Through a local curvature analysis for a small patch of point cloud around the pick-point, the 4 surface types can be classified: 1. Planar surface: The absolute values of the two principal curvatures are both small. 2. Parabolic surface: The absolute value of one of the two principal curvatures is small. 3. Elliptic surface: Two principal curvatures are both not small and have the same sign. 4. Hyperbolic surface: Two principal curvatures are both not small and have different signs. According to the curvatures: 1. Planar: Fit plane 2. Parabolic: Fit cone, fit cylinder 3. Elliptic: Fit torus, fit sphere 4. Hyperbolic: Fit torus Note: 1. A cylinder is a special instance of cone with zero vertex angle. 2. A sphere is a special instance of torus with zero mean radius (spindle torus). The radius of sphere is equal to the tube radius of spindle torus. void function curvature2surface begin: if (planar) fit a plane; else if (parabolic) begin: fit a cone; if (small vertex angle) fit a cylinder; end: else if (elliptic) begin: fit a torus; if (small mean radius) fit a sphere; end: else fit a torus; end: spindle torus, mean radius, tube radius, vertex angle, 3-D object recognition, point cloud, feature extraction, least squares, Hough transform, RANSAC, plane, sphere, cylinder, cone, torus, implicit curve, implicit surface, parametric curve, parametric surface, wall, pipe, reducer, elbow, orthogonal distance fitting, segmentation, automation, local curvature analysis, differential geometry, Gaussian error model, curve fitting, surface fitting, principal component analysis, PCA, surfcurv, curvsurf, LNCS 3151.
Semi-automatic extraction of geometric primitives per 1 point picking. - YouTube |
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