Can local NURBS refinement be achieved by modifying only the user interface?

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

Can local NURBS refinement be achieved by modifying only the user interface?

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

Can local NURBS refinement be achieved by modifying only the user interface?

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

Can local NURBS refinement be achieved by modifying only the user interface?

© 2015 The Authors. NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user's interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.

Adaptive fitting algorithm of progressive interpolation for Loop subdivision surface

Subdivision surface and data fitting have been applied in data compression and data fusion a lot recently. Moreover, subdivision schemes have been successfully combined into multi-resolution analysis and wavelet analysis. This makes subdivision surfaces attract more and more attentions in the field of geometry compression. Progressive interpolation subdivision surfaces generated by approximating schemes were presented recently. When the number of original vertices becomes huge, the convergence speed becomes slow and computation complexity becomes huge. In order to solve these problems, an adaptive progressive interpolation subdivision scheme is presented in this article. The vertices of control mesh are classified into two classes: active vertices and fixed ones. When precision is given, the two classes of vertices are changed dynamically according to the result of each iteration. Only the active vertices are adjusted, thus the class of active vertices keeps running down while the fixed ones keep rising, which saves computation greatly. Furthermore, weights are assigned to these vertices to accelerate convergence speed. Theoretical analysis and numerical examples are also given to illustrate the correctness and effectiveness of the method.

Photogrammetry-Based 3D Printing Reproduction Method for Oil Paintings

This paper proposes a new oil painting reproduction method using 3D printing to compensate for the deficiencies of the existing methods. First, 3D reconstruction of oil paintings is completed by photogrammetry; the oil painting color and the 3D geometric information are recovered better by acquiring several sets of orthophotomaps, and modeling accuracy is ensured with a control mesh or by flattening. Next, the contours and hypsometric tints of the 3D model for oil paintings are generated using contour tracing algorithm, and the image segmentation of renderings is completed using RGB image segmentation algorithm, with the layered section extracted from each layer and the 3D geometric information converted into 2D plane information. Finally, the 3D models of oil paintings are presented through UV inkjet printing with images superimposed layer upon layer, and stereoscopic reproduction of oil paintings is completed based on the orthophotomaps printed from the 3D models.

A Mesh Deformation Method with Multiple Editing Granularities

This paper proposes a mesh deformation method being able to quickly exchange between different editing granularities. The method firstly simplifies the original model mesh to obtain an accuracy-specified control mesh while preserving user’s pre-configured control handle vertices, and then computes the original mesh vertices’ mean value coordinates on the control mesh. Next, uses the Laplacian deformation to deform the control mesh with user’s editing, and then computes the deforming result based on the new control mesh and the previous mean value coordinates. Users can quickly generate a different accuracy control mesh of the new mesh again for deforming with a different granularity. Users only need edit some control vertices, which contains user’s specified handles, so the manipulation is convenient. Experiments show that users can deform models with this method, while changing the granularity fluently and preserving mesh’s features.

FAST MESH INTERPOLATION AND MESH DECOMPOSITION WITH APPLICATIONS

A new approach for constructing a smooth subdivision surface to interpolate the vertices of an arbitrary mesh is presented. The construction process does require setting up neither any linear systems, nor any matrix computation, but is simply done by iteratively moving vertices of the given mesh locally until control mesh of the required interpolating surface is reached. The new interpolation method has the simplicity of a local method in effectively dealing with meshes of a large number of vertices. It also has the capability of a global method in faithfully resembling the shape of a given mesh. Furthermore, the new method is fast and does not require a fairing step in the construction process because the iterative process converges to a unique solution at an exponential rate. Another important result of this work is, with the new iterative process, each mesh (surface) can be decomposed into a sum of simpler meshes (surfaces) which carry high-and low-frequency information of the given model. This mesh decomposition scheme provides us with new approaches to some classic applications in computer graphics such as texture mapping, denoising/smoothing/sharpening, and morphing. These new approaches are demonstrated in this paper and test results are included.