Computer Aided Geometric Design

Implicitization usually focuses on plane curves and (hyper)surfaces, in other words, varieties of codimension 1. In this paper we shift the focus on space curves and, more generally, on varieties of codimension larger than 1, and ...

• Present an algorithm based on Chow forms to implicitize high codimensional varieties.

In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology ...

• The algebraicity of the persistent homology of the offset filtration is proved.

• A framework is given to represent curve segments or surface patches using semi-algebraic sets.

We provide a framework for representing segments of rational planar curves or patches of rational tensor product surfaces with no singularities using semi-algebraic sets. Given a rational planar curve segment or a rational tensor ...

• The Gauss–Lobatto polygon of Pythagorean hodograph curves is introduced.
• A ...

The Gauss–Legendre polygon of Pythagorean hodograph (PH) curves can be used as the rectifying control polygon, which has (i) the end point interpolation property, (ii) the rectifying property, and (iii) the same degree of freedom as ...

• We compare existing and new multisided gradient mesh primitives.
• Two new ...

The gradient mesh is a powerful vector graphics primitive capable of representing detailed and scalable images. Borrowing techniques from 3D graphics such as subdivision surfaces and generalised barycentric coordinates, it has been ...

Point clouds provide rich geometric information about a shape and a deep neural network can be used to learn effective and robust features. In this paper, we propose a novel local feature descriptor, which employs a Siamese network to ...

• This paper introduces a low complexity and low-dimensional local descriptor.
• We ...

• Stochastic isogeometric analysis method for random responses of plates is proposed.

This paper proposes the stochastic isogeometric analysis (IGA) method in conjunction with the perturbation technique for random response analysis of plate structures. Specifically, the benchmark solutions of stochastic deflection ...

Generalized barycentric coordinates (GBC) are widely used in computer graphics and related areas and there are a few kinds of GBC in the literature. In this paper we propose positive and smooth Gordon-Wixom coordinates (PSGWC) for the ...

• We propose positive and smooth Gordon-Wixom coordinates (PSGWC) for planar polygon.

• Methods to construct rational curves with rational arc lengths by direct integration are developed.

A methodology for the construction of rational curves with rational arc length functions, by direct integration of hodographs, is developed. For a hodograph of the form r ′ ( ξ ) = ( u 2 ( ξ ) − v 2 ( ξ ) , 2 u ( ξ ) v ( ξ ) ) / w 2 ( ...