Technical Drawing Solid and Plane Geometry

http://dx.doi.org/x.15446/dyna.v81n188.38147

Aeroplane geometry drawing tutorial

Tutorial de dibujo geométrico

Eduardo Gutiérrez de Ravé, Francisco J. Jiménez-Hornero & Ana B. Ariza-Villaverde

Deptartamet of Graphic Engineering, University of Córdoba, Córdoba, Espana, eduardo@uco.es

Received: May 18^th, 2013. Received in revised form: June 19^th, 2013.Accepted: September 25^th, 2013.

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Abstract
A tutorial has been developed with the aim of making geometry cartoon educational activity easier. It arises as a helpful tool for lecturers and engineering undergraduate students, with the objective of giving support to theoretical and practical lessons in plane geometry drawing. This piece of cake-to-use tutorial provides users with interactivity, applied videos, self-evaluation, fundamental lessons, and "footstep by step" education due to the unlike levels of conceptual complication included in its contents.

Keywords: Airplane Geometry, Geometric Design, Geometric constructions, CAGD.

Resumen
Se ha desarrollado un tutorial para facilitar la docencia del dibujo geométrico. Con la thought de servir de apoyo a las explicaciones teóricas y prácticas de los conceptos correspondientes a los trazados geométricos planos necesarios en la ingeniería. Este tutorial es de fácil manejo y permite interactividad con el usuario, animaciones prácticas, autoevaluaciones, explicaciones amplias del temario y la enseñanza "paso a paso" de los conceptos gracias a los diferentes niveles de complejidad conceptual que incluye en su contenido.

Palabras clave: Geometría métrica, Diseño Geométrico, Construcciones Geométrica, CAGD.

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i. Introduction

In technical cartoon, geometric construction constitutes ane of the fundamentals for engineering students. By and large, the chief goal of geometry pedagogy is to improve spatial skills [one]. Virtually of this ability is caused during elementary and loftier school courses, but some acquisition is left for undergraduate studies [ii]. In full general, geometry is a discipline which interrelates with other subjects such every bit computer science, mathematics, computational geometry, computer-aided design and geometric solid modeling [3]. Geometry is necessary for work in various fields such equally computer graphics, engineering, architecture, and cartography.

Geometry belongs to schoolhouse curricula. On the other manus, geometric construction teaching is being abandoned in the training of future engineers due to the incorporation of Computational Geometry (CG) and Dynamic Geometry (DG) teaching, that brings in dynamicity to the traditional ruler-and-compass geometry learning process. During the 1980s several programs were ready for the purpose of simulating geometric constructions carried out with traditional methods [4]. Botana & Valcarce (2002) [5] introduced "Discover", a program for learning and teaching geometry that permits the replacement of the traditional ruler-and-compass past electronic substitutes. During the 1990s, DG has been increasingly used for teaching, mainly in high schools, although the traditional Euclidean tools are still existence replaced by virtual tools in computers. Current software DG systems, such equally Cabri-Géomètre [6], SketchPad [7], Cinderella [eight,9] iGeom [10], and Geometry Adept [11-13] present spider web-based versions, enabling students to use them worldwide through a web browser. Liu et al. (2007) [14] propose a pen-based intelligent dynamic lecture system for geometry teachers. Plane Geometry plays an of import role in learning, research and engineering. Pythagoras is a software simulator for dynamic geometry [15]. The use of Net and computers tin bring peachy benefits to the didactics of geometry, choosing or creating appropriate programs and methodologies that accept advantage of the computer's positive characteristics [16]. DG programs take proven to be an excellent resources for teachers and students [17]. C.a.R. is a dynamic geometry plan simulating compass and ruler constructions on a computer [18]. However, on a computer, much more is possible, and every bit Hoyles & Noss (2003) [19] have shown, Dynamic Geometry systems are ''pedagogic tools finely tuned for the exploration of a mathematical domain''. DG can be understood every bit existence an alternative to traditional ruler-and-compass geometry, which produces static constructions. However, for engineering students and, specifically, mechanical engineering students (designing manufacturing products) [3] it is necessary to acquire the fundamentals and pace-by-pace processes in geometrical construction. Likewise, they must larn a noesis of Geometry and Drawing, which has not been sufficiently promoted in pre-university or university education during recent years [2]. The use of tools that explain underlying processes in a comprehensive manner [20] introduces immersive collaborative learning into geometry educational activity and applies 3D dynamic geometry to go far easier. Some authors take understood that it is necessary to gain prior noesis of plane geometry cartoon in order to learn 3D structure, and to improve spatial skills. Computer-Aided Education has been of swell benefit to teachers and students [xiv].

