Articles (KMA)
Permanent URI for this collection
Browse
Recent Submissions
Item Evolution-based tool path and motion planning optimization for 5-axis CNC machining of free-form surfaces(2026) Chichell, Juan Zaragoza; Bizzarri, Michal; Ibarra, Judith Echevarrieta; Perez, Aritz; Bartoň, MichaelManufacturing of free-form geometries using 5-axis Computer Numerically Controlled (CNC) machining brings challenges in path-and motion-planning as one typically wants to minimize the manufacturing time of the object under consideration, while keeping the machining error within fine machining tolerances that ranges in tens of microns. We propose an optimization-based pipeline that, for a given toroidal and/or cylindrical flat-end cutter, simultaneously optimizes its milling paths together with its local positioning represented by the rotation and tilt functions. The proposed strategy is validated on a variety of benchmark surfaces, with different hyperparameters for the objective function and initial conditions, showing that our results provide high-quality approximations of free-form geometries using by-construction non-colliding motions of the given tool.
Item On tool wear optimized motion planning for 5-axis CNC machining of free-form surfaces using toroidal cutting tools(2025) Kruppa, Kinga; Chichell, Juan Zaragoza; Bizzarri, Michal; Bartoň, MichaelWe propose a computational framework for motion planning for 5-axis CNC machining of free-form surfaces. Given a reference surface, a set of contact paths on it, and a shape of a toroidal cutting tool as input, the proposed algorithm designs the tool motions that are by construction locally and globally collision-free, and offers a trade-off between approximation quality and tool wear using an optimization-based framework. The proposed algorithm first quickly constructs 2D time-tilt configuration spaces along each contact path, detecting regions that are collision-free. The configuration spaces are then merged into a single time-tilt configuration space to find a global tilt function to control the overall motion of the tool. An initial collision-free tilt function in B-spline form is first estimated and then optimized to minimize the machining error while distributing the tool wear as uniformly as possible along the entire cutting edge of the tool while staying in the collision-free region. Our algorithm is validated on both synthetic free-form surfaces and industrial benchmarks, showing that one can considerably reduce the tool wear without degrading the machining accuracy.Item Evaluation of breastfeeding self-efficacy among postnatal women(2025) Valachová, Jana; Dušová, Bohdana; Greplová, Kateřina; Marek, PatriceAim: The aim of this study was to evaluate mothers’ breastfeeding self-efficacy (maternal confidence) in associationwith demographic and clinical characteristics. Design: An observational longitudinal study. Methods: Data were collectedwith the Breastfeeding Self-Efficacy Scale – Short Form (BSES-SF) questionnaire from 102 breastfeeding women three daysafter delivery in three hospitals, and at the third and sixth weeks at home. Results: Parity was a key finding in the overallassessment of breastfeeding self-efficacy, with multiparous women demonstrating higher breastfeeding self-efficacy thanprimiparous women at all three time points (day three: p < 0.001; week three: p = 0.015; week six: p = 0.037). Strongcorrelations were found between all paired time points (p < 0.001). Analysis of individual questions revealed differencesprimarily related to parity, while other demographic and clinical characteristics showed only occasional significant differences.In terms of time, it was found that women need most support in the first three weeks after birth. Conclusion: The results of thisstudy provide evidence-based guidance for healthcare professionals on how to offer effective, individualized support to womenin initiating and continuing breastfeeding, both in clinical settings and at home, as well as on how to ensure accuratecommunication between both parties to help achieve this goal.Item Smooth surface finishing for 5-axis flank CNC machining of free-form geometries using custom-shaped tools(2025) Bizzarri, Michal; Rajain, Kanika; Bartoň, MichaelGeometric modeling is traditionally a key part of an efficient manufacturing pipeline as one can decide, in virtual realm, what specific manufacturing tools to use and how to move them. Flank milling is the finishing stage of 5-axis Computer Numerically Controlled (CNC) machining, a stage where the machining accuracy is equally important as the smooth surface finish of the to-be-manufactured workpiece. The benchmark machining geometries such as propellers or blisks are doubly-curved surfaces and one typically needs several paths of the tool to get highly accurate surface finish. However, navigating a tool to move tangentially (i.e., in flank fashion) to the surface is very restrictive and in order to get highly accurate approximation, one typically has to compromise the smoothness across the neighboring paths.To connect neighboring paths in smooth ($G^1$-continuous) fashion using a conical tool is possible only for reasonably flat target geometries, such as spiral bevel gears, however, for a general free-form surface conical tools do not offer sufficient degrees of freedom. In this work, we consider generally curved, custom-shaped, cutting tools, whose shape is a design parameter computed by the proposed optimization-based framework to adapt their motions globally to the input free-form surface, supporting a feature of $G^1$ connection across the neighboring paths. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that optimizing the shape of the tool offers more flexibility to produce $G^1$ connections between neighboring strips and outperforms conical tools both in terms of the approximation error and the smoothness.
