Introduction to three-dimensional modeling: Geometric solids
It's common knowledge that there are plenty of softwares and applications dedicated to 3D modeling: some of them are easy to use, others require a good knowledge of geometry principles. However, the most famous of them all is AutoCAD.
AutoCAD is a computer-aided design (CAD) program used for 2-D and 3-D design and drafting. AutoCAD is developed and marketed by Autodesk Inc. and was one of the first CAD programs that could be executed on personal computers.
Over the past few years, I used the program to create 2D layouts and I thought it was quasi-impossible for me to create 3D models on the same platform but it turns out that it is not as hard as it might seem and with a little bit of practice and knowledge of the basics of the software, it could be possible to design anything from basic shapes which is the theme of the second class to complex architectural forms and structures.
Before starting the modeling of any object, it is necessary to understand it not only three-dimensionally but also how it is projected onto 2D plans along with sections because every model emerges from 2D layouts. The following examples show us the basics of the modeling part of the object:
Tetrahedron:
Starting with a circle (the CIRCLE command, and then we enter the coordinates of the central point and the lentgh of the radius) drawn on the XY plan to serve to purpose of a guide to us to indicate the 3 points that will allow us to draw the base of the tetrahedron. The division is made possible with the DIVIDE command and the points are connected with POLYLINE. To create the surface of the equilateral triangle we use the SHADE command and we connect the three points.
For the 3D, we create another face that has a common segment with the base triangle. The surface is duplicated using COPY to obtain a similar one and then we use the command ALIGN to connect segments from the two triangles. After, using UCS (UCS then 3P) we change the drawing plan so that we draw an OZ axis that intersects with the center of the circle that will allow us to make the rotation.
The finish the volume with two more faces, we use the command POLAR ARRAY with a defined faces set of 3 around the OZ axis and the final tetrahedron volume is finished and we do not forget to go back to the original referential axis with UCS WORLD.
Cube:
The method of the cube is pretty much similar to the previous one. The 2D base plan is drawn using a circle and divided into 4 segments and using POLYLINE the square is drawn, we copy and align it to the base. We use after UCS to rotate the newly duplicated square at 90°. After we do that, we use the command EXTRUDE to raise the base plan to the height defined by the vertical square.
Ochtaedron:
We start by the base plan which is a square using the CIRCLE and DIVIDE method as it was covered in both of the previous solids. We create one of the faces which is a triangle and we align it to the base and we create the pyramid, and then with MIRROR we copy and rotate the volume after changing the reference axis to OZ using UCS (3P).
Dodecahedron:
The base is a pentagon and it's drawn using CIRCLE divided into 6 and joined by POLYLINE and the surface with REGION which allow us to automatically delete the contour and only have the surface. Afterwards, we duplicate the pentagon and use ALIGN to join it to the base shape. In order to make the 3D volume the lateral face has to be angled and to do so a new lateral face must be created. The angle of the plans are obtained by joining the lateral faces. In TOP VIEW, the line under which the two faces connect represents the bisector between two plans in 2D. The plan is after angled using UCS and after rotated. Having the lateral plane under the right angle, it is be copied around the base plan using POLAR ARRAY with a set number of 5 elemets. The rotation axis has the origin in the center of the base plan. Having half of the volume the other has to be tuned on top by using ALIGN.
Icosahedron:
First of all, a pentagonal pyramid is created using exactly the same method it was adopted for creating the tetrahedron but thi time with five faces. A lateral face is created after changing the reference axis to OZ and aligning it to one of the segments of the base. It needs to be copied again and aligned to the first lateral face so that it's connected to the base and to the new triangle. Using ARRAY with a set number of 5 we create the middle volume using only two of the lateral triangles together. For the remaing part of the solid, we duplicate the top pyramid with COPY and we align it to the bottom part of the middle volume.
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