Advances in Computer Graphics (online 2020-2021)
Advances in Computer Graphics (online 2020-2021)
PART 1: TRIANGULATIONS
November 12, 2020:
Voronoi diagram when a new site is inserted. Delaunay triangulation: general aspects, construction, duality with the Voronoi diagrams
November 5, 2020:
The Fortune's algorithm; neighbors; the complexity of a Voronoi diagram
October 29, 2020:
Voronoi diagrams; general aspects; methods of construction
October 22, 2020:
Graham-scan algorithm, Constraints for a triangulation
October 15, 2020:
Isomorphic triangulations, ear-cutting technique; point insertion technique
October 8, 2020:
Triangulations: definition (valid and regular triangulation), basic formulas, some estimates
October 1, 2020:
General aspects about this course. Contents. Introduction to Triangulations
January 14, 2021:
Summarize the main points of this course.
January 7, 2021:
Sufficient conditions for a PH curve to be a helix. Counterexample for the necessity. PH quintics.
December 17, 2020:
PH cubics in R3, a geometrical characterization; connection with the geometry of helices in R3
December 10, 2020:
PH curves in R3; use of quaternions
December 3, 2020:
Characterization of a PH cubics in terms of Bezier control polygon; a method to construct PH curves
November 26, 2020:
Characterization of a PH curves; degree of freedom; invariance with respect to translations and rotations
November 19, 2020:
Pythagorean triples (integers and polynomials); the hodograph for a curve
One suggests the following two books, but any other (correct) information is welcome:
M.I.Munteanu, A.I.Nistor, Algoritmi de triangulare. Casa Editoriala Demiurg, 2008
Rida T. Farouki, Pythagorean Hodograph Curves: Algebra and Geometry Inseparable. Springer, 2008
The algorithm to obtain the final mark :
20% - homework and/or project
40% - laboratory activity; exercises
40% - written and oral examination
Office hours: by appointment
Subiecte de examen (schita):
Notiuni generale de triangulare (definitie, proprietati, formula Euler Poincare)
Triagularea unei multimi de puncte (3 pasi)
Triangulari cu constrangeri
Diagrame Voronoi (proprietati generale, constructie, exemple)
Complexitatea unei diagrame Voronoi (teorema cu nr. de varfuri si nr. de laturi, teorema de caracterizare pt varfuri si laturi)
Algoritmul lui Fortune (descriere generala si exemplu)
Triangularea Delaunay
Inserarea unui punct intr-o triangulare Dalaunay
Curbe PH plane – notiuni generale
Cubice PH plane
Algoritm de construire a curbelor PH plane (folosind numere complexe)
Curbe PH plane de grad 4
Curbe PH de grad 5
Curbe PH in spatiu – notiuni generale
Cubice PH in spatiu
Utilizarea cuaternionilor in studiul curbelor PH in spatiu