Curved Finite Elements and Curve Approximation

The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves

Gift of Rest

Posting about ­­­­­­­­the blessing of Sabbath rest from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/the-gift-of-rest

Millennials and the Reformation

If there is one thing that serving millennials has taught me, it’s that the state of the church in its current form might be in peril. But the state of their faith might not be in jeopardy at all. Posting about ­­­­­­­­denominational identity from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/the-millennials-and-the-reformation

My Service Conversion

We are called to serve because service is God\u27s gift to us before it is ever his commandment. Posting about the purpose of Christian service from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/my-service-conversion

Call to Gladness

Can we humble ourselves to receive this Messiah, not re-cast in the image of our own desires but as the Deliverer we really need? Posting about ­­­­­­­­accepting Christ with gladness from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/a-call-to-gladness

Why They\u27re Leaving and Why It Matters: Gen Z\u27s Mass Exodus from Church

Whether we want to admit it or not, the Church has an image problem. Today’s iteration of the Church isn’t appealing to Gen Z. Posting about ­­­­­­­­reasons for the decline in church affiliation from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation. https://inallthings.org/why-theyre-leaving-and-why-it-matters-gen-zs-mass-exodus-from-church

Easter: She Called Him Rabboni

Posting about the resurrection story from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/easter-she-called-him-rabboni

Err on the Side of Action

When we become so afraid of doing the wrong thing that we fail to even try to do the right thing, something is askew. Posting about ­­­­­­­­actively helping those in need from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation. http://inallthings.org/err-on-the-side-of-action

Liberia: One Year Later

While the places of the world that get ransacked by natural disasters and crises of incomprehensible proportions—places like Liberia—cry out to their brethren of humanity for aid and assistance, what we too often forget is that we who come in the form of help have our own poverties that stand in need of healing as well. I am reminded of this every time I return to Liberia. Posting about Liberia since the 2014 Ebola crisis from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world. http://inallthings.org/liberia-one-year-later