Triangular Bézier sub-surfaces on a triangular Bézier surface

This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch

Square Root Cubature Kalman Filter-Kalman Filter Algorithm for Intelligent Vehicle Position Estimate

AbstractA new filtering algorithm, adaptive square root cubature Kalman filter-Kalman filter (SRCKF-KF) is proposed to reduce the problems of amount of calculation, complex formula-transform, low accuracy, poor convergence or even divergence. The method uses cubature Kalman filter (CKF) to estimate the nonlinear states of model while its linear states are estimated by the Kalman filter (KF). The simulation and practical experiment results show that, compared to the extended Kalman filter (EKF) and unscented Kalman filter (UKF). The modified filter not only enhances the numerical stability, guarantees positive definiteness of the state covariance, but also increases accuracy, which has high practicability

Preparation of Blue TiO2 for Visible-Light-Driven Photocatalysis

Titanium dioxide (TiO2), which is regarded as a semiconductor photocatalyst, has drawn attention in the applications of photocatalysis, including hydrogen evolution reaction, carbon dioxide reduction, pollutant degradation, and biocatalytic or dye-sensitized solar cells due to its low toxicity, superior photocatalytic activity, and good chemical stability. However, there are still some disadvantages such as too large energy bandgap (~3.34 eV and ~3.01 eV for anatase and rutile phases, respectively) in the absorbance of all ranges of lights, which limits the photoelectrochemical performance of TiO2. Herein, we like to introduce photocatalytic blue TiO2 that is obtained by the reduction of TiO2. The blue TiO2 consists of Ti3+ state with high oxygen defect density that can absorb the visible and infrared as well as ultraviolet light due to its low energy bandgap, leading to enhance a photocatalytic activity. This chapter covers the structure and properties of blue TiO2, its possible applications in visible-light-driven photocatalysis, and mainly various synthetic methods even including phase-selective room-temperature solution process under atmospheric pressure