In this work, a reckoner application chosen PGDT, acronym of Plane Geometry Drawing Tutorial, has been developed based on computational and dynamic geometry with the aim of facilitating the educational activity and learning of plane geometry concepts. Thus, the topics included in PGDT are the following ones: 1. Drawing tools, 2. Uncomplicated Geometric Constructions, iii. Working with line segments, four. Angles, 5. Triangles, 6. Regular Polygons, vii. Tangencies, 8. Quadrilaterals, nine. Circles and connection, ten. Power, 11. Inversive geometry, 12. Scales, 13. Geometric movements, 14. Homothetic transformation and Similarity (geometry), 15. Affinity.

From a total of 225 methods, 26 of them are explicative and practise not require any data introduction. All the topics considered here are useful for technology and they are mainly focused on geometric constructions.

2. Methods

PGDT has been adult under the Windows operating system (WOS) for the purpose of providing the user with a visual, applied and easy-to-use tool for the execution of dissimilar Graphical methods. Although Windows is not the merely operating system offering those features, it has been chosen because it is one of those most used by students in their personal computers. Delphi is the programming linguistic communication selected for implementing the awarding. Information technology is a powerful compiler that hands manages windows and icons of work environments running under WOS.

In PGDT, the following relevant aspects have been taken into account: i) to visualize the parameters of resulting geometric elements (i.due east. coordinates, perimeter, area); ii) to set an error control during the pace by stride learning process of geometric constructions 3) to describe bones mathematic functions and drawing algorithms. These aspects accept been developed in the following contents included in PGDT:

1. Learning of drawing tool handling by means of videos that explain pace past stride the use of the ruler-and-compass.
2. Theoretical description of each topic: the on-folio program structure allows the user to admission at each moment to its contents. The subject matter is conspicuously ordered in chapters, sections, subsections and methods. Each part is explained on the blackboard, where the user is able to visualize and control the method's execution.
3. Practices and exercises: These permit the improvement of theoretical and practical knowledge interactively using a dynamic data input.

2.1. Application structure

PGDT has two levels: interface and processing, with three and 2 independents units, respectively. Those levels are described as follows:

1. Interface level including the following units i) Application management: used for decision-making user operations such equally awarding closing, resizing and restoring. ii) Lessons index: this shows all the contents and methods of PGDT. iii) Videos: Tutorial videos.
   At this level, three windows are bachelor to the user: main, indexes and video windows. These are described below.
2. Processing level consisting of the next units i) Operations: for videos visualization and lesson-method caption. two) Help: On line assessment

2.i.ane. Interface level

(PGDT interface has iii windows. User can introduce or select parameters and receive some messages by means of dialog boxes.

Chief window.

In Fig. 1, the primary window components can be observed. This window is used as a system advice and is divided into ii views: Theory-Holding Manager and Blackboard, the offset ane showing the theoretical explanation of the selected method too as input data properties. In the second view, the graphic output of the selected method can be observed.

The program enables the creation of geometric objects, such as points, lines, arcs, circumferences, rectangles, ellipses, by using dynamic measures and the modification of their backdrop. In addition, options for saving and press the theory and the graphical methodology are provided, too as graphic tools similar zoom, gridding, rulers or squared patterns. Three colors are used for geometric object representation on the blackboard, red for input, bluish for auxiliary structure elements and green for solutions Finally, PGDT includes on-line aid.

PGDT main windows contain the post-obit items: i) Window frame, ii) Application menu, iii) Toolbar I, iv) Blackboard, five) Theory and Belongings managing director, six) Toolbar 2, vii) Console bulletin, eight) Status Bar.

• Window frame. The functions of this application facilitate window handling. It is composed of: Championship Bar, Card admission (maximization, minimization and restoration of window, movement and resizing and application closing), and fast access to principal functions of WOS carte.
• Menu. Includes the post-obit submenus: File (Print and Save in RTF type for text and BMP for blackboard graphics), Draw (this allows graphic object selection), Edition (to copy, cut, paste or delete the graphic objects on the blackboard), Display (with an index showing all the lessons and methods), Videos, Zoom, Rules, Grid, Help on-line and References.
• Toolbar I. Straight access to: forwards and backward, alphabetize, video, saving, printing, copying, pasting, cutting, deleting, showing grids and rules on the blackboard, graphic object display and zoom tools.
• Blackboard. This is rectangular with the origin of the coordinates in the top left hand corner. Blackboard is used for drawing and showing results.
• Theory and Property manager. Shows theory contents related to the selected method and properties of graphic elements on the blackboard. It is possible to change properties and geometric parameters of input graphic elements. Theory shows the text, including explicative steps. Property shows characteristics of selected graphic objects, coordinates, color and nomenclature used.
• Toolbar II. This is divided into 2 sections. In the section on the left the post-obit actions are found: Human action/Des, Line, Arc, Rectangle, Ellipse, Circle, Indicate. In the correct mitt department the following actions are establish: blackboard cleaning, starting method, "backward" and "forward", and ending method and index.
• Console message. This shows messages when user needs to put information on the blackboard.
• Status bar. This shows the actions in progress.

