A marching method for parametric surface/surface intersection
Computer Aided Geometric Design
The NURBS book
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The approximation power of moving least-squares
Mathematics of Computation
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Interactive boolean operations on surfel-bounded solids
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2004 Papers
Curvature formulas for implicit curves and surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
A survey of point-based techniques in computer graphics
Computers and Graphics
Implementation of a divide-and-conquer method for intersection of parametric surfaces
Computer Aided Geometric Design
The domain of a point set surface
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Constructing 3D motions from curvature and torsion profiles
Computer-Aided Design
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In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data). We use the moving least-squares (MLS) surface as the underlying surface representation for acquired point-sampled geometry. Based on the MLS surface definition, we derive closed formula for computing curvature of planar curves on the MLS surface. A set of intersection algorithms including line and MLS surface intersection, curvature-adaptive plane and MLS surface intersection, and polygonal mesh and MLS surface intersection are successively developed. Further, an algorithm for NURBS and MLS surface intersection is then developed. It first adaptively subdivides NURBS surfaces into polygonal mesh, and then intersects the mesh with the MLS surface. The intersection points are mapped to the NURBS surface through the Gauss-Newton method. Based on the above algorithms, a prototype system has been implemented. Through various examples from the system, we demonstrate that direct Boolean intersection between designed geometry and acquired geometry offers a useful and effective means for the shape modeling applications where point-cloud data is involved.