Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deformable curve and surface finite-elements for free-form shape design
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
A physically based approach to 2–D shape blending
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Feature-based image metamorphosis
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Scheduled Fourier volume morphing
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Shape transformation for polyhedral objects
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
Animating images with drawings
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Feature-based volume metamorphosis
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
History consideration in reconstructing polyhedral surfaces from parallel slices
Proceedings of the 7th conference on Visualization '96
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Optimal surface reconstruction from planar contours
Communications of the ACM
Digital Image Warping
Distance Field Manipulation of Surface Models
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Feature-based Surface Decomposition for Correspondence and Morphing Between Polyhedra
CA '98 Proceedings of the Computer Animation
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
VIS '94 Proceedings of the conference on Visualization '94
Wavelet frame based surface reconstruction from unorganized points
Journal of Computational Physics
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Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that combines these two tasks into a single step. We create a transformation between two N-dimensional objects by casting this as a scattered data interpolation problem in N + 1 dimensions. For the case of 2D shapes, we place all of our data constraints within two planes, one for each shape. These planes are placed parallel to one another in 3D. Zero-valued constraints specify the locations of shape boundaries and positive-valued constraints are placed along the normal direction in towards the center of the shape. We then invoke a variational interpolation technique (the 3D generalization of thin-plate interpolation), and this yields a single implicit function in 3D. Intermediate shapes are simply the zero-valued contours of 2D slices through this 3D function. Shape transformation between 3D shapes can be performed similarly by solving a 4D interpolation problem. To our knowledge, ours is the first shape transformation method to unify the tasks of implicit function creation and interpolation. The transformations produced by this method appear smooth and natural, even between objects of differing topologies. If desired, one or more additional shapes may be introduced that influence the intermediate shapes in a sequence. Our method can also reconstruct surfaces from multiple slices that are not restricted to being parallel to one another.