Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
International Journal of Computer Vision
Smooth invariant interpolation of rotations
ACM Transactions on Graphics (TOG)
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Dynamic Programming Generation of Curves on Brain Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the curvature of curves and surfaces defined by normalforms
Computer Aided Geometric Design
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces: 730
Journal of Computational Physics
Motion of curves constrained on surfaces using a level-set approach
Journal of Computational Physics
Rapid and accurate computation of the distance function using grids
Journal of Computational Physics
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Constrained interpolation with rational cubics
Computer Aided Geometric Design
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Geometric design of motions constrained by a contacting surface pair
Computer Aided Geometric Design
Existence of set-interpolating and energy-minimizing curves
Computer Aided Geometric Design
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computer Aided Geometric Design
Fourth order partial differential equations on general geometries
Journal of Computational Physics
Fair curve networks in nonlinear geometries
SIGGRAPH '05 ACM SIGGRAPH 2005 Sketches
Constructing spherical curves by interpolation
Advances in Engineering Software
Skinning with dual quaternions
Proceedings of the 2007 symposium on Interactive 3D graphics and games
C-DIST: efficient distance computation for rigid and articulated models in configuration space
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Reconstruction of deforming geometry from time-varying point clouds
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Bézier curves and C2 interpolation in Riemannian manifolds
Journal of Approximation Theory
Note on curve and surface energies
Computer Aided Geometric Design
Constrained curve fitting on manifolds
Computer-Aided Design
Recursive computation of Hermite spherical spline interpolants
Journal of Computational and Applied Mathematics
Geometric skinning with approximate dual quaternion blending
ACM Transactions on Graphics (TOG)
Efficient distance computation in configuration space
Computer Aided Geometric Design
Subdivision schemes for the fair discretization of the spherical motion group
Journal of Computational and Applied Mathematics
MLS-based scalar fields over triangle meshes and their application in mesh processing
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Generalized penetration depth computation based on kinematical geometry
Computer Aided Geometric Design
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computer Aided Geometric Design
Existence of set-interpolating and energy-minimizing curves
Computer Aided Geometric Design
Patch layout from feature graphs
Computer-Aided Design
Merging and smoothing machining boundaries on cutter location surfaces
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Nonparametric Regression between General Riemannian Manifolds
SIAM Journal on Imaging Sciences
Couple points --- a local approach to global surface analysis
Proceedings of the 7th international conference on Curves and Surfaces
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
Approximating geodesics on point set surfaces
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
ACM Transactions on Graphics (TOG)
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Variational interpolation in curved geometries has many applications, so there has always been demand for geometrically meaningful and efficiently computable splines in manifolds. We extend the definition of the familiar cubic spline curves and splines in tension, and we show how to compute these on parametric surfaces, level sets, triangle meshes, and point samples of surfaces. This list is more comprehensive than it looks, because it includes variational motion design for animation, and allows the treatment of obstacles via barrier surfaces. All these instances of the general concept are handled by the same geometric optimization algorithm, which minimizes an energy of curves on surfaces of arbitrary dimension and codimension.