Isometric Projection Research Articles

“Protean Mechanism”: Robert Willis and the Technics of Architectural History

Abstract Robert Willis’s writing in the nineteenth century was foundational to the development of the discipline of architectural history. Closely related to other Cambridge scientists, including William Farish and William Whewell, Willis deployed similar methods and forms of conceptualization in his writings about medieval architecture. He focused on five areas in particular: the isometric projection, the building as kit-of-parts, detailed technical forms of description using illustrations and specialized vocabularies, the machine tool, and new tools for measuring cogwheels and architectural profiles. Using an interdisciplinary approach and drawing upon contemporary ideas of political economy by Karl Marx and Charles Babbage, this article resituates Willis’s writing in the context of the separation of manual from intellectual labor under industrial capitalism, arguing that the architectural historian was complicit both with the forms of abstraction required of professionalization and with the alienation of labor.

Landscape Design and Green Space Perception Enhancement Based on Panoramic Imaging and Segnet

Green view rate is an intuitive evaluation criterion used for green space perception. Traditional research on green view rate is mostly calculated based on flat images, which cannot fully reflect the subjective human perception of green volume in three-dimensional space. Based on the panoramic image, we propose the concept of panoramic green perception rate, obtain spherical panoramic photos by panoramic camera, convert isometric cylindrical projection into isoprojective cylindrical projection, and use the convolutional neural network model based on semantic segmentation to automatically identify the area of vegetation to achieve automatic recognition and measurement of panoramic green perception rate. The results were compared with manual discrimination and showed that the average intersection ratio (mIoU) of greenery recognition using Dilated ResNet-105 was 62.53%, and the average difference with manual recognition was 9.17%.

Parametric modeling logic analysis and precision control method application of nonlinear landscape structures based on Rhino+Grasshopper platform: A case study of the Flying Goose viewing platform in Beijing

The development of digital technology has made non-linear landscape structures mainstream and has brought new challenges to design methods. The efficiency and accuracy of applying Rhino+Grasshopper parametric modelling to such structures has gained the attention of design practitioners and scholars. However, there are still research gaps in this approach in current research. Therefore, this study uses the Flying Goose viewing platform as a case study to supplement the lack of specific case studies on non-linear landscape structures; it analyses the modelling logic through three parts: morphological characteristics, structural system, appendages and decoration to supplement the lack of systematic knowledge on modelling logic; it analyses the four methods of unfolding control, isometric projection, function shaping and linear interference. The analysis and discussion of the four core precision control methods used in the Rhino+Grasshopper parametric modelling process complements the current lack of specific research on Rhino+Grasshopper parametric modelling morphological precision control methods. The aim is to provide a systematic analysis of the modelling logic of non-linear landscape structures and a detailed analysis of the precision control methods on top of the non-linear landscape structures morphological realisation, providing a theoretical basis and application examples for future research of the same type.

Navigation Line Extraction Method for Broad-Leaved Plants in the Multi-Period Environments of the High-Ridge Cultivation Mode

Navigation line extraction is critical for precision agriculture and automatic navigation. A novel method for extracting navigation lines based on machine vision is proposed herein using a straight line detected based on a high-ridge crop row. Aiming at the low-level automation of machines in field environments of a high-ridge cultivation mode for broad-leaved plants, a navigation line extraction method suitable for multiple periods and with high timeliness is designed. The method comprises four sequentially linked phases: image segmentation, feature point extraction, navigation line calculation, and dynamic segmentation horizontal strip number feedback. The a* component of the CIE-Lab colour space is extracted to preliminarily extract the crop row features. The OTSU algorithm is combined with morphological processing to completely separate the crop rows and backgrounds. The crop row feature points are extracted using an improved isometric segmented vertical projection method. While calculating the navigation lines, an adaptive clustering method is used to cluster the adjacent feature points. A dynamic segmentation point clustering method is used to determine the final clustering feature point sets, and the feature point sets are optimised using lateral distance and point line distance methods. In the optimisation process, a linear regression method based on the Huber loss function is used to fit the optimised feature point set to obtain the crop row centreline, and the navigation line is calculated according to the two crop lines. Finally, before entering the next frame processing process, a feedback mechanism to calculate a number of horizontal strips for the next frame is introduced to improve the ability of the algorithm to adapt to multiple periods. The experimental results show that the proposed method can meet the efficiency requirements for visual navigation. The average time for the image processing of four samples is 38.53 ms. Compared with the least squares method, the proposed method can adapt to a longer growth period of crops.

