We present a new and efficient method to compute the intersection point between a convex planar quadrilateral and a ray. Contrary to other methods, the bilinear coordinates of the intersection point are computed only for rays that hit the quadrilateral. Rays that do not hit the quadrilateral are rejected early. Our method is up to 40% faster compared to previous approaches.

We present a new definition of distortion and quality measures for high-order hexahedral (quadrilateral) elements. This definition leads to two direct applications. First, it can be used to check the validity and quality [1] of a high-order hexahedral (quadrilateral) mesh. Second, it allows the generation of high-order curved meshes [2, 3, 4, 5] composed of valid and high-quality hexahedral (qu...

A multilevel adaptive refinement technique is presented for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are re...

A P1-nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements, which contain quadratic polynomials or polynomials of degree greater than 2, our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges. One of the benefits of using our elem...

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the mot...

Some relations in a complete quadrilateral are derived. In connection with these relations some special conics related to the angular points and sides of the quadrilateral are discussed. A theorem of Carnot valid for a triangle is extended to a quadrilateral.

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts th...

Murine double minute clone 2 (MDM2), p14 alternate reading frame (p14arf), and nucleophosmin (NPM) regulate p53 activity. A total of 200 biopsies, including normal bronchial, pre-invasive and invasive tissues, were examined for changes in NPM, p14arf, MDM2 and p53 expression patterns by immunohistochemistry and immunofluorescence with confocal microscopy. NPM and p14arf displayed a diffuse nucl...

This work presents a new approach to conformal all-quadrilateral mesh adaptation. Most current quadrilateral adaptivity techniques rely on mesh refinement or a complete remesh of the domain. In contrast, we introduce a new method that incorporates both conformal refinement and coarsening strategies on an existing mesh of any density or configuration. Given a sizing function, this method modifie...

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...