A method in creating 3D models: From shape to shape, from shapes to model (October 2016)

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1 A method in creating 3D models: From shape to shape, from shapes to model (October 2016) M. Sinan Serbetcioglu, BS* Abstract In this paper, we try to create 3D models by using some geometrical primitives. Firstly, we define common primitives that we use. We have chosen 3 primitives; surface, cylinder and ellipsoid. Then we reach 3D models and shapes by transforming and deforming these primitives. Our purpose is to determine some general approach in creating 3D models in computer graphics. I observed some 3d software by using this method. When our examples are looked at, it can be seen this method is successful in creating models. So, you can use this method or its similar (by using different primitives and different deformations and transformations). Therefore, you can create software such as CAD or a game. Keywords Computer graphics, 3D primitives, Meshing, 3D models and shapes, Transformations, Deformations, CAD, Game Engine I I. INTRODUCTION n computer graphics, one of the most important problems is lack of 3d models that we can use. Even if we face lots of models in books, internet or any other platform, when we want to find a complex model that we remind, as it is known, it is nearly impossible to find. Also, when we consider there are nearly infinite numbers of 3D models in the world, we must commonly create these models in each time by using some modeling software instead of looking for the model in another platform. So, the problem is creating these complex models easily in a short time. primitive that you choose to create a part of a 3d model or form. Another problem is not easy and efficient to reach a shape that is wanted with these. So, we must easily and efficiently reach a 3D model by using correct deformations and transformations. In our design, we use rectangular polygons to mesh primitives and models instead of triangles. Main cause is that triangular meshing is more complex and texture mapping is nearly impossible in triangular meshing. When you see our example models you will think you can easily create graphical software from the beginning to the end. I II. CHOOSING PRIMITIVES n our example design, we choose 3 primitives; surface, cylinder and ellipsoid as you can see Figure1,2,3. When we look at various modeling software we see these primitives that are used: cube, cylinder, tube, sphere, torus, cone, capsule etc. So, we must show these 3 primitives are enough to create 3D parts. To do this, we will try to reach other primitives from 3 primitives. We will deform and transform 3 primitives and reach other ones like cube, torus, cone, and capsule. Our method, using primitives, is already used in most of modeling software and tools. However, it is still not easy creating these models. One of the main problems is there is no common primitives in software packages. When you change software to another, you will see the different primitives and it is difficult to decide which *Correspondence to M. Sinan Şerbetçioğlu ( msserbetcioglu@kilis.edu.tr). 1

2 When we apply tightening to all polygons in rectangular surface we can reach triangular surface in order to use it later. We reach from Figure 4.a to Figure 4.b and from Figure 4b to Figure 4c. Another way of reaching a circle is transforming a cylinder to 2d. When you scaled one side of cylinder with 0, you can get circle. We can reach from Figure 6.a to Figure 6.b and from Figure 6.b to Figure 6.c. By using this cylinder tube, we can also reach other 2d primitives. Creating cylinder tube with only 3 edges gives us a triangular tube and triangle. We can reach from Figure 7.a to Figure 7.b and From Figure 7.b to Figure 7.c. When we apply tightening two times along x axis and y axis we can nearly reach a circle. We reach from Figure 5.a to 5.b and from 5.b to 5.c 2

3 With same way we can reach other polygons in 2d such as pentagon, hexagon or etc. We can reach from Figure 8.a to Figure 8.b and from Figure 8.b to Figure 8.c. With the same way, we can reach cylinder from cylinder tube. When we multiply x and z values of top and bottom vertices by 0(scaling about x-axis and z-axis off) and translate about y-axis we reach cylinder. We reach from Figure 10.a to Figure 10.b. You can see solid vision of Figure 10.b in Figure 10.c. Our 2D primitives are all created with rectangular surface and cylinder tube. Let us work on 3D parts now. Firstly, we will create cube from cylinder tube. Creating 4-edge cylinder tube is a rectangular tube and when we close opened sides of tube we will reach cube. In order to close the opened sides we must scale x-axis and z-axis off and transform about y-axis for top and bottom polygons. We can reach from Figure 9.a to Figure 9.b. You can see the solid vision of cube in Figure 9.c. When we tighten cylinder about y-axis we reach cone and truncated cone as you can see in Figure 11.a, Figure 11.b. Figure 11.c shows solid vision of Figure 11.b. 3

