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Spherical harmonic map for topological sphere. The David head surface is mapped to the unit sphere, the mapping is conformal. All such kind of
mappings form a 6 dimensional group.
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Holomorphic 1-form for surfaces with both handles and boundaries.
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Hyperbolic Ricci flow for high genus surface conformal mapping.
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Euclidean Ricci flow for multi-holed annulus conformal mapping. The surface is mapped to a planar annulus, with
all boundaries are circular. The centers and the radii of the inner circles are automatically determined by the
geometry of the original surface, which can be used as the fingure prints of the shapes.
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SlitMap for multi-holed annulus surface. First, we compute special holomorphic 1-forms, the integration of the 1-form
maps the surface to an annulus with circular slits, the boundaries are mapped to the slits. The map can also maps the surface
to a rectangle with horizontal slits.
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Surface conformal parameterization using LSCM with two fixed vertices and free boundary condition.
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Harmonic map for topological disks. The human face surface is mapped to a convex planar domain.
User can specify the boundry conditions. If the boundary map is a homeomorphism, then the mapping is a diffeomorphism.
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Holomorphic 1-form for a genus two surface. The holomorphic 1-form induces a natural quad-remeshing of the surface.
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Volumetric hex-remeshing based on Ricci flow.
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Mesh Spline conversion using conformal mapping.
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Mesh Spline conversion using conformal mapping using spherical harmonic maps.
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Euclidean ricci flow or holomorphic 1-form methods for generating geometry image of David head model.
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Euclidean and hyperbolic Ricci flow conformal parameterization for david head with two holes.
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Euclidean Ricci flow conformal parameterization for david head with two holes. Two boundaries are mapped to
straight lines, one boundary is mapped to a circle.
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Euclidean Ricci flow conformal parameterization. Two input surfaces differ by an isometric deformation, the second one
obtained by benting the first one. The conformal mapping images are identical.
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Converting mesh to TSplines using holomorphic 1-form.
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Texture synthesis using conformal parameterizaiton.
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Geometric texture synthesis using Ricci flow method.
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Non-photo realistic rendering using Euclidean Ricci flow. Design a special vector field, with prescribed singularities.
This is equivalent to design a flat metric,
with prescribed cone singularities. By using Euclidean Ricci flow, it can be easily achieved.
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Surface polycube maps using Euclidean Ricci flow. Deform a surface to a polycube map
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The universal covering space of a genus one mesh (kitten) with the flat metric tessellates the plane.
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Harmonic 1-form, conjugate harmonic 1-form and holomorphic 1-form on a genus 2 surface.
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Conformal parameterizations for surfaces with different topologies and geometries.
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Conformal parameterizations and texture mapping for surfaces with different topologies and geometries.
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