Isometric projection with reconstruction

Isometric projection with reconstruction

Восстановление внешнего облика мужчины из шемахинского могильника периода раннего средневековья

Introduction. Until now, no work has been carried out to reconstruct the external appearance of the ancient population of Transcaucasia. In order to fill this gap, this study of the skull of a man from an early medieval catacomb burial in the Shamakhi region of Azerbaijan was undertaken. Craniometric and odontometric measurements determined the sex, racial type, age at death, revealed pathologies of the dentition and various traumatic injuries. The purpose of the work was to obtain primary information about the appearance of people who lived in the first centuries of our era on the territory of Azerbaijan and thereby attract scientific attention to this problem. Materials and methods. The skull, found in 1949 by the expedition of R.M. Kasimova with the participation of G.F. Debets, underwent an anthropological study according to classical programs to determine age, gender and race. Lifetime appearance restoration in the form of a graphic portrait in isometric projection was carried out according to the method of M.M. Gerasimov and E.V. Veselovskaya using Adobe Photoshop CC 2020 graphics editor. Results. A table of individual measurements of the skull is presented, lifetime dimensions of the head are calculated, and a verbal description of the appearance is given. In racial terms, the subject can be attributed to the Caspian subtype of the Indo-Mediterranean race, the most characteristic modern representatives of which are Azerbaijanis, which also illustrates the reconstructed graphic appearance. Discussion. The metric data of the skull were compared with similar characteristics of the closest male samples, which included a total of over 1300 skulls from the Caucasus, Central Asia, and Southwestern Europe. Based on the results of applying the corresponding discriminant analysis equations, it was found that the studied skull in the racial format belongs to the Caspian anthropological type. Conclusion. As a result of the reconstruction of the appearance of the skull of a man from the early medieval burial ground in the Shamakhi region of Azerbaijan, paleoanthropological material unique for the Transcaucasian region was obtained for the first time. Previous archaeogenetic studies confirmed its belonging to the local population of Transcaucasia.

Tensor Train Random Projection

This work proposes a Tensor Train Random Projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a Tensor Train (TT) representation with TT-ranks equal to one. Based on the tensor train format, this random projection method can speed up the dimension reduction procedure for high-dimensional datasets and requires fewer storage costs with little loss in accuracy, compared with existing methods. We provide a theoretical analysis of the bias and the variance of TTRP, which shows that this approach is an expected isometric projection with bounded variance, and we show that the scaling Rademacher variable is an optimal choice for generating the corresponding TT-cores. Detailed numerical experiments with synthetic datasets and the MNIST dataset are conducted to demonstrate the efficiency of TTRP.

Оценка метрических свойств отображения геопространственной информации средствами картографических веб-технологий для района Арктики и континентального шельфа

In this article we discuss methods of displaying geospatial information for the Arctic region and the continental shelf using various web technologies in order to solve applied tasks associated with the development of the regional infrastructure. The assessment of the main projections’ metric capabilities basic for cartographic services is carried out, and the functionality of search and demonstration tasks that can be solved by means of such information systems is determined. The necessity of optimizing the approach to data design is noted. The proposed method for displaying geospatial information in the form of a single unified isometric cartographic projection will enable determining the position of objects within the planned accuracy of topographic maps at scale of 1

Methods for displaying data using web technologies for the Arctic region and the continental shelf

