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, France 14 octobre 2010 R´ eunion ICAR Recovering Primitives in 3D CAD / R.B´ eni` ere 1/17

Introduction Primitives Extraction Problems Conclusion Objective 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 Objective 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 Objective 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 Objective 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 Previews Benk˜ o et al . 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 Previews Benk˜ o et al . 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 Previews Benk˜ o et al . 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 : Segmentation 1 Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17

Introduction Primitives Extraction Problems Conclusion Previews Benk˜ o et al . 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 : Segmentation 1 Classification 2 Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17

Introduction Primitives Extraction Problems Conclusion Previews Benk˜ o et al . 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 : Segmentation 1 Classification 2 Fitting 3 Recovering Primitives in 3D CAD / R.B´ eni` ere 3/17

Introduction Primitives Extraction Problems Conclusion Curvature 2D and 3D N P C R Curvature 2D : Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17

Introduction Primitives Extraction Problems Conclusion Curvature 2D and 3D N P C R Curvature 2D : ⇒ K p = 1 R Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17

Introduction Primitives Extraction Problems Conclusion Curvature 2D and 3D N P C R Curvature 2D : ⇒ K p = 1 R Curvature 3D : N PL S P C Dir min Dir max Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17

Introduction Primitives Extraction Problems Conclusion Curvature 2D and 3D N P C R Curvature 2D : ⇒ K p = 1 R Curvature 3D : N PL 2 Principal Curvatures S ( k max et k min ) P C 2 Principal Directions Dir min Dir max ( Dir max et Dir min ) Normal Recovering Primitives in 3D CAD / R.B´ eni` ere 4/17

Introduction Primitives Extraction Problems Conclusion Primitive curvature features 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 Primitive curvature features The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : P1 P2 Plane ⇒ k max = k min = 0 Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17

Introduction Primitives Extraction Problems Conclusion Primitive curvature features The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : P1 P2 Plane ⇒ k max = k min = 0 P1 P2 1 Sphere ⇒ k max = k min = rSp � = 0 Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17

Introduction Primitives Extraction Problems Conclusion Primitive curvature features The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : P1 P2 Plane ⇒ k max = k min = 0 P1 P2 1 Sphere ⇒ k max = k min = rSp � = 0 P1 P2 1 Cylinder ⇒ k min = 0 et k max = rCy Dir min = Generating line Recovering Primitives in 3D CAD / R.B´ eni` ere 5/17

Introduction Primitives Extraction Problems Conclusion Primitive curvature features The points contained in Plane, Sphere, Cone or Cylinder have specific features on curvature : P1 P2 Plane ⇒ k max = k min = 0 P1 P2 1 Sphere ⇒ k max = k min = rSp � = 0 P1 P2 1 Cylinder ⇒ k min = 0 et k max = rCy Dir min = 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 Discrete Curvature 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 Discrete Curvature In a mesh, we compute a discrete curvature for each point. We use the Euler formula k n = k max cos 2 ( θ ) + k min sin 2 ( θ ) With θ the angle between n and Dir max . The neighbors are studied to approximate k max , k min and θ . Recovering Primitives in 3D CAD / R.B´ eni` ere 6/17

Introduction Primitives Extraction Problems Conclusion Discrete Curvature In a mesh, we compute a discrete curvature for each point. We use the Euler formula k n = k max cos 2 ( θ ) + k min sin 2 ( θ ) With θ the angle between n and Dir max . The neighbors are studied to approximate k max , k min 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 Discrete Curvature In a mesh, we compute a discrete curvature for each point. We use the Euler formula k n = k max cos 2 ( θ ) + k min sin 2 ( θ ) With θ the angle between n and Dir max . The neighbors are studied to approximate k max , k min 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 Planes Extraction From Curvatures Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17

Introduction Primitives Extraction Problems Conclusion Planes Extraction From Curvatures Group all adjacent points with k max = k min = 0 Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17

Introduction Primitives Extraction Problems Conclusion Planes Extraction From Curvatures Group all adjacent points with k max = k min = 0 Recovering Primitives in 3D CAD / R.B´ eni` ere 7/17

Introduction Primitives Extraction Problems Conclusion Planes Extraction From Curvatures Group all adjacent points with k max = k min = 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 Planes Extraction From Curvatures Group all adjacent points with k max = k min = 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 Spheres Extraction From Curvatures Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17

Introduction Primitives Extraction Problems Conclusion Spheres Extraction From Curvatures Group all adjacent points with k max = k min ≈ K Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17

Introduction Primitives Extraction Problems Conclusion Spheres Extraction From Curvatures Group all adjacent points with k max = k min ≈ K Recovering Primitives in 3D CAD / R.B´ eni` ere 8/17