Abstract: Aiming at the current methods of drawing curves onto point clouds which are weak robustness while dealing with multi-layer point set surface models, and are lack of guiding by intuitive geometric features contained in point clouds, an approach based on spatial grid and directed by curvature map is proposed. Firstly, subdivide point clouds into spatial grids and estimate curvature based on three parameters Shepard surface. Secondly, choose data point (point used to construct initial curve) according to geometric features illustrated in curvature image, then search the nearest non-empty grid (a grid contains at least one measured point) intersected with the projected ray started at the above data point. Subsequently, construct the k-nearest neighborhoods of the above nearest valid grid as the target point cloud surface for point projection algorithm, then calculate the projection of the chosen data point. Thirdly, interpolate each projected vertex of chosen data point to construct the initial curve. And finally, construct normal curve with the same knot sequences as the initial curve to determine project directions of curve, then apply binary division algorithm and projection algorithm based on spatial grids to project the initial curve onto point set surfaces. Application comparison shows that the introduction of spatial grids remarkably improves the stability of point projection algorithm, and the guidance by curvature map enhances users’abilities of discernment and analysis of geometric features implied in point cloud surfaces.

Key words: Curvature estimation, Curve, Point projection, Point set surfaces, Reverse engineering, Spatial grid