Design of Compact Planar B-spline Curves using DP Control Point Selection with Multi-level Error Functions

다국어 초록 (Multilingual Abstract)

In this paper, we consider the problem of representing some given planar curves on a two-dimensional plane as so-called compact B-spline curves by using only the dominant control points. In particular, we here develop a method for selecting the dominant control points by introducing the dynamic programming (DP) approach and a new idea of knot points selection using a multi-level error function where the term multi-level means that not only function values of a given curve are considered, but also the derivatives. Moreover, we offer a way to represent compact planar B-spline curves using non-uniform rational B-splines (NURBS). We demonstrate performance with experimental studies using handwriting data. The results of this paper will be useful for improving usability in the design of the so-called dynamic font-based characters.

목차 (Table of Contents)

• Abstract
• 1. Introduction
• 2. Problem Statement
• 3. Reconstructing Compact Planar B-spline Curves using DP Control Point Selection with Multi-level Error Functions
• 4. Experimental Studies
• 5. Concluding Remarks
• References

참고문헌 (Reference)

1 X. Zhang, "Time-Domain Calculation of Microstrip Components and The Curve-Fitting of Numerical Results" 313-316, 1989

2 R. Hu, "Optimization of Point Selection on Digital Ink Curves" 525-530, 2012

3 H. Fujioka, "Optimal Smoothing Splines for Detecting Extrema from Observational Data" 1 (1): 111-132, 2006

4 H. Kano, "Optimal Curve Fitting and Smoothing using Normalized Uniform Bsplines: A tool for studying complex systems" 169 (169): 96-128, 2005

5 H. Ni, "Moving Least Square Curve and Surface Fitting with Interpolation Conditions" 300-304, 2010

6 T. Lyche, "Knot Removal for Parametric B-spline Curves and Surfaces" 4 (4): 217-230, 1987

7 D. F. Rogers, "Introduction to NURBS: with Historical Perspective" Academic Press 2001

8 H. Nakata, "Generation of Japanese Cursive Sentences using Optimal Smoothing Splines" 44 (44): 134-142, 2003

9 R. Soontornvorn, "Design of Compact Planar B-spline Curves Using DP Control Point Selection" 1476-1479, 2018

10 Y. Mieno, "Data Compression of Digital-Ink with Pen-Slips Using Multi-level L1 Smoothing Splines" 1787-1792, 2015

11 W. L. Xu, "Curve Fitting Approach to Motion Planning of Nonholonomic Chained Systems" 811-816, 1999

12 H. Fujioka, "Constructing and Reconstructing Characters, Words and Sentences by Synthesizing Writing Motions" 36 (36): 661-670, 2006

13 H. Park, "B-spline Curve Fitting based on Adaptive Refinement using Dominant points" 39 : 439-451, 2007

14 H. Park, "B-spline Curve Fitting Using Dominant Point" 3992 : 362-366, 2006

15 C. de Boor, "A Practical Guide to Splines" Springer 2001

16 T. Tjahjowidodo, "A Fast Non-Uniform Knots Placement Method for B-Spline Fitting" 1490-1495, 2015

17 N. Ray, "A Concave Cost Formulation for Parametric Curve Fitting: Detection of Leukocytes from Intravital Microscopy Images" 53-56, 2010