Index window
This window allows the selection of lessons included in PGDT, Fig. ii.

Video window
This window shows videos independent in the tutorial (Fig. 3). These videos are focused on geometric constructions past means of rulers (square and bevel).

2.1.2. Processing level

In this section, PGDT execution procedure is explained. Options described are: i) Video showing ii) Selecting topic- method, iii) Explanation of method selected, iv)

Selecting properties of graphic elements, 5) Drawing on the blackboard

1. To show a video, the icon access is found in Toolbar I. Moreover, a voice explaining the method shown tin can be heard.
2. Selecting topic-method, this is activated by pressing icon "Muestra el Índice". A window emerges containing 15 tutorial topics and their corresponding methods.
3. Explanation of the selected method. The icons "astern" and "forward" are in Toolbar II and permit the user to run through the steps of the method. Information technology is possible to apply the method by introducing new data through the icon "Limpiar dibujo". If the selected method is merely a theoretical ane, these icons volition non be shown in Toolbar 2.
4. Selecting properties of graphic objects. This option permits users to cull and alter backdrop of input graphic objects that will be shown in red on the blackboard. Merely the configurable properties tin be modified (Fig. 4)
5. Drawing on the blackboard, by using the mouse.

3. Example of application

The background knowledge related to tangency is a relevant geometry subject in technical design because information technology is involved in many frequent systems such as rod-crank and gears. For this reason, the drawings of tangent lines to circles have been chosen as examples of awarding.

The starting time case corresponds to drawing tangent lines from indicate P exterior to a circumvolve. The proposed method is composed of 6 steps. The required graphic object inputs are completed in the first 2 steps and they are placed on the blackboard. Thus, the circle is introduced by drawing it on the blackboard. Coordinates of its center and radius can be modified through the window properties by the keyboard (Fig. five).

The post-obit steps begin past drawing the line linking indicate P and center O (Fig. vi) and finish past calculating the geometric solutions shown in Fig. 7.

The second application case is shown in Fig. eight. It deals with the calculation of common tangents to two independent circles in 9 steps. Fig. 8a shows the two circles drawn on the lath past the user, and Fig. 8b depicts internal and external tangents drawn past the program and the corresponding tangency points

4. Conclusions

This piece of work introduces an application to be used in graphics engineering teaching and learning. I of the main difficulties in encouraging a wider utilize of DG programs is creating content and evaluating and guiding students during learning activities. This problem is overcome by using the proposed calculator application due to the dynamic data entry corresponding to each exercise, and showing the solution pace by pace. Thereby, teachers can choose the necessary parameters in an easy way. One manner to motivate students to think nigh their own mental models is to allow them to manipulate variables, by changing their values and trying to observe how they behave. It is essential to fulfil this requirement in this kind of computer tool. The application is able to run on computers with depression-processing capabilities thus facilitating its required diffusion through east-learning platforms or web.

References

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E. Gutiérrez de Ravé obtained his agronomic engineering science PhD (1987) from the University of Córdoba (Spain). He is currently full professor in the Section of Graphic Engineering and Geomatics at the University of Córdoba. His inquiry is focused in reckoner aided blueprint, curves and surfaces and computer graphics.

F.J. Jiménez-Hornero obtained his agronomic engineering PhD (2003) from the University of Córdoba (Spain). He is currently full professor in the Department of Graphic Engineering and Geomatics at the University of Córdoba. His research is focused in computational fluids mechanics, multifractals and calculator graphics.

A.B. Ariza-Villaverde obtained her agronomic engineering PhD (2013) from the University of Córdoba (Spain). She is currently developing her research activity as grant holder in the Department of Graphic Engineering and Geomatics at the University of Córdoba. Her research lines are GIS, centric maps, multifractals and computer graphics.

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