In this article we discuss the principles of geospatial data design, which underlie the methods of displaying information based on the projection methods for the Arctic region and the continental shelf, using various web technologies. Various cartographic services were stud-ied depending on their functionality, the software development geography, and the associated mathematical system basis. We assessed the metric capabilities of the main projections under-lying the mapping services and determined the search functionality and demonstration tasks that can be solved by means of similar information systems. It is pointed out that it is neces-sary to provide the analytical functions for services and geoportals, which is necessary for mapping tools in making decisions. The principle of increasing accuracy, unification, ease of use was supported by the development of the unified approach for choosing a projection, that is the Unified Isometric Cartographic Projection. The use of this projection will make it possible to approach the data design issue in a unified manner, which, on the whole, will increase the cartographic security of the region and will make it possible to solve the cartographic problems in the unified manner. The accurate evaluation of the data obtained on the basis of this projec-tion showed that the results can be within the two meters accuracy. Such metric parameters are sufficient to make the design decisions on the infrastructure facilities’ development in the Arctic region and the continental shelf. In order to improve and develop the geoportal “The Arctic Spatial Data Infrastructure” (Arctic SDI), the option of improving its mathematical basis is a promising direction. In addition, the use of the Unified Isometric Cartographic Projection in a GIS user environment will remove the issue of the complex search for the optimal projection. Regardless of the tasks of mapping, when choosing the element needed (GIS user environment, 2D and 3D mapping services, databases) that defines the web mapping technology, data de-signing according to the single principle will remove a number of technical issues and incon-veniences, bringing it closer to the best option.

Subspace Learning and Feature Selection via Orthogonal Mapping

A plethora of dimensionality reduction (DR) techniques, stemming from statistics, machine learning, or graph theory, has been developed. Their ultimate objective is to eliminate data redundancy without a significant information loss. A general formulation, known as graph embedding, offers a unified framework for describing several well-known DR algorithms. In this paper, the inclusion of several DR algorithms within this unified framework is demonstrated. The enforcement of orthogonality to the projection matrix within this framework is proven to be of vital importance, since Orthogonal Neighborhood Preserving Projections, Orthogonal Locality Preserving Projections, Orthogonal Isometric Projection, Orthogonal Linear Discriminant Analysis, and Orthogonal Local Tangent Space Alignment algorithms outperform their non-orthogonal counterparts, e.g., Neighborhood Preserving Embedding, Locality Preserving Projections, Isometric Mapping, Linear Discriminant Analysis, and Local Tangent Space Alignment. One may simultaneously also impose the $\ell _{2,1}$ norm regularization on the projection matrix, seeking for row-sparsity. This leads to the known Joint Feature Selection and Subspace Learning (JFSSL) framework. All DR algorithms are employed within JFSSL. It is proven that the use of orthogonal mapping algorithms within JFSSL against their non-orthogonal counterparts does not improve the recognition rate of NN classifier.

Another New Design for an Old Map

Another New Design for an Old Map

THE IDEALIZED MODELS OF SOFTWARE SYSTEMS REENGINEERING

Content. Software systems are used in a variety of branches of life and human activities, but they are most widely used in industries where it is necessary to work with many routine operations – this applies to industry, production, transportation, training and info communications. Of course, in the process of exploiting these systems there is an evolutionary aging of the different types of security. This trend leads to a deterioration of high-speed, information-communication, graphic, time and other characteristics, up to the complete failure of the software system. The subject of the article is aimed to the design of ergative systems, project management and programs for re-designing or improving these systems. Reengineering allows the system to evolve, by making positive changes to its structure in order to improve operational characteristics and technical support. Objective. To form a representation of the estimation of resource cost parameters for the reengineering of software systems with the help of a mathematical tools for describing design models. Method. The idea of the article is based on the Boehm method and the principles of building an Archimedes spiral. Author’s research led to the idea of combining Boehm and Archimedes structures, adapting them to the software engineering methodology and transferring them to a cylindrical coordinate system. The basis of the obtained models is laid spiral principle of the organization of the reference. Results. The article deals with the process of creating and visualizing mathematical models in relation to the process of reengineering software systems. Transactions with these models can occur in projections of time and cost, in the isometric projection of software components, and in the logarithmic projection of lines of software code. Conclusions. For the first time, idealized models of reengineering have been formed, which will allow to increase the accuracy of cost estimation from the redesign of software systems. The model of cost visualization for reprogramming of software systems has been improved, which will increase the efficiency of forecasting the order of expenses. For the first time dependencies were obtained on the construction of the graphical cost model trajectory from the introduced reengineering automation coefficient and the similarity coefficient of the components that would make changes to the configuration of the model. The proposed idealized models for reengineering of software system security are evolutionary spirals, which are constructed in a cylindrical coordinate system. Reengineering, which will be accomplished with the help of developed idealized reengineering models, will not only reduce the cost of reprogramming software systems, but also increase the efficiency of technical support, increase the life cycle of software systems which are already in service and overcome the contradictions between the rapid pace of development of science, technology and processes of designing new software systems.

