This paper explores the challenge of teaching a machine how to reverse-engineer the grid-marked surfaces used to represent data in 3D surface plots of two-variable functions. These are common in scientific and economi...
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ISBN:
(纸本)9783030863319
This paper explores the challenge of teaching a machine how to reverse-engineer the grid-marked surfaces used to represent data in 3D surface plots of two-variable functions. These are common in scientific and economic publications;and humans can often interpret them with ease, quickly gleaning general shape and curvature information from the simple collection of curves. While machines have no such visual intuition, they do have the potential to accurately extract the more detailed quantitative data that guided the surface's construction. We approach this problem by synthesizing a new dataset of 3D grid-marked surfaces (SurfaceGrid) and training a deep neural net to estimate their shape. Our algorithm successfully recovers shape information from synthetic 3D surface plots that have had axes and shading information removed, been rendered with a variety of grid types, and viewed from a range of viewpoints.
Curvature flow (planar geometric heat flow) has been extensively applied to image processing, computervision, and material science. To extend the numerical schemes and algorithms of this flow on surfaces is very sign...
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Curvature flow (planar geometric heat flow) has been extensively applied to image processing, computervision, and material science. To extend the numerical schemes and algorithms of this flow on surfaces is very significant for corresponding motions of curves and images defined on surfaces. In this work, we are interested in the geodesic curvature flow over triangulated surfaces using a level set formulation. First, we present the geodesic curvature flow equation on general smooth manifolds based on an energy minimization of curves. The equation is then discretized by a semi-implicit finite volume method (FVM). For convenience of description, we call the discretized geodesic curvature flow as dGCF. The existence and uniqueness of dGCF are discussed. The regularization behavior of dGCF is also studied. Finally, we apply our dGCF to three problems: the closed-curve evolution on manifolds, the discrete scale-space construction, and the edge detection of images painted on triangulated surfaces. Our method works for compact triangular meshes of arbitrary geometry and topology, as long as there are no degenerate triangles. The implementation of the method is also simple.
Discretized Marching Cubes (DMC) is a standard method in computergraphics and visualization for constructing 3D surfaces in data represented on a regular grid. After thresholding, it builds high-resolution surfaces b...
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ISBN:
(纸本)9788086943022
Discretized Marching Cubes (DMC) is a standard method in computergraphics and visualization for constructing 3D surfaces in data represented on a regular grid. After thresholding, it builds high-resolution surfaces by tiling surface patches halfway between objects and background in the data. This paper shows that if surfaces are built locally, in a high-resolution sub-grid of a cell instead of directly in a cell, sharp surfaces can be generated in order to preserve concave and convex object features. The main advantage is the improved geometric models that are extracted. This makes lower approximation errors and lower triangle counts possible.
For surfaces, such as Bezier or B-splines, or NURBS with positive weights, which are defined by networks of control points and for which identifiable pieces of surface are known to lie within the convex hull of a subs...
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ISBN:
(纸本)0819410314
For surfaces, such as Bezier or B-splines, or NURBS with positive weights, which are defined by networks of control points and for which identifiable pieces of surface are known to lie within the convex hull of a subset of the control points, recursive division is one of the most robust interrogation techniques available, guaranteeing except in very singular circumstances to find all components of the intersection. Offset surfaces, used where an object has a small non-zero thickness, and to determine cutter center loci where a cutting point must lie on a given surface, have not had this option. This paper describes a technique for applying recursive division interrogation to offset surfaces, where the offset is either constant or a function of surface normal. Sections I and ii recapitulate the standard theory of recursive subdivision interrogation and the definition of offset surfaces. Section iiI explores the concept of procedural interface, and section IV introduces that of a Quantized Hull. Sections V to Vii suggest a naive method of recursive division interrogation, discover why it does not work, and show how it may be salvaged.
The proceedings contain 34 papers. The topic discussed include: simplification of digital filtering algorithms using multirate concepts;controlled redundancy in interpolation-based neural nets;morphological decomposit...
The proceedings contain 34 papers. The topic discussed include: simplification of digital filtering algorithms using multirate concepts;controlled redundancy in interpolation-based neural nets;morphological decomposition of natural surfaces;modeling with multivariate B-spline surfaces over arbitrary triangulations;resolvents and their applications in computer-aided geometric design;fast space-variant texture-filtering techniques;and range image segmentation by controlled-continuity spline approximation for parallel computation.
C++ classes for the building and prototyping of spline applications are described. Flexibility, extensibility, and maximal code reuse are achieved by separating the concept of a basis from the implementations of curve...
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ISBN:
(纸本)081940747X
C++ classes for the building and prototyping of spline applications are described. Flexibility, extensibility, and maximal code reuse are achieved by separating the concept of a basis from the implementations of curves, functions, and surfaces.
We present results on optimal recovery of band- and energy-limited signals from their inaccurate samples or inner products involving prolate spheroidal wave functions.
ISBN:
(纸本)081940747X
We present results on optimal recovery of band- and energy-limited signals from their inaccurate samples or inner products involving prolate spheroidal wave functions.
Elimination theory was originally developed in the 18th and 19th centuries to find solvability criteria for a system of polynomial equations. We present some new resolvent methods that are suitable to solve important ...
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ISBN:
(纸本)081940747X
Elimination theory was originally developed in the 18th and 19th centuries to find solvability criteria for a system of polynomial equations. We present some new resolvent methods that are suitable to solve important problems in computer aided geometric design (CAGD), including implicitization, inversion, intersection, computation of self intersection points, and detection of unfaithful parametrizations of rational curves and surfaces.
We survey research in progress involving the hierarchical fitting of regular data to tensor product splines. The approach is suitable for data in any dimension and for splines in any number of variables.
ISBN:
(纸本)081940747X
We survey research in progress involving the hierarchical fitting of regular data to tensor product splines. The approach is suitable for data in any dimension and for splines in any number of variables.
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