Deepneuralnetworksbecamewidespreadinnumerousfieldsofimageprocessing, includingsemanticsegmen tation. U-Net is a popular choice for semantic segmentation of microscopy images, e.g. histological sections. In this paper,...
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In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAH...
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In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAHT） B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., t^n-5}, n 7〉 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.
As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane ca...
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As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane.
Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right heli...
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Minimal surface is extensively employed in many areas. In this paper, we propose a control mesh representation of a class of minimal surfaces, called generalized helicoid minimal surfaces, which contain the right helicoid and catenoid as special examples. We firstly construct the Bézier-like basis called AHT Bézier basis in the space spanned by {1, t, sint, cost, sinht, cosht}, t∈[0,α], α∈[0,5π/2]. Then we propose the control mesh representation of the generalized helicoid using the AHT Bézier basis. This kind of representation enables generating the minimal surfaces using the de Casteljau-like algorithm in CAD/CAGD mod- elling systems.
Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical...
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Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.
The designing of offset curves and surfaces is an essential task in many industrial applications such as the generation of tool-path geometry in numerical-control machining and robot-path planning. The paper discuses ...
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The designing of offset curves and surfaces is an essential task in many industrial applications such as the generation of tool-path geometry in numerical-control machining and robot-path planning. The paper discuses problems that are encountered in the designing of offsets, gives a brief survey of existing techniques, and suggests some directions for future research.
This paper presents the matrix representation for the hyperbolic polynomial B-spline basis and the algebraic hyperbolic Bézier basis in a recursive way, which are both generated over the space Ωn=span{sinht, cos...
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This paper presents the matrix representation for the hyperbolic polynomial B-spline basis and the algebraic hyperbolic Bézier basis in a recursive way, which are both generated over the space Ωn=span{sinht, cosht, tn-3, , t, 1} in which n is an arbitrary integer larger than or equal to 3. The conversion matrix from the hyperbolic polynomial B-spline basis of arbitrary order to the algebraic hyperbolic Bézier basis of the same order is also given by a recursive approach. As examples, the specific expressions of the matrix representation for the hyperbolic polynomial B-spline basis of order 4 and the algebraic hyperbolic Bézier basis of order 4 are given, and we also construct the conversion matrix between the two bases of order 4 by the method proposed in the paper. The results in this paper are useful for the evaluation and conversion of the curves and surfaces constructed by the two bases.
This paper presents a novel approach to consider optimal multi-degree reduction of Bézier curve with G1-continuity. By minimizing the distances between corresponding control points of the two curves through degre...
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This paper presents a novel approach to consider optimal multi-degree reduction of Bézier curve with G1-continuity. By minimizing the distances between corresponding control points of the two curves through degree raising, optimal approximation is achieved. In contrast to traditional methods, which typically consider the components of the curve separately, we use geometric information on the curve to generate the degree reduction. So positions and tangents are preserved at the two endpoints. For satisfying the solvability condition, we propose another improved algorithm based on regularization terms. Finally, numerical examples demonstrate the effectiveness of our algorithms.
In this paper, we propose a novel free-form deformation （FFD） technique, RDMS-FFD （Rational DMS-FFD）, based on rational DMS-spline volumes. RDMS-FFD inherits some good properties of rational DMS-spline volumes and...
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In this paper, we propose a novel free-form deformation （FFD） technique, RDMS-FFD （Rational DMS-FFD）, based on rational DMS-spline volumes. RDMS-FFD inherits some good properties of rational DMS-spline volumes and combines more deformation techniques than previous FFD methods in a consistent framework, such as local deformation, control lattice of arbitrary topology, smooth deformation, multiresolution deformation and direct manipulation of deformation. We first introduce the rational DMS-spline volume by directly generalizing the previous results related to DMS-splines. How to generate a tetrahedral domain that approximates the shape of the object to be deformed is also introduced in this paper. Unlike the traditional FFD techniques, we manipulate the vertices of the tetrahedral domain to achieve deformation results. Our system demonstrates that RDMS-FFD is powerful and intuitive in geometric modeling.
DIscrete REConstruction Techniques (DIRECT) is a program system for generating test images, for computing their projections, for performing reconstructions, for comparing reconstructed images, and for visualizing the ...
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