This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh1 G2continuously using regular Coons B-spline surfaces, which are popular in industrial CAD/CAM systems. We first decompose all non-quadrangular facets into quadrilaterals. The tangential and second-order derivative vectors are then estimated on each vertex of the quads. A least-square adjustment algor...

We show how to combine, into one unified spline complex, C2 tensorproduct bi-cubic NURBS and G2 bi-cubic rational splines. The G2 splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to bridge the differing continuity. We transform the G2 splines to splines that are C2 in homogeneous ...

In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "lim" with arbitrary linear regular summability methods G we consider the notion of a generalized continuity ((G1,G2)-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.

The intergenerational transmission of aggressive parenting behavior was examined within the context of a prospective longitudinal study of adolescent and young adult adjustment. Thirty-nine young adults (G2; 33 females, 6 males) who had participated in early phases of this study with their parents (G1) continued their involvement with their young children (G3; 17 females, 22 males, mean age = 2...

PN (point-normal) triangles are cubic Bézier triangles which meet at their edges to surface a triangular mesh, but this only achieves G0 continuity. We define blending regions that span the edges shared by adjacent pairs of triangular domains and blend the corresponding Bézier triangles using a univariate blending function formulated in terms of barycentric coordinates. This produces G2 continu...

PURPOSE Harsh, abusive, and rejecting behavior by parents toward their children is associated with increased risk for many developmental problems for youth. Earlier research also shows that children raised by harsh parents are more likely to treat their own children harshly. The present study evaluated nurturing and supportive behaviors of spouses or cohabiting romantic partners hypothesized to...

Prospective studies of intergenerational continuity in parenting quality remain scarce, with little attention given to the potential role of social competence as a mediator of continuity. This study examined social competence as a mediator in the pathway from 1st generation (G1) to 2nd generation (G2) parenting quality. A normative sample of children and their parents were assessed in childhood...

This prospective, longitudinal investigation examined mechanisms proposed to explain continuities in parenting behavior across 2 generations (G1, G2). Data came from 187 G2 adults, their mothers (G1), and their children (G3). Prospective information regarding G2 was collected both during adolescence and early adulthood. G1 data were collected during G2's adolescence, and G3 data were generated ...

The interpolation of a planar sequence of points p0, . . . , pN by shape-preserving G 1 or G2 PH quintic splines with specified end conditions is considered. The shape-preservation property is secured by adjusting ‘tension’ parameters that arise upon relaxing parametric continuity to geometric continuity. In the G2 case, the PH spline construction is based on applying Newton–Raphson iterations ...