Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Proceedings of the fourteenth annual symposium on Computational geometry
Contour interpolation and surface reconstruction of smooth terrain models
Proceedings of the conference on Visualization '98
Interpolating nets of curves by smooth subdivision surfaces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
An Algorithm for Polygon Subdivision Based on Vertex Normals
CGI '97 Proceedings of the 1997 Conference on Computer Graphics International
G1 Surface Interpolation for Irregularly Located Data
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Interpolating Patches Between Cubic Boundaries
Interpolating Patches Between Cubic Boundaries
Implicit surface reconstruction from contours
The Visual Computer: International Journal of Computer Graphics - Special section on implicit surfaces
Contour interpolation by straight skeletons
Graphical Models
b-morphs between b-compatible curves in the plane
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Topologically correct reconstruction of tortuous contour forests
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Defining, contouring, and visualizing scalar functions on point-sampled surfaces
Computer-Aided Design
Topologically correct reconstruction of tortuous contour forests
Computer-Aided Design
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The topic of interpolation between slices has been an intriguing problem for many years, as it offers means to visualize and investigate a three-dimensional object given only by its level sets. A slice consists of multiple non-intersecting simple contours, each defined by a cyclic list of vertices. An interpolation solution matches between a number of such slices (two or more at a time), providing means to create a closed surface connecting these slices, or the equivalent morph from one slice to another. We offer a method to incorporate the influence of more than two slices at each point in the reconstructed surface. We investigate the flow of the surface from one slice to the next by matching vertices and extracting differential geometric quantities from that matching. Interpolating these quantities with surface patches then allows a nonlinear reconstruction which produces a free-form, nonintersecting surface. No assumptions aremade about the input, such as on the number of contours in each slice, their geometric similarity, their nesting hierarchy, etc., and the proposed algorithm handles automatically all branching and hierarchical structures. The resulting surface is smooth and does not require further subdivision measures.