In this site, you can find our underwriting book Java Graphics Programming and articles that address commonly used algorithms in computer graphics and computer aided geometric design. We post our book and articles here in hope to encourage free share of scientific information among researchers and industry professionals in the world.

Articles posted here are derived from either our published papers or our research notes. It should be noted algorithms discussed in these articles are workable in real life computing. However, they are neither the best approaches nor the only methods used by researchers and programming professionals. If you know any better algorithms in this area, please let us know so that we can educate ourselves and share the information with other visitors.

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BOOK/TUTORIAL:

• Java Graphics Programming
  An introduction to Java graphics programming with emphasis on the applications of computer aided design.

• Polynomial Evaluation
  • Polynomial Evaluation Using Horner Method
    This article tells you how to evaluate a canonical, Legendre, and Tchebyshev polynomial efficiently.
  • Efficient Computation of Binomial Coefficients and Applications
    Binomial coefficients can be computed very efficiently by the construction of Pascal triangle. Analogous to this construction, we shall derive efficient methods to compute b_k=ĺ_i=0^k C_kⁱ a_i etc.
  • B-spline Curve and Surface Evaluation
    This article discusses how to evaluate B-spline curve and surface efficiently.
• Basis Conversion
  • Converting B-spline curve to Bézier spline curve
    We discuss how to convert a B-spline curve to a Bézier spline curve using Boehm's knot insertion method.
  • Basis conversion among Bézier, Tchebyshev and Legendre
    This article discusses conversion of polynomial basis.
• Approximation
  • Least Squares Plane
    Given a set of 3D points, it discusses the best fit plane in a sense of least squares approximation.
  • Least Squares Line
    Given a set of 3D points, it shows you how to find the best fit line in a sense of least squares approximation.
  • Least Squares Circle
    Given a set of 3D points, this article tells you how to find the best fit circle in a sense of least squares approximation.
  • Least Squares Approximation by B-spline Curves and Surfaces
    This article discuss on how you can create a B-spline curve or surface to approximate a cloud of points.
  • Least Squares Approximation by Legendre Series
    Given an analytic function f(x,y),, it discusses the best fit polynomial in a sense of least squares approximation.
• Curve Offsetting
  • Curve offsetting based on Legendre series
    Curve offsetting is one of the most important geometric operations in CAD/CAM systems due to its immediate applications to NC machining. Based on the use of the Legendre series, we present a stable and efficient method for offsetting planar B-spline curves. Our approach provides users with easy control of approximation accuracy and flexibility to determine the degree of an offset curve.
• Curve Characterisation
  • Identification of Inflection Points and Cusps on Rational Curves
    A simple method to identify inflection points and cusps on 2-D and 3-D rational curves is proposed.
• Mechanical Properties of Computer Generated Model
  • Centroid, Area, and Moments of Inertia for Laminas
    An efficient method to compute centroid, area, and moments of inertia for laminas accurately.
• Miscellaneous
  • Comparison of Floating-point Values
    As a rule of thumb in programming, we should avoid direct comparison of two floating-point values for equality because computer has limited precision. It is widely regarded that direct comparisons of floating-point values are the sources of instability that can be triggered by arithmetic computations, change of compilers, or even change of compiling options. This article discuss how we should compare them in CAD systems.