We use basic results from graph theory to design algorithms for constructing three-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. The best previous result generated a drawing bounded by an O( √ n) × O( √ n) × O( √ n) box, with each edge route containing up to 16 bends. Our algorithms initiate the study of bend=bounding box trade-o issues for thre...

This paper introduces a novel method for affine invariant matching using Zwickels that is especially well suited for images of man-made structures. Zwickels are sections defined by two intersecting line segments, dividing the neighborhood around the intersection point into two sectors. The information inside the smaller sector is used to compute an affine invariant representation. We rectify th...

r down tò 2 , it is a weakly monotone increasing function. But in a monotone function, a value can only appear once (or in one continuous range). Since the function is divided into two weakly monotone regions, a xed value can appear at most twice (or in two continuous ranges). This suuces to show that there can be at most two intersections between (I r) and O r , one in each weakly monotone reg...

Given a spatio-temporal network (ST network) whose edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of distinct minimum spanning trees of the ST network. The TSMST computation problem aims to identify a collection of distinct minimum spanning trees and their respective timesub-intervals under the constraint that the edge weight functions are piec...

The aim of this paper is to present a method that can be used for getting better point cloud by structured light photogrammetry. The data is from the project of 3D reconstruction of old Beijing model. The object we scanned is the 1:1000 model of old Beijing city of 1950’s. The main contents of the model are a large number of building and house models. The distinguishing feature of structured li...

Ray tracing and rasterization have long been considered as two fundamentally different approaches to rendering images of 3D scenes, although they compute the same results for primary rays. Rasterization projects every triangle onto the image plane and enumerates all covered pixels in 2D, while ray tracing operates in 3D by generating rays through every pixel and then finding the closest interse...

In this contribution, we are concerned with the detection and reened localization of 3D point landmarks. We propose multi-step diierential procedures which are generalizations of an existing two-step procedure for subpixel localization of 2D point landmarks. This two-step procedure combines landmark detection by applying a diierential operator with reened localization through a diierential edge...

Intersection and measured intersection graphs are quite common in the literature. In this paper we introduce the analogous concept of measured difference graphs: Given an arbitrary hypergraph H = {H1, ..., Hn}, let us associate to it a graph on vertex set [n] = {1, 2, ..., n} in which (i, j) is an edge iff the corresponding sets Hi and Hj are “sufficiently different”. More precisely, given an i...

A G-design of order n is a pair (P, B) where P is the vertex set of the complete graph Kn and B is an edge-disjoint decomposition of Kn into isomorphic copies of the simple graph G. Following terminology, we call these copies "blocks". Given a particular the intersection problem asks for which k is it possible to find two (P, Bl) and (P, B 2) of order n, with IBI n B21 = k, that is, with k comm...

In this contribution, we are concerned with the detection and reened subvoxel localization of 3D point landmarks. We propose multi-step differential approaches which are generalizations of an existing two-step approach for subpixel localization of 2D point landmarks. This two-step approach combines landmark detection by applying a diierential operator with reened localization through a diierent...