Hyperplane families creating envelopes

Dissertation Rational Parametrizations for Envelopes of Quadric Families

'Rationale B–Spline Darstel-lungen funktioneller Formen für die CAD/CAM Technik' (P09790–MAT).

On quadratic two-parameter families of spheres and their envelopes

In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean R3. The four dimensional cyclographic model of the set of spheres in R3 is an appropriate framework to show that a quadratic triangular Bézier patch in R4 corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the enve...

Creating grander families: older adults adopting younger kin and nonkin.

PURPOSE There is a dearth of research on older adoptive parents caring for minor children, despite a growing number of such adoptions finalized each year. This study offers a large-scale investigation of adoptive families headed by older parents. We describe these families and explore how preadoptive kinship between the adoptive parent and the child impacts adoption outcomes. DESIGN AND METHO...

Families and Schools in Partnership: Creating Connections for Student Success

Hyperplane Priors

The requirement of transformation invariance of a probability distribution is employed to derive prior probabilities for the coefficients of the equation describing a hyperplane. In two dimensions, this is a straight line, in three dimensions an ordinary plane etc. We treat the general case of n dimensions and propose a procedure to normalize the resulting distributions in order to make them pr...