4 With same way we can reach a pyramid from cube. When we tighten cube about y-axis we reach a pyramid. You reach Figure 12.b from Figure 12.a. And Figure 12.c shows solid vision of Figure 12.b. Now, we will reach capsule from ellipsoid or sphere. We can reach it by scaling x-axis and z-axis off. We reach Figure 14.b from Figure 14.a. And you can see solid vision of Figure 14.b in Figure 14.c. Now, we try to reach a torus from cylinder. We need translate and rotate each sector of cylinder this time. We reach from Figure 13.a to Figure 13.b and from Figure 13.b to Figure 13.c. Figure 13.d shows solid vision of Figure 13.c. As you see, we can reach other primitives from these 3 primitives; rectangular surface, cylinder tube and ellipsoid (or sphere) with correct transformations and deformations. So, we can choose these 3 primitives for design. If you create 80-90% of shapes or parts in the real life, it s enough for design because more perfect design will be more complex and not efficient. 4

5 III. MESHING OF PRIMITIVES IV.MATERIAL PROPERTIES AND SHADING OF PRIMITIVES As you see in examples, all 2d and 3d parts or shapes can be produced from 3 primitives. All these primitives have common meshing properties. These primitives have n*m vertices. This means a two dimensional array can keep it in memory. Even we can keep it in a one dimensional array or linked list structure. We must choose a programming language like Java, C++, Delphi and graphical library OpenGL, Direct3D here. We will use C++and OpenGL in this design. You can prefer same or another one. Material properties of a primitive are related with light of the environment. According to light, normal, and other material properties of a primitive, shading change. Material properties are simply only one color. But more complexly, we can use shininess, diffusion, specular, ambient and transparency properties for primitives. In the examples below Figure 16, you can understand better what these properties means. Firstly, we define vector definition that is used for a point or a normal. Secondly, we define vertex definition which its node is used n*m times in a primitive. And then polygons come. You can see these data structures in Table1. Here we use Gouraud shading and it needs normal for each vertex and polygon. For example, this rectangular surface has 11x11 vertices and 10x10 polygons. We need 121 vertices and 100 polygons in the memory. For each property, we must add a float to our primitive and some OpenGL code to show function. And we must add a vector for color property. You can see the effect of color property in Figure 17. 5

6 V.MORE COMPLEX SHAPES In real life, most of the shapes are not same color. For that reason we must add texture mapping to our design to reach more realistic parts or shapes. To create a simple shape, for example a planet or a wall, we can need to use texture mapping. You can see how a bitmap is loaded to a primitive in Figure 18 and Figure 19. How can we add a window to this primitive? There is two way of opening a window on wall. Either we use more than one shape or we will make some polygons invisible in the shape. Invisibility gives us better results and more complex shapes. In order to do that, we need add a property to polygon data structure as you see in Table 1. Figure 20 gives us results of visibility. V.DESIGN OF SHAPES We have made choices for design of shapes. Now, we can make design of shapes programmatically. In Table 2, you can see data structures for shape class. 6