A Mission Impossible? Learning the Logic of Space with Impossible Figures in Experience-Based Mathematics Education

Most visual effects based on mathematically and physically describable phenomena and formalizable processes. Creating visual illusions, paradox structures and ‘impossible’ figures through playful and artistic procedures, holds an exciting pedagogical opportunity for raising students’ interest towards mathematics and natural sciences and technical aspects of visual arts. The Experience Workshop Math-Art Movement has a number of pedagogical methods, which are connected to visual paradoxes and perspective illusions. In the first part of our article, we introduce classroom exercises connected to the Hungarian artist Tamás F. Farkas’s paradox structures and impossible figures. There are certain digital games as well, which employ visual illusions as a part of their game mechanic. Most of these games were not designed as an educational game, but they may be used for educational purposes, to clarify mathematical concepts behind and related to visual illusions (symmetry, perspective, isometric projection etc.). In the second part of the article we analyze which characteristics of these games can contribute to the pedagogic impact, and how to best take advantage of them in an educational context.

Block imbedding and interlacing results for normal matrices

A pair of matrices is said to be imbeddable precisely when one is an isometric projection of the other on a suitable subspace. The concept of imbedding has been the subject of extensive study. Particular emphasis has been placed on relating the spectra of the matrices involved, especially when both matrices are Hermitian or normal. In this paper, the notion of block imbedding is introduced and shown to be intimately connected to an extension of interlacing for eigenvalues of normal matrices. Thus, a generalization of a classic Theorem of K. Fan and G. Pall is obtained, which is then applied to yield bounds on the number of eigenvalues of a block imbeddable pair in a closed, convex set. Moreover, a wide class of normal matrices, for which block imbedding applies, is indicated. Finally, comments and links on the necessary imbedding conditions of D. Carlson and E.M. de Sa, and J.P. Queiro and A.L. Duarte are provided.

Efficacy of Interactive Whiteboard on Psychomotor Skills Achievement of Students in Isometric and Orthographic Projection

This paper discusses importance of technology education and evidences of declining performance of junior secondary school students in basic technology subject. Potentials on interactive whiteboard (IWB) as one of the new technologies to meet the challenges of the 21stcentury are also discussed. The efficacy of IWB for teaching Isometric and Orthographic projection concepts in Technical Drawing aspect of Basic Technology was determined using a pretest-posttest, non-equivalent, non-randomized quasi-experimental design. A 2x2x3 factorial design was employed. Ninety Four (49 males and 45 females) and (31 high, 51 medium and 12 low achievers) JSS-1 students from two secondary schools in Abuja Metropolis made-up the sample. The schools were randomly assigned to experimental and control groups. The experimental group was taught selected concepts of Isometric and Orthographic Projections using IWB and (Chalkboard) traditional method were used for the control group. A validated Basic Technology Achievement Test (BTAT) comprised of 25-item multiple-choice object test was employed for data collection. The reliability coefficient of BTAT was 0.88 using Kuder-Richardson (KR-20). The hypotheses were tested using ANCOVA and Scheffe post-hoc analysis. Results revealed that the students taught with IWB performed better than the control group. Also, high achievers performed better than medium and low achievers respectfully. The IWB was found also to be gender friendly. Based on the findings, it was recommended that the use of IWB should be encouraged in Nigerian schools.

