Higher Order Automatic Differentiation with Dual Numbers

In engineering applications, we often need the derivatives of functions defined by a program. The approach chosen for derivative computation must be algebraic to allow computer implementation. A particular solution to obtain first derivatives is the application of dual numbers. This paper proposes simple and compact generalizations of this idea to obtain derivatives of arbitrary order for single or multi-variate functions and the automatic handling of 0/0 ambiguities in the calculations. We also provide the C++ code that takes advantage of operator overloading and recursion. The method is demonstrated by path animation, Gaussian curvature computation, and curve fairing.

Curvature variation factor and its application

Evaluation on curvature variation is a significant problem in the field of curve fairing, and traditional evaluation is generally performed by observing curvature plots qualitatively. By using the theory of B-spline wavelet, the concept of curvature variation factor (CVF) is put forth in this paper to describe curvature variation quantitatively. It is verified that the quantitative evaluation results by the CVF method agree well with the traditional qualitative judgments. Based on CVF, a new curve-fairing algorithm is further put forward, whose validness is verified by an example. The advantage of the CVF-based algorithm is that it can realize different fairing effect to meet different requirements under diverse circumstances only by adjusting the shape error.

A Method for Garment Design Drawing Extraction from Garment Image

The method proposed in this paper mainly proceeds in three steps: first, original silhouette edge can be automatically obtained though processing the image with morphology tools. Second, as existing effects of printed pattern, texture noise in the original silhouette edge should be removed and the silhouette should be faired. In this step, texture noise segment recognition algorithm and curve fairing algorithm based on feature point extraction are proposed. Third, style curves are extracted through the mouse interactive operation. In addition, the problems about finding intersections, symmetric point calculation and using what kind of spline to fit style curves are discussed.

A Multiresolution Fairing Approach for NURBS Curves

Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed example is given to show the effectiveness of this multiresolution fairing method.

Wavelet-Based Multiresolution NURBS Curve Fairing

A multiresolution approach is presented for NURBS curve fairing based on nonuniform semiorthogonal B-spline wavelets built. This method provides greater flexibility and applicability than uniform B-spline wavelets for multiresolution curve fairing. An example is presented to validate effectiveness of this multiresolution fairing method. Furthermore, the algorithm can be easily applied to NURBS curves in three dimensions as well as in two.