082--93.

21. Alcázar J.G., Hermoso C. (2016), "Involutions of Polynomially Parametrized Surfaces", Journal of Computational and Applied Mathematics Vol. 294, pp. 23-38.

22. Alcázar J.G., Caravantes J., Díaz Toca G.M. (2015), "A new method to compute the singularities of offsets to rational plane curves", Journal of Computational and Applied Mathematics, Vol. 290, pp. 385-402.

23. Alcázar J.G., Hermoso C., Muntingh G. (2015), "Symmetry detection of rational space curves from their curvature and torsion", Computer Aided Geometric Design Vol. 33, pp. 51-65.

24. Marvá M., Alcázar J.G., Bravo de la Parra R., Poggiale J.C. (2015), "A simple geometrical condition for the existence of periodic solutions of planar periodic systems. Application to some biological models", Journal of Mathematical Analysis and Applications, Vol. 423, Issue 2, pp. 1469-1479.  

25. Alcázar J.G., Hermoso C., Muntingh G. (2014), "Detecting similarity of Rational Plane Curves", Journal of Computational and Applied Mathematics vol. 269, pp. 1-13. 

26. Alcázar J.G., Hermoso C., Muntingh G. (2014), "Detecting Symmetries of Rational Plane and Space Curves", Computer Aided Geometric Design vol. 31, issues 3-4, pp. 109-209. 

27. Alcázar J.G. (2014), "Efficient detection of symmetries of polynomially parametrized curves", Journal of Computational and Applied Mathematics, vol. 255, pp. 715-724,

28. Alcázar J.G. (2013), "On the topology of algebraic curves continuously depending on parameters, and applications", International Journal of Algebra and Computation, Vol. 23, No. 7, pp- 1591-1610. 

29. Alcázar J.G., Díaz Toca G.M.(2012), "On the Shape of Curves Rational in Polar Coordinates", Computer Aided Geometric Design, vol. 29, pp. 665-675.

30. Alcázar J.G. (2012), "Computing the Shapes Arising in a Family of Space Rational Curves Depending on a Parameter", Computer Aided Geometric Design, vol. 29, issue 6, pp. 315-331.

31. Alcázar J.G. (2012), "Local Shape of Generalized Offsets to Algebraic Curves", Journal of Symbolic Computation, vol. 47 (3), pp. 327-341

32. Alcázar J.G. (2011), "Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter", Proceedings CASC 2011, Lecture Notes in Computer Science.

33. Alcázar J.G. (2011), "The Shape of Conchoids to Algebraic Curves", Proceedings VII International Conference on Curves and Surfaces, Lecture Notes in Computer Science.

34.Alcázar J.G., Díaz Toca G.M. (2010), "Topology of 2D and 3D Rational Curves", Computer Aided Geometric Design 27 (7), 483-502.

35. Alcázar J.G. (2010), "Applications of Level Curves to Some Problems on Algebraic Surfaces", Contribuciones Científicas en Honor de Mirian Andrés, Universidad de La Rioja.

36. Alcázar J.G. (2009), "On the Shape of Rational Algebraic Curves Depending on One Parameter", Computer Aided Geometric Design, vol. 27, issue 2, pp. 162-17

37. Alcázar J.G. (2009) "Good Local Behavior of Offsets to Implicit Algebraic Curves", Mathematics in Computer Science,  vol. 2, nº 4, pp. 635-652.

38. Alcázar J.G. (2008) "Good Global Behavior of Offsets to Plane Algebraic Curves", Journal of Symbolic Computation, vol. 43, pp. 659-680. 

39. Alcázar J.G. (2008) "Good Local Behavior of Offsets to Regularly Parametrized Surfaces", Journal of Symbolic Computation vol. 43 (December), pp. 845-857.

40. Alcázar J.G., Sendra J.R. (2007) "Local Shape of Offsets to Rational Algebraic Curves", Journal of Symbolic Computation, vol. 41, pp. 338-351. An extended version was published as Technical Report SFB 2006-2 (RICAM, Austria).

42. Alcázar J.G., Schicho J., Sendra J.R.(2007) "A delineability-based method for Computing Critical Sets of Algebraic Surfaces", Journal of Symbolic Computation, vol 42 (June), pp. 678-691.

43. Alcázar J.G., Sendra J.R. (2005) "Computation of the Topology of Real Algebraic Space Curves", Journal of Symbolic Computation 39, pp. 719-744. A preliminary version was published as RISC-Linz Report Series Nº 04-02. 

Editorial Work:

From Theoretical to Applied Geometry” (2020), Special issue of the Computer Aided Geometric Design (CAGD) on the congress CGTA 2019. Guest editors: Marjeta Knez, Martin Peternell, Juan G. Alcázar.

Talks, presentations, etc. (inverse chronological order):

Advised Ph. D. Theses:

  1. Emily Quintero, “Computation of affine equivalences, similarities and symmetries of certain types of curves and surfaces” (in the frame of a grant from the Carolina Foundation), defended June 23rd, 2021.

Additional material for some publications: