Recovering Primitives in 3D CAD meshes Roseline B eni` ere G. - - PowerPoint PPT Presentation
Introduction Primitives Extraction Problems Conclusion Recovering Primitives in 3D CAD meshes Roseline B eni` ere G. Subsol, G. Gesqui` ere, F . Le Breton and W. Puech LIRMM, Montpellier, France C4W, Montpellier, France LSIS, Arles,
Introduction Primitives Extraction Problems Conclusion
Roseline B´ eni` ere
ere, F . Le Breton and W. Puech
LIRMM, Montpellier, France C4W, Montpellier, France LSIS, Arles, France
14 octobre 2010 R´ eunion ICAR
Recovering Primitives in 3D CAD / R.B´ eni` ere 1/17
Introduction Primitives Extraction Problems Conclusion
In CAD an object is usually modeled by a structured combination of primitives
Recovering Primitives in 3D CAD / R.B´ eni` ere 2/17
Introduction Primitives Extraction Problems Conclusion
In CAD an object is usually modeled by a structured combination of primitives But to use, we often need to discretized it into a 3D mesh
Recovering Primitives in 3D CAD / R.B´ eni` ere 2/17
Introduction Primitives Extraction Problems Conclusion
In CAD an object is usually modeled by a structured combination of primitives But to use, we often need to discretized it into a 3D mesh And the initial model can be lost or not correspond anymore
Recovering Primitives in 3D CAD / R.B´ eni` ere 2/17
Introduction Primitives Extraction Problems Conclusion
In CAD an object is usually modeled by a structured combination of primitives But to use, we often need to discretized it into a 3D mesh And the initial model can be lost or not correspond anymore So a primitive extraction algorithm is needed to reconstruct the initial representation
Recovering Primitives in 3D CAD / R.B´ eni` ere 2/17
Introduction Primitives Extraction Problems Conclusion
Benk˜
Algorithms for reverse engineering boundary representation models Computer-Aided Design 33(11) : 839-851 2001 Bohm et al. Curvature based range image classification for object PROC SPIE INT SOC OPT ENG 4197 : 211-220 2000
Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17
Introduction Primitives Extraction Problems Conclusion
Benk˜
Algorithms for reverse engineering boundary representation models Computer-Aided Design 33(11) : 839-851 2001 Bohm et al. Curvature based range image classification for object PROC SPIE INT SOC OPT ENG 4197 : 211-220 2000 Same Process :
Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17
Introduction Primitives Extraction Problems Conclusion
Benk˜
Algorithms for reverse engineering boundary representation models Computer-Aided Design 33(11) : 839-851 2001 Bohm et al. Curvature based range image classification for object PROC SPIE INT SOC OPT ENG 4197 : 211-220 2000 Same Process :
1
Segmentation
Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17
Introduction Primitives Extraction Problems Conclusion
Benk˜
Algorithms for reverse engineering boundary representation models Computer-Aided Design 33(11) : 839-851 2001 Bohm et al. Curvature based range image classification for object PROC SPIE INT SOC OPT ENG 4197 : 211-220 2000 Same Process :
1
Segmentation
2
Classification
Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17
Introduction Primitives Extraction Problems Conclusion
Benk˜
Algorithms for reverse engineering boundary representation models Computer-Aided Design 33(11) : 839-851 2001 Bohm et al. Curvature based range image classification for object PROC SPIE INT SOC OPT ENG 4197 : 211-220 2000 Same Process :
1
Segmentation
2
Classification
3
Fitting
Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17
Introduction Primitives Extraction Problems Conclusion
Curvature 2D :
N P C R
Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17
Introduction Primitives Extraction Problems Conclusion
Curvature 2D :
N P C R
⇒ Kp = 1
R
Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17
Introduction Primitives Extraction Problems Conclusion
Curvature 2D :
N P C R
⇒ Kp = 1
R
Curvature 3D :
N S P C PL
Dirmin Dirmax
Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17
Introduction Primitives Extraction Problems Conclusion
Curvature 2D :
N P C R
⇒ Kp = 1
R
Curvature 3D :
N S P C PL
Dirmin Dirmax
2 Principal Curvatures (kmax et kmin) 2 Principal Directions (Dirmax et Dirmin) Normal
Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17
Introduction Primitives Extraction Problems Conclusion
The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature :
Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17
Introduction Primitives Extraction Problems Conclusion
The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : Plane ⇒ kmax = kmin = 0
P2 P1 Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17
Introduction Primitives Extraction Problems Conclusion
The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : Plane ⇒ kmax = kmin = 0
P2 P1
Sphere ⇒ kmax = kmin =
1
rSp = 0
P2 P1
Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17
Introduction Primitives Extraction Problems Conclusion
The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : Plane ⇒ kmax = kmin = 0
P2 P1
Sphere ⇒ kmax = kmin =
1
rSp = 0
P2 P1
Cylinder ⇒ kmin = 0 et kmax =
1
rCy
P1 P2
Dirmin = Generating line
Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17
Introduction Primitives Extraction Problems Conclusion
The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : Plane ⇒ kmax = kmin = 0
P2 P1
Sphere ⇒ kmax = kmin =
1
rSp = 0
P2 P1
Cylinder ⇒ kmin = 0 et kmax =
1
rCy
P1 P2
Dirmin = Generating line Cone ⇒ idem Cylinder but with a variable radius
Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17
Introduction Primitives Extraction Problems Conclusion
In a mesh, we compute a discrete curvature for each point.