Item S-packing colorings of distance graphs G(Z,{2,t})(2021) Brešar, Boštjan; Ferme, Jasmina; Kamenická, KarolínaThe smallest k such that G has an S-packing k-coloring is the S-packing chromatic number of G. The S-packing chromatic numbers of the graphs G(Z,{2,t}), where S is any sequence with a(i) is an element of {1, 2} for all i, are determined.Item A Quest for Simple and Unified Proofs in Regularity Theory: Perturbation Stability(2023) Cibulka, Radek; Roubal, TomášIoffe’s criterion and various reformulations of it have become a standard tool in proving theorems guaranteeing metric regularity of a (set-valued) mapping. First, we demonstrate that one should always use directly the so-called general criterion which follows, for example, from Ekeland’s variational principle, and that there is no need to make a detour through the slope-based consequences of this general statement. Second, we argue that when proving perturbation stability results, in the spirit of Lyusternik-Graves theorem, there is no need to employ the concept of a lower semicontinuous envelope even in the case of an incomplete target space. The gist is to use the “correct” function to which Ekeland’s variational principle is applied; namely, the distance function to the graph of the set-valued mapping under consideration. This approach originates in the notion of graphical regularity introduced by L. Thibault, which is equivalent to the property of metric regularity. Our criteria cover also both metric subregularity and metric semiregularity, which are weaker properties obtained by fixing one of the points in the definition of metric regularity.Item Traveling waves for monostable reaction-diffusion-convection equations with discontinuous density-dependent coefficients(2024) Drábek, Pavel; Jung, Soyeun; Ko, Eunkyung; Zahradnikova, MichaelaThis paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with p-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us to treat discontinuous diffusion with possible degenerations and singularities at 0 and 1, as well as only piecewise continuous convective velocity. Our approach is based on comparison arguments for an equivalent non-Lipschitz first-order ODE. We formulate sufficient conditions for the existence and non-existence of these generalized solutions and discuss how the convective velocity affects the minimal wave speed compared to the problem without convection. We also provide brief asymptotic analysis of the profiles, for which we need to assume power-type behavior of the diffusion and reaction terms.Item Symmetries of planar algebraic vector fields(2024) Alcazar, Juan Gerardo; Lávička, Miroslav; Vršek, JanIn this paper, we address the computation of the symmetries of polynomial (and thus also rational) planar vector fields using elements from Computer Algebra. We show that they can be recovered from the symmetries of the roots of an associated univariate complex polynomial which is constructed as a generator of a certain elimination ideal. Computing symmetries of the roots of the auxiliary polynomial is a task considerably simpler than the original problem, which can be done efficiently working with classical Computer Algebra tools. Special cases, in which the group of symmetries of the polynomial roots is infinite, are separately considered and investigated. The presented theory is complemented by illustrative examples. The main steps of the procedure for investigating the symmetries of a given polynomial vector field are summarized in a flow chart for clarity.Item Approximate inner solvers for block preconditioning of the incompressible Navier-Stokes problems discretized by isogeometric analysis(2024) Egermaier, Jiří; Honnerová, HanaWe deal with efficient numerical solution of the steady incompressible Navier-Stokes equations (NSE) using our in-house solver based on the isogeometric analysis (IgA) approach. We are interested in the solution of the arising saddle-point linear systems using preconditioned Krylov subspace methods. In the present paper, we focus on selecting efficient approximate solvers for solving subsystems within block preconditioning methods. