Pessimal Guesses may be Optimal: A Counterintuitive Search Result
IEEE Transactions on Pattern Analysis and Machine Intelligence
Filling polygonal holes with rectangular patches
Theory and practice of geometric modeling
A triangulation algorithm from arbitrary shaped multiple planar contours
ACM Transactions on Graphics (TOG)
The homotopy model: a generalized model for smooth surface generation from cross sectional data
The Visual Computer: International Journal of Computer Graphics - Special issue on computer graphics international '89(CGI'89)
ACM Transactions on Graphics (TOG)
Reconstruction of C1 closed surfaces with branching
Geometric modelling
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Sectional-curvature preserving skinning surfaces
Computer Aided Geometric Design
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Shape reconstruction from contours using isotopic deformation
CVGIP: Graphical Models and Image Processing
Optimal surface reconstruction from planar contours
Communications of the ACM
A system for reconstructing and visualising three-dimensional objects
Computers & Geosciences
Surface Reconstruction Between Simple Polygons via Angle Criteria
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Conversion of complex contour line definitions into polygonal element mosaics
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Beta-connection: Generating a family of models from planar cross sections
ACM Transactions on Graphics (TOG)
Joint registration and averaging of multiple 3D anatomical surface models
Computer Vision and Image Understanding
Cross-sectional design with curvature constraints
Computer-Aided Design
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This paper proposes a framework for constructing G1 surfaces that interpolate data points on parallel cross sections, consisting of simple disjoined and non-nested contours, the number of which may vary from plane to plane. Using appropriately estimated cross tangent vectors at the given points, we split the problem into a sequence of local Hermite problems, each of which can be one of the following three types: "one-to-one", "one-to-many" or "many-to-many".The solution of the "one-to-many" branching problem, where one contour on the i-plane is to be connected to M-contours on the (i+1)-plane, is based on combining skinning with trimming and hole filling. More specifically, we firstly construct a G1 surrounding curve of all M-contours on the (i+1)-plane, consisting of contour portions connected with linear segments, the so-called bridges. Next, we build a surface that skins the i-plane contour with the (i+1)-plane surrounding curve and trim suitably along the bridges. The resulting multi-sided hole is covered with quadrilateral Gordon-Coons patches that possess G1 continuity. For this purpose, we develop a hole-filling technique that employs shape-preserving guide curves and is able to preserve data symmetries. The "many-to-many" problem is handled by combining the "one-to-many" methodology with a zone-separation technique, that achieves to split the configuration into two "one-to-many" problems. The methodology, implemented as a C++ Rhino v3.0 plug-in, is illustrated via a synthetic example.