Recovering Primitives in 3D CAD / R.B´ eni` ere 6/17
Introduction Primitives Extraction Problems Conclusion
In a mesh, we compute a discrete curvature for each point. We use the Euler formula kn = kmax cos2(θ) + kmin sin2(θ) With θ the angle between n and Dirmax. The neighbors are studied to approximate kmax, kmin and θ.
Recovering Primitives in 3D CAD / R.B´ eni` ere 6/17
Introduction Primitives Extraction Problems Conclusion
In a mesh, we compute a discrete curvature for each point. We use the Euler formula kn = kmax cos2(θ) + kmin sin2(θ) With θ the angle between n and Dirmax. The neighbors are studied to approximate kmax, kmin and θ. To determine the point which will be used, we fix a k-neighborhood.
Recovering Primitives in 3D CAD / R.B´ eni` ere 6/17
Introduction Primitives Extraction Problems Conclusion
In a mesh, we compute a discrete curvature for each point. We use the Euler formula kn = kmax cos2(θ) + kmin sin2(θ) With θ the angle between n and Dirmax. The neighbors are studied to approximate kmax, kmin and θ. To determine the point which will be used, we fix a k-neighborhood. Concave Point Convex Point Saddle Point Plane Point Spheric Point
Recovering Primitives in 3D CAD / R.B´ eni` ere 6/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures
Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin = 0
Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin = 0
Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin = 0 Equation Coefficients : ax + by + cz + d = 0 are approximated by a least square regression
Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin = 0 Equation Coefficients : ax + by + cz + d = 0 are approximated by a least square regression
Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures
Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin ≈ K
Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin ≈ K
Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin ≈ K The radius and the center are approximated by a least square method ⇒ The average of the curvature inverse is used to validate it
Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group all adjacent points with kmax = kmin ≈ K The radius and the center are approximated by a least square method ⇒ The average of the curvature inverse is used to validate it
Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17
Introduction Primitives Extraction Problems Conclusion
Features of Cones and Cylinders :
P P r r S Principale Directions Principale Curvatures Axis 1 Axis 2 Axis 1 Axis 2 P 1 / r P 1 / r
α
Recovering Primitives in 3D CAD / R.B´ eni` ere 9/17
Introduction Primitives Extraction Problems Conclusion
Features of Cones and Cylinders :
P P r r S Principale Directions Principale Curvatures Axis 1 Axis 2 Axis 1 Axis 2 P 1 / r P 1 / r
α
Criterion of belonging to a same cone : If P1 et P2 ∈ same cone ⇒ α1 = α2
P2 1/Cur2 1/Cur1 P1 P’2 P’1 Dir0_1 Dir0_2 n2 n1
α1 α2
Recovering Primitives in 3D CAD / R.B´ eni` ere 9/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures
Recovering Primitives in 3D CAD / R.B´ eni` ere 10/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group adjacent points by the criterion of belonging
Recovering Primitives in 3D CAD / R.B´ eni` ere 10/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group adjacent points by the criterion of belonging
Recovering Primitives in 3D CAD / R.B´ eni` ere 10/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group adjacent points by the criterion of belonging For each point : pointAxisTheo = point + normal ∗ radius ⇒ Rotation Axis ⇒ α angle between Axis and Dir=0