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination.Item A closure for Hamilton-connectedness in {K1,3,Γ3}-free graphs(2024) Kabela, Adam; Ryjáček, Zdeněk; Skyvová, Mária; Vrána, PetrWe introduce a closure technique for Hamilton-connectedness of {K(1,3),Gamma(3)}-free graphs, where Gamma(3) is the graph obtained by joining two vertex-disjoint triangles with a path of length 3. The closure turns a claw-free graph into a line graph of a multigraph while preserving its (non)-Hamilton-connectedness. The most technical parts of the proof are computer-assisted.The main application of the closure is given in a subsequent paper showing that every 3-connected {K(1,3),Gamma(3)}-free graph is Hamilton-connected, thus resolving one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness.Item On tiling spherical triangles into quadratic subpatches(2024) Bizzarri, Michal; Lávička, Miroslav; Vršek, Jan; Bartoň, Michael; Kosinka, JiříVarious interpolation and approximation methods arising in several practical applications in geometric modeling deal, at a particular step, with the problem of computing suitable rational patches (of low degree) on the unit sphere. Therefore, we are concerned with the construction of a system of spherical triangular patches with prescribed vertices that globally meet along common boundaries. In particular, we investigate various possibilities for tiling a given spherical triangular patch into quadratically parametrizable subpatches. We revisit the condition that the existence of a quadratic parameterization of a spherical triangle is equivalent to the sum of the interior angles of the triangle being pi, and then circumvent this limitation by studying alternative scenarios and present constructions of spherical macro-elements of the lowest possible degree. Applications of our method include algorithms relying on the construction of (interpolation) surfaces from prescribed rational normal vector fields.Item Home Advantage in Ice Hockey Matches Without Spectators(2024) Marek, Patrice; Vávra, FrantišekMeasures to combat the COVID-19 pandemic have provided a unique dataset that can be analysed to test the influence of spectators on match results. Strict measures were introduced in the Czech Republic, where more than half of the 2020–2021 season was played completely without spectators. The matches of the Czech Extraliga from the last seven seasons (a total of 2604 matches were played between the seasons of 2016–2017 and 2022–2023) were used in the analysis of the influence of spectators on results. Previously developed models from association football were used to perform the analysis. The results of the analysis show that in matches without spectators, the influence of home advantage decreased significantly.Item On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining(2023) Bizzarri, Michal; Barton, Michael; Ponce-Vanegas, FelipeWe study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2, the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopesItem The most general structure of graphs with hamiltonian or hamiltonian connected square(2024) Ekstein, Jan; Fleischner, HerbertOn the basis of recent results on hamiltonicity, [5], and hamiltonian connectedness, [9], in the square of a 2-block, we determine the most general block-cutvertex structure a graph G may have in order to guarantee that G^2 is hamiltonian, hamiltonian connected, respectively. Such an approach was already developed in [10] for hamiltonian total graphs.Item Symmetry group detection of point clouds in 3D via a decomposition method(2024) Bizzarri, Michal; Hruda, Lukáš; Lávička, Miroslav; Vršek, JanAnalyzing 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 method for detecting the entire symmetry group of 3D point clouds. Our approach decomposes the point cloud into simpler shapes whose symmetry groups are easier to find. The exact symmetry group of the original point cloud is then derived from the symmetries of these individual components. The method presented in this paper is a direct extension of the approach recently formulated in Bizzarri et al. (2022a) for discrete curves in plane. The method can be easily modified also for perturbed data. This work contributes to the advancement of