IEEE Transactions on Pattern Analysis and Machine Intelligence
Offsetting operations in solid modelling
Computer Aided Geometric Design
Piecewise-circular curves for geometric modeling
IBM Journal of Research and Development
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
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
2-D shape blending: an intrinsic solution to the vertex path problem
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Warping and morphing of graphical objects
Warping and morphing of graphical objects
Improved constructions of Delaunay based contour surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Optimal surface reconstruction from planar contours
Communications of the ACM
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
NPAR '02 Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering
Shape Averaging and it's Applications to Industrial Design
IEEE Computer Graphics and Applications
Shape Blending Using the Star-Skeleton Representation
IEEE Computer Graphics and Applications
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Inbetweening for computer animation utilizing moving point constraints
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
The problems of computer-assisted animation
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Reconstruction and Simplification of Surfaces from Contours
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
ACM SIGGRAPH 2004 Papers
Implicit surface reconstruction from contours
The Visual Computer: International Journal of Computer Graphics - Special section on implicit surfaces
Tightening: curvature-limiting morphological simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Proceedings of the 2005 ACM symposium on Solid and physical modeling
ACM SIGGRAPH 2005 Papers
Efficient Shape Matching Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the twenty-second annual symposium on Computational geometry
3D Surface Matching and Recognition Using Conformal Geometry
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
MEDIVIS '06 Proceedings of the International Conference on Medical Information Visualisation--BioMedical Visualisation
2D shape deformation using nonlinear least squares optimization
The Visual Computer: International Journal of Computer Graphics
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Nonlinear interpolation between slices
Proceedings of the 2007 ACM symposium on Solid and physical modeling
G1-smooth branching surface construction from cross sections
Computer-Aided Design
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
As-rigid-as-possible shape deformation and interpolation
Journal of Visual Communication and Image Representation
Curve matching for open 2D curves
Pattern Recognition Letters
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
SAMBA: steadied choreographies
CAe '12 Proceedings of the Eighth Annual Symposium on Computational Aesthetics in Graphics, Visualization, and Imaging
Tweening boundary curves of non-simple immersions of a disk
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
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We define b-compatibility for planar curves and propose three ball morphing techniques (b-morphs) between pairs of b-compatible curves. B-morphs use the automatic ball-map correspondence, proposed by Chazal et al. [12], from which they derive vertex trajectories (Linear, Circular, Parabolic). All are symmetric, meeting both curves with the same angle, which is a right angle for the Circular and Parabolic. We provide simple constructions for these b-morphs using the maximal disks in the finite region bounded by the two curves. We compare the b-morphs to each other and to other simple morphs (Linear Interpolation (LI), Closest Projection (CP), Curvature Interpolation (CI), Laplace Blending (LB), Heat Propagation (HP)) using seven measures of quality deficiency (travel distance, distortion, stretch, local acceleration, surface area, average curvature, maximal curvature). We conclude that the ratios of these measures depends heavily on the test case, especially for LI, CI, and LB, which compute correspondence from a uniform geodesic parameterization. Nevertheless, we found that the Linear b-morph has consistently the shortest travel distance and that the Circular b-morph has the least amount of distortion.