SIAM Journal on Computing
Wires: a geometric deformation technique
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Efficient computation of geodesic shortest paths
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Free-form deformations via sketching and manipulating scalar fields
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Scattered Data Techniques for Surfaces
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A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
SMI '04 Proceedings of the Shape Modeling International 2004
Energy-minimizing splines in manifolds
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Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
VIS '04 Proceedings of the conference on Visualization '04
Computing the shortest path: A search meets graph theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Geodesic Bézier curves on triangle meshes
ACM SIGGRAPH 2006 Research posters
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Straightest geodesics on polyhedral surfaces
ACM SIGGRAPH 2006 Courses
Interpolating and approximating implicit surfaces from polygon soup
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Design of tangent vector fields
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Handle-aware isolines for scalable shape editing
ACM SIGGRAPH 2007 papers
Error bounds and optimal neighborhoods for MLS approximation
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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A novel technique that uses the Moving Least Squares (MLS) method to interpolate sparse constraints over mesh surfaces is introduced in this paper. Given a set of constraints, the proposed technique constructs, directly on the surface, a smooth scalar field that interpolates or approximates the constraints. Three types of constraints: point-value, point-gradient and iso-contour, are introduced to provide flexible control of the scalar field design. Furthermore, the framework also provides the user control over the region of influence and rate of influence decrease of the constraints, through parameter adjustment. We demonstrate that the scalar fields resulted from this framework can be used in several mesh applications such as skin deformation, region selection and curve drawing.