Processamento Geométrico
2020 – trabalhos

12/3: curvas paramétricas

Aproximação uniforme, aproximação adaptativa, decimação

Douglas–Peucker (1973), Wikipedia
Ramer (1972), An iterative procedure for the polygonal approximation of plane curves
Ballard (1981), Strip trees: a hierarchical representation for curves
de Figueiredo (1995), Adaptive sampling of parametric curves

17/3: bordas de regiões em imagens

Extração, decimação, aproximação por cúbicas: letters.png · letters.pbm · letters.eps

Plass–Stone (1983), Curve-fitting with piecewise parametric cubics
Schneider (1990), An algorithm for automatically fitting digitized curves, Graphics Gems, p. 612–626
Doué–Rubio (1995), Efficient and robust 2d shape vectorization, Graphics Gems V, p. 323–337
Selinger (2001), Potrace: Transforming bitmaps into vector graphics

Veja os livros Graphics Gems na biblioteca.

24/3: simulação de um scanner

Simulação da aquisição de formas 2d em imagens usando um scanner com sensores 1d, efeito da discretização espacial do scan e da resolução espacial e de profundidade do scanner, reconstrução de formas

Day (2009), Curve and Surface Reconstruction
Amenta–Bern–Eppstein (1998), The crust and the beta-skeleton: combinatorial curve reconstruction
de Figueiredo (1995), Computational morphology of curves [doi]
Cheng et al. (2005), Curve reconstruction from noisy samples
Rupniewski (2014), Curve reconstruction from noisy and unordered samples
Mukhopadhyay–Das (2007), Curve reconstruction in the presence of noise

31/3: reconstrução de regiões

reconstrução de regiões no plano a partir de amostras, triangulação de Delaunay, remoção de arestas longas, alpha shapes, concave hull; dados: 1 · 2 · 3 · 4 · 5

Zahn (1971), Graph-theoretical methods for detecting and describing gestalt clusters [doi]
Edelsbrunner–Kirkpatrick–Seidel (1983), On the shape of a set of points in the plane
Medeiros–Velho–Lopes (2004), Restricted BPA: applying ball-pivoting on the plane [doi]
Methirumangalath–Parakkat–Muthuganapathy (2015), A unified approach towards reconstruction of a planar point set
Peethambaran–Muthuganapathy (2015), A non-parametric approach to shape reconstruction from planar point sets through Delaunay filtering

7/4: malhas para regiões

geração de malhas triangulares em regiões poligonais no plano: triangulação do polígono da borda, inserção de pontos, suavização laplaciana

Devadoss–O'Rourke (2011), Discrete and Computational Geometry
Shewchuk (2005), Triangle, a two-dimensional quality mesh generator and delaunay triangulator
Geuzaine–Remacle (2020), Gmsh, a three-dimensional finite element mesh generator

14/4: estruturas de dados para malhas

sopas de triângulos, listas de vérticles, winged edge, halfedge, corner table; dados: soup.txt · face.off · mannequin.off

Botsch et al. (2001), Polygon Mesh Processing, Chapter 2: slides
Stanford cs468 (2012), Mesh Data Structures
Campagna–Kobbelt–Seidel (1998), Directed edges - a scalable representation for triangle meshes
Formato OFF
Cignoni et al. (2008), MeshLab
Rusinkiewicz (2020), trimesh2

21/4: suavização de polígonos

suavização laplaciana, subdivisão por corte de cantos; dados: taubin2.txt

Botsch et al. (2001), Polygon Mesh Processing, Chapter 4: slides
Stanford cs468 (2012), Smoothing
Chaikin (1974), An algorithm for high-speed curve generation
Riesenfeld (1975), On Chaikin's algorithm
de Boor (1987), Cutting corners always works
Joy (1996), Chaikin's algorithms for curves
Chaikin (2019), Chaikin's Algorithm

28/4: subdivisão de Catmull–Clark

superfícies de subdivisão de Catmull–Clark e Loop; dados: 1 · 2 · 3 · 4 ·

Stanford cs468 (2012), Subdivision
Catmull–Clark (1978), Recursively generated B-spline surfaces on arbitrary topological meshes
Loop (1987), Smooth subdivision surfaces based on triangles
Stam (1998), Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Warren–Weimer (2002), Subdivision methods for geometric design
Loop–DeRose (1990), Generalized B-spline surfaces of arbitrary topology

5/5: suavização de malhas

operadores diferenciais discretos, operador de Laplace–Beltrami; dados: iphigenie e os acima

Botsch et al. (2001), Polygon Mesh Processing, Chapter 3: slides
Botsch et al. (2001), Polygon Mesh Processing, Chapter 4: slides
Stanford cs468 (2012), Smoothing

12/5: simplificação de malhas

Botsch et al. (2001), Polygon Mesh Processing, Chapter 7: slides
Stanford cs468 (2012), Simplification
Schroeder et al. (1992), Decimation of triangle meshes
Garland–Heckbert (1999), Surface simplification using quadric error metrics · project page · qslim

2/6: parametrização e remeshing

Turk (1992), Re-tiling polygonal surfaces
Turk (1991), Generating textures on arbitrary surfaces using reaction-diffusion