Computer Aided Geometric Design

Geometric surface models are extensively utilized in brain imaging to analyze and compare three-dimensional anatomical shapes. Due to the intricate nature of the brain surface, rather than examining the entire cortical surface, we are introducing ...

The Pythagorean-Hodograph curve (PH curve) is a valuable curve type extensively utilized in computer-aided geometric design and manufacturing. This paper presents an approach to approximate a planar algebraic curve within a bounding box by ...

• Proposing a framework to G2 approximate planar algebraic curves with correct topology and certified error control.
• Proposing a construction method of planar quintic PH curve with invariant convexity based on G2 interpolation.
• ...

Analyzing the symmetries present in point clouds, which represent sets of 3D coordinates, is important for understanding their underlying structure and facilitating various applications. In this paper, we propose a novel decomposition-based ...

• We present a theoretical framework to assess exact point clouds symmetries via decomposition-based method.
• The exact symmetry group of the 3D point cloud is derived from the symmetries of simpler components.
• The method can be ...

In this paper, we present a novel face-based random walk method aimed at addressing the 3D semantic segmentation issue. Our method utilizes a one-dimensional convolutional neural network for detailed feature extraction from sequences of ...

• Segment 3D meshes using a hybrid architecture, gated recurrent units, and 1D convolutional neural networks.
• Extraction of geometric features from 3D mesh faces using mathematical algorithms; random walks.
• Apply deep learning ...

With the help of the Cox-de Boor recursion formula and the recurrence relation of the Bernstein polynomials, two categories of recursive algorithms for calculating the conversion matrix from an arbitrary non-uniform B-spline basis to a Bernstein ...

• We propose two algorithms to compute the conversion matrix from B-spline basis functions to Bézier polynomials.
• One algorithm computes the entries of the conversion matrix directly by recursion.
• Another algorithm computes the ...

A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the ...

• Introducing β-involutes and β-evolutes in “non-intrinsic description”.
• Introducing a novel parametrization method for general T-surfaces.
• Presenting a novel algorithm for reconstructing T-surfaces from point clouds.
• ...

Whilst Paul de Casteljau is now famous for his fundamental algorithm of curve and surface approximation, little is known about his other findings. This article offers an insight into his results in geometry, algebra and number theory.

Related to ...

• Insight into de Casteljau's contributions to geometry, algebra, and number theory.
• Algebraic smoothing with polar forms using Aitken, de Boor, de Casteljau.
• Metric geometry advances: 14-point strophoid, geometric optics, regular ...

With great enthusiasm and admiration we would like to pay tribute to Paul de Faget de Casteljau for his essential contribution to CAGD. Motivated by the development of automated human-computer collaboration for car industry, not only was he the ...

• Review Chebyshevian blossoms in keeping with de Casteljau's work.
• Review dimension elevation and associated convergence properties with some (new) examples.
• Illustrate design and convergence in rational spaces defined by poles.

Earlier results on various quaternionic Bézier parametrizations of Darboux cyclides are extended to bidegree ( 2 , 1 ) parameterizations of a wider class of surfaces containing at least two families of circles. The focus is on one special family ...

• Quaternionic Bezier formulas of bidegree (2,1) for rational parametrization of surfaces are studied.
• In particular, new parameterizations for one-oval and two-oval Darboux cyclides are generated.
• Any surfaces that include two ...

Feature curves are space curves identified by color or curvature variations in a shape, which are crucial for human perception (Biederman, 1995). Detecting these characteristic lines in 3D digital models becomes important for recognition and ...

• Overview of three HT-based approaches for spatial profiles identification and approximation.
• Feature curves representation for 3D digital models.
• Discussion of the advantages, limitations, and applicability of each method.
• ...