Palm Vein Verification Using Multiple Features and Isometric Projection

Biometric authentication has been widely studied for many years and attracted much attention due to its large ability security application. Palm vein is more immovable and more difficult to fake than other biometrics such as fingerprint, palm print and face. Since palm veins exist inside of the body, it is exceedingly hard to be forged. Palm vein authentication uses the unique patterns of the palm vein to identify individuals at a high level of accuracy. In the proposed work, the palm vein image enhancement algorithm proposed based on Gaussian matched filtering and then two types of feature extraction are extracted. The global features based on wavelet coefficients and locale feature based on local binary pattern (LBP). In the propose work, a linear dimensionality reduction algorithm, called Isometric Projection is used. Finally, the Manhattan Distance (MHD) matching method is proposed to verify the test palm vein images. The experimental result shows the EER to the proposed method is 0.17488%.

Research on Airborne Radar Reconnaissance Map Projection Location Error Correction Method

Airborne radar reconnaissance system will produce a map projection angle error in actual, which further causing the positioning error. To correct these errors, the paper proposed a map projection positioning error correction algorithm. The algorithm firstly calculate the reference point using the Mercator isometric projection, and then calculate map correction angle with the inverse projection, at last eliminating the error caused by reference distance estimation using the iterative cross positioning, which improving the location accuracy. Experiments show that this method is reasonable and effective.

SPATIAL ABILITY, 3D MODELING AND STYLES OF THINKING IN RELATION TO BRAIN HEMISPHERE DOMINANCE

The progress of neuroscience and the understanding of children's styles of thinking are opening up new teaching styles that take into account differences in individual cognitive perception. Students can be classified into three distinctive perceptive types, according to the pronounced activity of one cerebral hemisphere in their thinking and information processing: left-hemisphere, right-hemisphere, and integrative type that does not exhibit a considerable dominance of one particular hemisphere. The purpose of the research was to establish differences in the 3D modeling encouraged progression of spatial ability between the left-hemisphere, right-hemisphere and integrative types of students. Computerized 3D modeling employed during technical extra-curricular activity in lower secondary school (grades 6 to 9) may affect the spatial ability of students, which according to other studies, appears to be predominantly connected with the right brain hemisphere. Research was conducted among a variety of lower secondary school students across Slovenia aged 11 – 15 years. Data on spatial ability and its development was collected using a hybrid spatial intelligence test conducted on two separate occasions, while assessment of the learning perception type of students – depending on hemispheric dominance – was obtained using a self-evaluation questionnaire. The 3D modeling of technical objects and objects drawn in orthographic or isometric projection was done with the software Trimble SketchUp. Key words: cognitive development, 3D modeling, hemispheric dominance, spatial ability.

山水画の構成手法と池泉鑑賞式庭園の景観構成に関する研究

This paper is a part of the research intends to shed light on the model of ideal scenery in Muromachi period. The aim of this paper is to clarify weather the landscape painting affected the landscape composition of viewing pond gardens in the period. There are eight gardens still exist, and each garden consists of upper part with main stone arrangements and lower one with pond in common. The landscapes of gardens are analyzed by the arrangement of garden elements according to the line of view. In consequence, we have following two distinct types of landscape composition: ‘diagonal type’ and ‘orthogonal type’. Five gardens of ‘diagonal type’ are characterized by the composition that stone arrangements lined along diagonal vector show the unification of garden elements. Three gardens of ‘orthogonal type’ show the vector toward the artificial hills in the center contrasts garden elements lined horizontal. Each spatial composition is illustrated with isometric projection, and considered by comparison to two configuration methods of landscape paintings: ‘three perspective drawing’ and ‘one corner’ composition.

Learning orthogonal projections for Isomap

We propose a dimensionality reduction technique in this paper, named Orthogonal Isometric Projection (OIP). In contrast with Isomap, which learns the low-dimension embedding, and solves problem under the classic Multidimensional Scaling (MDS) framework, we consider an explicit linear projection by capturing the geodesic distance, which is able to handle new data straightforward, and leads to a standard eigenvalue problem. We consider the orthogonal projection, and analyze the properties of orthogonal projection, and demonstrate the benefits, in which Euclidean distance, and angle at each pair in high-dimensional space are equivalent to ones in low-dimension, such that both global and local geometric structure are preserved. Numerical experiments are reported to demonstrate the performance of OIP by comparing with a few competing methods over different datasets.