Related papers: T-Base: A Triangle-Based Iterative Algorithm for S…

We present an isogeometric analysis technique that builds on manifold-based smooth basis functions for geometric modelling and analysis. Manifold-based surface construction techniques are well known in geometric modelling and a number of…

In computed tomography, the approximation quality of a scan of a physical object is typically limited by the acquisition modalities, especially the hardware including X-ray detectors. To improve upon this, we experiment with a…

We present a method for generating orthogonal quadrilateral meshes subject to user-defined feature alignment and sizing constraints. The approach relies on computing integrable orthogonal frame fields, whose symmetries are implicitly…

This paper discusses the dimension of spline spaces with highest order smoothness over hierarchical T-meshes over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space with highest order…

If a (cusped) surface S admits an ideal triangulation T with no shears, we show an efficient algorithm to give S as a quotient of hypebolic plane by a subgroup of PSL(2, Z). The algorithm runs in time O(n log n), where n is the number of…

The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…

Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an…

This paper presents the first method for constructing bases for polynomial spline spaces over an arbitrary T-meshes (PT-splines for short). We construct spline basis functions for an arbitrary T-mesh by first converting the T-mesh into a…

This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a…

We describe a method to subdivide the surface of a sphere into spherical triangles of similar, but not identical, shapes and sizes. The Hierarchical Triangular Mesh (HTM) is a quad-tree that is particularly good at supporting searches at…

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…

We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…

In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…

Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…

We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…

In this paper, we present a new approach of creating PTAS to the TSP problems by defining a bounded-curvature surface embedded spaces. Using this definition we prove: - A bounded-curvature surface embedded spaces TSP admits to a PTAS. -…

In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges of the mesh. Given a spline space whose dimension is…

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry,…

Texture reconstruction techniques generally suffer from the errors in keyframe poses. We present a non-iterative method for seamless texture reconstruction of a given 3D scene. Our method finds the best texture alignment in a single shot…