A discrete square global grid system based on the parallels plane projection

Knowledge Innovation Project of Chinese Academy of Sciences [KZCX3-SW-347]; National Science Fund for Distinguished Young Scholar [40225004]

Parallels plane projection and its geometric features

A new equivalent map projection called the parallels plane projection is proposed in this paper. The transverse axis of the parallels plane projection is the expansion of the equator and its vertical axis equals half the length of the central meridian. On the parallels plane projection, meridians are projected as sine curves and parallels are a series of straight, parallel lines. No distortion of length occurs along the central meridian or on any parallels of this projection. Angular distortion and the proportion of length along meridians (except the central meridian) introduced by the projection transformation increase with increasing longitude and latitude. A potential application of the parallels plane projection is that it can provide an efficient projection transformation for global discrete grid systems.

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two-dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area-preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Peripheries of molecular projection in three-dimensional space and studies of quantitative structure-activity relationships

A new index, i.e., the periphery representation of the projection of a molecule from 3D space to a 2D plane is described. The results, correlation with toxicity of substituted nitrobenzenes, obtained by using periphery descriptors are much better than that obtained by using the areas (i.e., shadows) of projections of the compounds. Even better results were achieved by using the combination of periphery descriptors and the projections areas as well as the indicated variable K reflecting the action of group NO position on the benzene ring.

Applications of the method of three-dimensional projection of a molecule in quantitative structure-activity relationship of phenol derivatives

Five variables for phenol derivatives were calculated by molecular projection in three-dimensional space which were combined with eight quantum-chemical parameters and three Am indices. These variables were selected by using leaps-and-bounds regression analysis. Multiple linear regression analysis and artificial neural networks' were performed, and the results obtained by using. artificial neural networks are superior than that obtained by using multiple linear regression.

3D Pose from Three Corresponding Points Under Weak-Perspective Projection

Model-based object recognition commonly involves using a minimal set of matched model and image points to compute the pose of the model in image coordinates. Furthermore, recognition systems often rely on the "weak-perspective" imaging model in place of the perspective imaging model. This paper discusses computing the pose of a model from three corresponding points under weak-perspective projection. A new solution to the problem is proposed which, like previous solutins, involves solving a biquadratic equation. Here the biquadratic is motivate geometrically and its solutions, comprised of an actual and a false solution, are interpreted graphically. The final equations take a new form, which lead to a simple expression for the image position of any unmatched model point.

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

The psychology of immersion and development of a quantitative measure of immersive response in games

This study sets out to investigate the psychology of immersion and the immersive response of individuals in relation to video and computer games. Initially, an exhaustive review of literature is presented, including research into games, player demographics, personality and identity. Play in traditional psychology is also reviewed, as well as previous research into immersion and attempts to define and measure this construct. An online qualitative study was carried out (N=38), and data was analysed using content analysis. A definition of immersion emerged, as well as a classification of two separate types of immersion, namely, vicarious immersion and visceral immersion. A survey study (N=217) verified the discrete nature of these categories and rejected the null hypothesis that there was no difference between individuals' interpretations of vicarious and visceral immersion. The primary aim of this research was to create a quantitative instrument which measures the immersive response as experienced by the player in a single game session. The IMX Questionnaire was developed using data from the initial qualitative study and quantitative survey. Exploratory Factor Analysis was carried out on data from 300 participants for the IMX Version 1, and Confirmatory Factor Analysis was conducted on data from 380 participants on the IMX Version 2. IMX Version 3 was developed from the results of these analyses. This questionnaire was found to have high internal consistency reliability and validity.

How does cognition evolve? Phylogenetic comparative psychology.

Now more than ever animal studies have the potential to test hypotheses regarding how cognition evolves. Comparative psychologists have developed new techniques to probe the cognitive mechanisms underlying animal behavior, and they have become increasingly skillful at adapting methodologies to test multiple species. Meanwhile, evolutionary biologists have generated quantitative approaches to investigate the phylogenetic distribution and function of phenotypic traits, including cognition. In particular, phylogenetic methods can quantitatively (1) test whether specific cognitive abilities are correlated with life history (e.g., lifespan), morphology (e.g., brain size), or socio-ecological variables (e.g., social system), (2) measure how strongly phylogenetic relatedness predicts the distribution of cognitive skills across species, and (3) estimate the ancestral state of a given cognitive trait using measures of cognitive performance from extant species. Phylogenetic methods can also be used to guide the selection of species comparisons that offer the strongest tests of a priori predictions of cognitive evolutionary hypotheses (i.e., phylogenetic targeting). Here, we explain how an integration of comparative psychology and evolutionary biology will answer a host of questions regarding the phylogenetic distribution and history of cognitive traits, as well as the evolutionary processes that drove their evolution.