α = π ⇒ Cylinder : Average curvature ⇒ Radius α = π ⇒ Cone : Intersection between each plane created by the two principal directions of one point ⇒ Vertex
Recovering Primitives in 3D CAD / R.B´ eni` ere 10/17
Introduction Primitives Extraction Problems Conclusion
From Curvatures Group adjacent points by the criterion of belonging For each point : pointAxisTheo = point + normal ∗ radius ⇒ Rotation Axis ⇒ α angle between Axis and Dir=0
α = π ⇒ Cylinder : Average curvature ⇒ Radius α = π ⇒ Cone : Intersection between each plane created by the two principal directions of one point ⇒ Vertex
Recovering Primitives in 3D CAD / R.B´ eni` ere 10/17
Introduction Primitives Extraction Problems Conclusion
Recovering Primitives in 3D CAD / R.B´ eni` ere 11/17
Introduction Primitives Extraction Problems Conclusion
http ://shapes.aimatshape.net
Recovering Primitives in 3D CAD / R.B´ eni` ere 12/17
Introduction Primitives Extraction Problems Conclusion
The mesh can not have many point
Recovering Primitives in 3D CAD / R.B´ eni` ere 13/17
Introduction Primitives Extraction Problems Conclusion
The mesh can not have many point
Recovering Primitives in 3D CAD / R.B´ eni` ere 13/17
Introduction Primitives Extraction Problems Conclusion
The mesh can not have many point
Recovering Primitives in 3D CAD / R.B´ eni` ere 13/17
Introduction Primitives Extraction Problems Conclusion
A solution can be to segment the mesh (by the dihedral angle for example)
Recovering Primitives in 3D CAD / R.B´ eni` ere 14/17
Introduction Primitives Extraction Problems Conclusion
A solution can be to segment the mesh (by the dihedral angle for example)
Recovering Primitives in 3D CAD / R.B´ eni` ere 14/17
Introduction Primitives Extraction Problems Conclusion
A solution can be to segment the mesh (by the dihedral angle for example)
Recovering Primitives in 3D CAD / R.B´ eni` ere 14/17
Introduction Primitives Extraction Problems Conclusion
The mesh can not have many point
Recovering Primitives in 3D CAD / R.B´ eni` ere 15/17
Introduction Primitives Extraction Problems Conclusion
The mesh can not have many point
Recovering Primitives in 3D CAD / R.B´ eni` ere 15/17
Introduction Primitives Extraction Problems Conclusion
The mesh can not have many point
Recovering Primitives in 3D CAD / R.B´ eni` ere 15/17
Introduction Primitives Extraction Problems Conclusion
Our method take a Mesh
Recovering Primitives in 3D CAD / R.B´ eni` ere 16/17
Introduction Primitives Extraction Problems Conclusion
Our method take a Mesh⇒ extract primitives.
Recovering Primitives in 3D CAD / R.B´ eni` ere 16/17
Introduction Primitives Extraction Problems Conclusion
Our method take a Mesh⇒ extract primitives. Future Work Cut and Fuse Primitives to reconstruct the continue representation
Recovering Primitives in 3D CAD / R.B´ eni` ere 16/17
Introduction Primitives Extraction Problems Conclusion
Our method take a Mesh⇒ extract primitives. Future Work Cut and Fuse Primitives to reconstruct the continue representation Add a Segmentation step to the method
Recovering Primitives in 3D CAD / R.B´ eni` ere 16/17
Introduction Primitives Extraction Problems Conclusion
Our method take a Mesh⇒ extract primitives. Future Work Cut and Fuse Primitives to reconstruct the continue representation Add a Segmentation step to the method Deal with noisy mesh
Recovering Primitives in 3D CAD / R.B´ eni` ere 16/17
Introduction Primitives Extraction Problems Conclusion
Site : www.lirmm.fr/˜beniere Mail : roseline.beniere@lirmm.fr C4W site : www.c4w.com
Roseline B´ eni` ere, G. Subsol, G. Gesqui` ere, F. Le Breton and W. Puech, Recovering Primitives in 3D CAD meshes, SPIE, San Francisco, 2011
Recovering Primitives in 3D CAD / R.B´ eni` ere 17/17