Introduction to Cartesian Geometry and Cartesianization of Complex Shapes

Saidou, Nourddin

doi:10.11648/j.mcs.20190404.12

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…As already explained in our previous work see saidou [15], to study a cartesian form (Polygonal in R, R 2 , R 3 or polytopes in R n ) is easier to study than any form. To say easy to study is to say easy to control and manage, because the borders are composed of linear parts, see Figure 1 above.…”

Section: Introductionmentioning

confidence: 91%

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confidence: 99%

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Cartesianization of Complex Forms in Saidou’ Spaces

Saidou¹

2019

(GLM)

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In this work, we propose to define a new space that will be called locally Cartesian space (Saidou'Spaces). It is a space defined by a new topology whose fundamental system of neighborhood are compact cartesian subsets, theses subsets were already defined during our previous work, "Geometrical introduction to Cartesian geometry in complex shapes see [15]. It will have the same properties of a Banach space. Then, we will give the steps of a cartesianization method of complex shapes or region in this space. The objective sought by this technique is to find a cartesian form (denoted Car(A)), that approximates any form A, see Figure1 below. It should be noted that cartesianization will be a generalization of the polygonization whish remains the object of research for several researchers in the spaces R 2 Ref [12] [13] [6].

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Section: Introductionmentioning

confidence: 91%

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confidence: 99%

Cartesianization of Complex Forms in Saidou’ Spaces

Saidou¹

2019

(GLM)

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“…The geometry capability contains material regarding points, lines, angles, planes, volumes, and space. Geometry ability is also a process of obtaining information which is then resolved, and conclusions drawn (Dickson, 2017;Galitskaya & Drigas, 2020;Quezada, 2020;Saidou, 2019;Suprapto et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Ability to Develop CNC Machine Part Programs for Vocational High School Students in Indonesia

Kurniawan,

S. Wijanarka

2023

EJEDU

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The aims of this study are (1) to analyze the effect of the ability to read technical drawings on the ability to make CNC program parts; (2) to analyze the effect of geometry skills on the ability to make CNC program parts; (3) to analyze the effect of cutting parameter knowledge on the ability to make CNC program parts; and (4) analyze the effect of the ability to read technical drawings, geometry skills, and knowledge of cutting parameters simultaneously on the ability to make CNC program parts. This research is quantitative correlational research. The subjects of the study were 360 students of SMK class XII in the field of Mechanical Engineering in the city of Palembang, Indonesia, using a random sampling technique by Isaac and Michael equations so that a total sample of 187 students was obtained. The data collection method uses the test method. The data analysis used is a correlational statistical analysis between the three dependent variables and one independent variable. The results of the study: (1) The ability to read technical drawings has a positive and significant effect on the ability to make CNC programs by 11.17%; (2) Geometry ability has no significant effect on the ability to make CNC programs; (3) Knowledge of cutting parameters has a positive and significant effect on the ability to make CNC programs by 75.36%; and, (4) the ability to read technical drawings, geometry skills, and knowledge of cutting parameters have a positive and significant effect on the ability to make CNC programs by 89.9%.

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A Novel Method of Skeletonization of Complex Shapes Based on Bisectors

Saidou,

Zineddine,

Rhazzaf

2024

Comp. Open

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The mathematical skeleton of a complex form has been essential for a variety of scientific fields and of great interest to many researchers for decades. It is based on several concepts such as the reconstruction of forms and image processing. This paper aims to develop a novel mathematical algorithm to approximate the skeleton of a non-polygonal shape and to compare it to the most used methods. The mathematical technique of skeletonization is used as a reference to validate and compare the proposed method to the most used ones. The crux of the proposed technique is to Cartesianize the shape (polygonize in 2D), then skeletonize it. Moreover, this novel method is grounded upon the construction of bisectors on the simplex of the corresponding Cartesianized shape. Python is used to implement the algorithm proposed and test it on multiple shapes. The comparison of the results generated by the proposed algorithm and the Python predefined function skeletonize() shows that the proposed method is more effective and could be adjusted through the rate of Cartesianization of the target shape. The major contributions of this novel technique include the mitigation of some issues of existing methods, simplification, and optimization of the processing performance mainly in terms of algorithm complexity.

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Introduction to Cartesian Geometry and Cartesianization of Complex Shapes

Cited by 3 publications

References 7 publications

Cartesianization of Complex Forms in Saidou’ Spaces

Cartesianization of Complex Forms in Saidou’ Spaces

Analysis of the Ability to Develop CNC Machine Part Programs for Vocational High School Students in Indonesia

A Novel Method of Skeletonization of Complex Shapes Based on Bisectors

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