7 VI.FROM SHAPE TO SHAPE In our design, we reach complex shapes by transforming and deforming simple primitives. Each time we reach another shape. Common transformations in computer graphics world are translating, rotating and scaling. But there are various deformations that is handled by using different mathematical functions. Here, we don t give coding of these but we give some functions that can be easily coded. Let us give some examples to better understanding. SCALING In the Figure 23, we are scaling torus by 2. We need some mathematical functions to scale. It s simply multiply x, y, z values of all vertices by some coefficient, 2. Table 3 gives you codes for scaling. When you also write constructor function and show function the design will complete. You can add extra functions to your shape class. We give only data structure part of code here. After that design, you can reach such shapes in Figure 21 and 22. If cx=2, cy=1, cz=1, we can reach rectangle from square in Figure 24. When we apply same coefficients to a sphere we reach an ellipsoid as you can see in Figure 25. 7

8 angles for pitch, roll and heading. You can see a rotation example in Figure 28. TRANSLATING When we use translation we must addition with some coefficients in x, y, z values of vertices of the shape. You can see the code for translation in Table 4. This changes place of shape in x, y, z coordinates like in the Figure 26. TWISTING Now, we will start deformations and their functions. Here, we will give you some deformations that is used. Firstly, we start with twisting example. You can see twisting function about y-axis in Table 6. Also you can reach some deformations of the shape by transforming only a few vertices. In our example, we are firstly scaling cylinder tube off. Then we are closing open sides of cylinder by scaling x and z values of top and bottom vertices with 0. After that, we are scaling x and z values of top vertices by 2 and then we tightening bottom of cylinder. At last we use twisting function about y-axis. Figure 29 shows you transforming a screw from a cylinder tube step by step. ROTATING In order to rotate a shape we must use these functions in Table 5. Here, we can think cx, cy, cz coefficients as 8

9 With the same method we can twist a tin of cola as you see in Figure 30. If we tighten an ellipsoid we can reach different 3D shapes. TIGHTENING Let s start to give example of tightening function. In Table 7, you can see codes for tightening about y-axis. When we translate before tightening we reach a raindrop. A is some constant here. You can tighten 3D shapes with this function. Also you can find and use different tightening-expanding functions in your design. In Figure 31, you can see the effect of tightening to a square. If you translate square before tightening, you can reach different shapes. WAVING Let s see the effects of waving deformations. In Table 8, you can see waving function about x and y axis. You can create 5 more functions about waving; y-x, x-z, z-x, z-y, y-z. We can use waving for example in flags. In Figure 36, you can see waving a shape. 9

10 VII.FROM SHAPES TO MODEL After creating such complex shapes, model design nearly is finished. Because only thing what we do is combining this shapes and reaching complex models. In Figure 37, 38 and 39, you can see finished models. In Table 9, you can see data structures for model class. We will translate, rotate, or scale the shapes and combine them to create a model. Then we can reach such realistic models easily. 10

11 VII.CONCLUSION Firstly, we have chosen our 3d primitives for graphical shapes. And then we have decided meshing, texture mapping and shading properties of our primitives. We have coded data structures for shapes and models. After finishing whole coding with functions and procedures of shapes and models, we have reached 3D display software. We have used a known method here, reached models from transformation of complex shapes. Only difference from previous ones, we have used more complex shapes that has more properties. We can name this method with From shape to shape, from shapes to model. Surely, we cannot give whole code in a paper here. But it is a starting point for creating 3D software. You also can create 3D software or game engine by using this method. [2] Dave Shreiner, Graham Sellers, John Kessenich, Bill Licea-Kane, OpenGL Programming Guide, The Kronos OpenGL ARB Working Group,Addison-Wesley, pp 39-42,46-72, , [3] Donald Hearn, M. Pauline Baker, Computer Graphics, Printice Hall International Editions, pp [4] Randi J. Rost, OpenGL Shading Language, Addison-Wesley, Chapter 6, Chapter 9.3 M. Sinan Şerbetçioğlu, received the BS degree from Bilkent University, Ankara, Turkey, in He is currently Software Specialist at 7 Aralık University, Kilis, Turkey. His research includes 3D model creating, meshing, shading, texture mapping, data structures and classes for models, game engine design. REFERENCES [1] Mark Giambruno, 3D Graphics & Animation, New Riders, Chapter 3 11

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