A Review of T-Splines Surfaces

Background: Curved modeling technology is originated from the geometric lofting and designing of aircraft, automobiles, and ships. The control points of the traditional B-spline mesh should be placed regularly in rows and columns. A T-spline surface is a type of B-spline surface that allows T-junctions. It can overcome the limitations of traditional B-mesh topology and has its own advantages in surface splicing, surface fining, surface simplification, and so on. T-spline has wide application prospects in product modeling, art design, animation production, numerical control machining, volume data expression, and other aspects. Objective: The objective of this paper is to summarize the properties, algorithms, and applications of T-splines. It helps scholars in determining the research status of T-splines and further exploring the theories and applications of T-splines. Methods: This paper reviews the theories of T-splines and their applications from four aspects. First, we discuss the development of the concept, properties, algorithms, and reconstruction of the T-spline. Then, we conduct an isogeometric analysis using T-splines. Next, we demonstrate the applications of T-splines in actual scenarios. Finally, we present a brief summary of the paper and future expectations. Results: The paper provides a brief introduction of the relevant papers on T-splines. Currently, many studies have been carried out on theories and applications of T-spline. Among these, the spline theory on T-mesh has aroused widespread interest in engineering, especially in computer-aided geometric design (CAGD) and computer graphics. Conclusion: The T-spline surface is the most important new spline surface in the CADG field since the creation of the B-spline surface and non-uniform rational B-spline surface. Although the surface modeling technology based on the T-spline surface is developing rapidly, there are still some problems that need to be further studied.

A Saliency-Based Sparse Representation Method for Point Cloud Simplification

High-resolution 3D scanning devices produce high-density point clouds, which require a large capacity of storage and time-consuming processing algorithms. In order to reduce both needs, it is common to apply surface simplification algorithms as a preprocessing stage. The goal of point cloud simplification algorithms is to reduce the volume of data while preserving the most relevant features of the original point cloud. In this paper, we present a new point cloud feature-preserving simplification algorithm. We use a global approach to detect saliencies on a given point cloud. Our method estimates a feature vector for each point in the cloud. The components of the feature vector are the normal vector coordinates, the point coordinates, and the surface curvature at each point. Feature vectors are used as basis signals to carry out a dictionary learning process, producing a trained dictionary. We perform the corresponding sparse coding process to produce a sparse matrix. To detect the saliencies, the proposed method uses two measures, the first of which takes into account the quantity of nonzero elements in each column vector of the sparse matrix and the second the reconstruction error of each signal. These measures are then combined to produce the final saliency value for each point in the cloud. Next, we proceed with the simplification of the point cloud, guided by the detected saliency and using the saliency values of each point as a dynamic clusterization radius. We validate the proposed method by comparing it with a set of state-of-the-art methods, demonstrating the effectiveness of the simplification method.

Multifaceted Geometric Assessment towards Simplified Urban Surfaces Built by 3D Reconstruction

Large-scale three-dimensional (3D) reconstruction from multi-view images is used to generate 3D mesh surfaces, which are usually built for urban areas and are widely applied in many research hotspots, such as smart cities. Their simplification is a significant step for 3D roaming, pattern recognition, and other research fields. The simplification quality has been assessed in several studies. On the one hand, almost all studies on surface simplification have measured simplification errors using the surface comparison tool Metro, which does not preserve sufficient detail. On the other hand, the reconstruction precision of urban surfaces varies as a result of homogeneity or heterogeneity. Therefore, it is difficult to assess simplification quality without surface classification. These difficulties are addressed in this study by first classifying urban surfaces into planar surfaces, detailed surfaces, and urban frameworks according to the simplification errors of different types of surfaces and then measuring these errors after sampling. A series of assessment indexes are also provided to contribute to the advancement of simplification algorithms.

An Improved Surface Simplification Method for Facial Expression Animation Based on Homogeneous Coordinate Transformation Matrix and Maximum Shape Operator

Facial animation is one of the most popular 3D animation topics researched in recent years. However, when using facial animation, a 3D facial animation model has to be stored. This 3D facial animation model requires many triangles to accurately describe and demonstrate facial expression animation because the face often presents a number of different expressions. Consequently, the costs associated with facial animation have increased rapidly. In an effort to reduce storage costs, researchers have sought to simplify 3D animation models using techniques such as Deformation Sensitive Decimation and Feature Edge Quadric. The studies conducted have examined the problems in the homogeneity of the local coordinate system between different expression models and in the retainment of simplified model characteristics. This paper proposes a method that applies Homogeneous Coordinate Transformation Matrix to solve the problem of homogeneity of the local coordinate system and Maximum Shape Operator to detect shape changes in facial animation so as to properly preserve the features of facial expressions. Further, root mean square error and perceived quality error are used to compare the errors generated by different simplification methods in experiments. Experimental results show that, compared with Deformation Sensitive Decimation and Feature Edge Quadric, our method can not only reduce the errors caused by simplification of facial animation, but also retain more facial features.

3D Modeling from Multi-views Images for Cultural Heritage in Wat-Pho, Thailand

In Thailand, there are several types of (tangible) cultural heritages. This work focuses on 3D modeling of the heritage objects from multi-views images. The images are acquired by using a DSLR camera which costs around $1,500 (camera and lens). Comparing with a 3D laser scanner, the camera is cheaper and lighter than the 3D scanner. Hence, the camera is available for public users and convenient for accessing narrow areas. The acquired images consist of various sculptures and architectures in Wat-Pho which is a Buddhist temple located behind the Grand Palace (Bangkok, Thailand). Wat-Pho is known as temple of the reclining Buddha and the birthplace of traditional Thai massage. To compute the 3D models, a diagram is separated into following steps; <i>Data acquisition</i>, <i>Image matching</i>, <i>Image calibration and orientation</i>, <i>Dense matching</i> and <i>Point cloud processing</i>. For the initial work, small heritages less than 3 meters height are considered for the experimental results. A set of multi-views images of an interested object is used as input data for 3D modeling. In our experiments, 3D models are obtained from MICMAC (open source) software developed by IGN, France. The output of 3D models will be represented by using standard formats of 3D point clouds and triangulated surfaces such as .ply, .off, .obj, etc. To compute for the efficient 3D models, post-processing techniques are required for the final results e.g. noise reduction, surface simplification and reconstruction. The reconstructed 3D models can be provided for public access such as website, DVD, printed materials. The high accurate 3D models can also be used as reference data of the heritage objects that must be restored due to deterioration of a lifetime, natural disasters, etc.

Surface Simplification of 3D Animation Models Using Robust Homogeneous Coordinate Transformation

The goal of 3D surface simplification is to reduce the storage cost of 3D models. A 3D animation model typically consists of several 3D models. Therefore, to ensure that animation models are realistic, numerous triangles are often required. However, animation models that have a high storage cost have a substantial computational cost. Hence, surface simplification methods are adopted to reduce the number of triangles and computational cost of 3D models. Quadric error metrics (QEM) has recently been identified as one of the most effective methods for simplifying static models. To simplify animation models by using QEM, Mohr and Gleicher summed the QEM of all frames. However, homogeneous coordinate problems cannot be considered completely by using QEM. To resolve this problem, this paper proposes a robust homogeneous coordinate transformation that improves the animation simplification method proposed by Mohr and Gleicher. In this study, the root mean square errors of the proposed method were compared with those of the method proposed by Mohr and Gleicher, and the experimental results indicated that the proposed approach can preserve more contour features than Mohr’s method can at the same simplification ratio.