symmetry analysis in point clouds, providing a foundation for further research and enhancing applications in computer vision, robotics, and augmented reality.Item Reverse Faber-Krahn and Szegő-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions(2025) Anoop, T. V.; Bobkov, Vladimir; Drábek, PavelWe prove Szego-Weinberger inequality for problems with mixed boundary conditions of the Robin-Neumann boundarytype. We deal with higher eigenvalues and study the symmetries and nonradiality of the eigenfunctions. We also discuss the validity of the Payne conjecture for some special type of domains.Item S-packing colorings of distance graphs with distance sets of cardinality 2(2025) Holub, Přemysl; Melicharová, Petra; Brešar, Boštjan; Ferme, Jasmina; Jakovac, MarkoFor a non-decreasing sequence 𝑆 = (𝑠1, 𝑠2,…) of positive integers, a partition of the vertex set of a graph 𝐺 into subsets 𝑋1,…,𝑋𝓁, such that vertices in 𝑋𝑖 are pairwise at distance greater than 𝑠𝑖 for every 𝑖 ∈ {1,…,𝓁}, is called an 𝑆-packing 𝓁-coloring of 𝐺. The minimum 𝓁 for which 𝐺 admits an 𝑆-packing 𝓁-coloring is called the 𝑆-packing chromatic number of 𝐺. In this paper, we consider 𝑆-packing colorings of the integer distance graphs with respect two positive integers 𝑘 and 𝑡, which are the graphs whose vertex set is ℤ, and two vertices 𝑥, 𝑦 ∈ ℤ are adjacent whenever |𝑥−𝑦| ∈ {𝑘,𝑡}. We complement partial results from two earlier papers, thus determining all values of the 𝑆-packing chromatic numbers of these distance graphs for all sequence 𝑆 such that 𝑠𝑖 ≤ 2 for all 𝑖. In particular, if 𝑆 = (1, 1, 2, 2,…), then the 𝑆-packing chromatic number is 2 if 𝑘 + 𝑡 is even, and 4 otherwise, while if 𝑆 = (1, 2, 2,…), then the 𝑆-packing chromatic number is 5, unless {𝑘,𝑡} = {2, 3} when it is 6; when 𝑆 = (2, 2, 2,…), the corresponding formula is more complex.Item Mirroring in lattice equations and a related functional equation(2024) Hesoun, Jakub; Stehlík, Petr; Volek, JonášWe use a functional form of the mirroring technique to fully characterize equivalence classes of unbounded stationary solutions of lattice reaction-diffusion equations with eventually negative and decreasing nonlinearities. We show that solutions which connect a stable fixed point of the nonlinearity with infinity can be characterized by a single parameter from a bounded interval. Within a two-dimensional parametric space, these solutions form a boundary to an existence region of solutions which diverge in both directions. Additionally, we reveal a natural relationship of lattice equations with an interesting functional equation which involves an unknown function and its inverse.Item Every 3-connected {K1,3,Γ3}-free graph is Hamilton-connected(2025) Kabela, Adam; Ryjáček, Zdeněk; Skyvová, Mária; Vrána, PetrWe show that every 3-connected {K1,3, Γ3}-free graph is Hamilton-connected, where Γ3 is the graph obtained by joining two vertex-disjoint triangles with a path of length 3. This resolves one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness. The proof is based on a new closure technique, developed in a previous paper, and on a structural analysis of small subgraphs, cycles and paths in line graphs of multigraphs. The most technical steps of the analysis are computer-assisted.Item Rainbow bases in matroids(2024) Hörsch, Florian; Kaiser, Tomáš; Kriesell, MatthiasRecently, it was proved by Bérczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were left open.We first show that the problem remains hard if the matroid is graphic, answering a question of Bérczi and Schwarcz. As another special case, we consider the problem of deciding whether a given digraph can be factorized into subgraphs which are spanning trees in the underlying sense and respect upper bounds on the indegree of every vertex. We prove that this problem is also hard. This answers a question of Frank.In the second part of the article, we deal with the relaxed problem of covering the ground set of a matroid by rainbow bases. Among other results, we show that there is a linear function f such that every matroid that can be factorized into k bases for some k≥3 can be covered by f(k) rainbow bases if every partition class contains at most 2 elements.
