Examples of polygonal modeling in 3ds max. Lesson: Simple TV polygon modeling
What is polygonal 3D modeling and what is it used for?
Polygonal 3D modeling is an integral part of our daily life. Modern man encounters it almost every day, perhaps without even realizing it. Cinema, animation, computer games, virtual reality, etc. – all these are areas where polygonal 3D graphics are used.
With the advent of 3D printers, polygonal models have also been used for 3D printing of objects.
Due to the growing popularity of 3D printers, and the relatively simpler 3D modeling compared to surface/solid state, polygonal model formats have begun to be increasingly used by developers of CNC programs for computer numerical control (CNC) machines. Mainly CNC on wood, plastics and soft metals.
To have a correct understanding of 3D modeling and correctly set the task for the designer, it is enough to know a few fundamental principles.
Today there are two main directions in the development of 3D modeling of objects: polygonal and solid (surface).
The main direction where polygonal 3D modeling is used is 3D graphics. Solid State/Surface - Industrial Design.
Depending on what kind of final product you want to obtain, you can choose either solid (surface) 3D modeling or polygonal modeling.
For example, if you want to print a toy on a 3D printer or cut out a 3D relief of a picture from wood on a milling machine, then you should choose the polygonal format of the 3D model. If you are going to release any industrial product, then you will have to opt for a solid-state format. (see section “Technologies” Solid/surface 3D modeling).
The differences between the two formats lie in the principles of forming a 3D object. In polygonal 3D modeling, objects are built from polygons; in solid/surface 3D modeling, objects are built from geometric elements such as lines. curves, splines, etc., and based on these elements, various geometric shapes are built.
A polygon is a single surface element, represented in the form of a triangle or quadrangle, which is placed in a three-dimensional coordinate system. In fact, polygonal modeling is a descendant of a two-dimensional raster image (the well-known pixel), but in a three-dimensional coordinate system.
The quality of a polygonal 3D model is determined by the number of polygons and how their edges connect to each other. The rule always applies - the more polygons, the higher the detail of the polygonal 3D model.
In 3D modeling, with high detail of the polygonal model, the mating of the edges does not matter much if you are going to manufacture this product on a 3D printer or on a milling machine. As a rule, CNC systems on machines that accept this format have algorithms that make such errors in the polygonal 3D model insignificant.
Polygonal models are not used for the manufacture of complex parts on machine tools due to the impossibility of processing the part with various tools during the machining process. And this is an extremely important condition if an industrial part is being processed. There is a high probability that licensed CNC software for modern metalworking machines will not even have the import of polygonal models.
So, if your task is to manufacture a product with high precision, with straight holes, threads, etc., then you should choose surface/solid-state 3D modeling.
The most common format of a polygonal 3D model, accepted by most CNC programs, for generating control programs for machine tools is *.STL (Binary).
Less common are *.3DS, *.OBJ, *.ASC, *.PLY, *.FCS.
We would like to draw your attention to the fact that there is currently no effective converter for converting STL to IGS, STP (solid-state model). All solutions give mediocre results that cannot be used without additional modifications to the 3D model.
Converting a polygonal 3D model from one polygon format to another is usually done by resaving the 3D model file in the desired format.
Remember that the correct choice of data format before starting modeling, and the correct formulation of the task to the contractor of your order is the basis for obtaining the expected quality of the product!
This 3ds Max polygon modeling tutorial covers the most commonly used 3d operations using the Edit Poly modifier (or Editable Poly). This method is great for creating almost any object in 3ds Max.
First, let's create a simple Box primitive with the proportions of a real TV. 
Fig.1. Created the initial 3d primitive - Box
Let's apply a modifier to our box Edit Poly
Fig.2. Modifier applied Edit Poly
By pressing a key F4 On the keyboard in 3ds Max we turn on the display of the edges of our polygonal model.
In the modifier stack, we go to the polygon level to start modeling. And select the front polygon where we will start creating the screen. 
Fig.3. We went to the polygon level and selected the front one in the perspective window
Apply the operation to the selected polygon Inset to create a face as shown in the figure. It will serve as the basis for creating the screen. 
Fig.4. Applying the operation to the polygon Inset
We press the resulting polygon inward with the command Extrude.
Fig.5. Pressed the landfill with an operation Extrude
We subdivide the double-pressed polygon using the operation Tessellate(Subdivision), thereby increasing the detail of the front face for the possibility of its further deformation. In general, it is not recommended to abuse this operation in your models. 
Fig.6. We increase the detail of a face using an operation Tessellate
Go to the vertex level and select the central vertex of the screen. 
Fig.7. Selected central vertex
Activate soft selection mode Soft Selection(Thanks to it, we will be able to deform the object more smoothly). Pay attention to the Falloff and Bubble parameters. Falloff is responsible for the width of the capture zone of neighboring vertices. Bubble- for the form of distribution of weights. The coloration clearly shows the degree of capture.
Now let's move the central vertex forward a little to round out the screen. When finished, be sure to exit soft selection mode. 
Fig.8. Move the central vertex a little forward in soft selection mode
The screen is ready, now we need to prepare the back wall. Go back to the polygon level and select the back face. 
Fig.9. Selected the back edge of the TV
Apply the operation to the selected polygon Bevel(Bevel extrusion).
Height- amount of extrusion
Outline- degree of narrowing 
Fig. 10. Selected the back edge of the TV
We extrude the back edge again using the operation Extrude.
Height- amount of extrusion 
Consider the main components of the theory of polygonal modeling.
Quads vs TrisesN-gon
So, what's the difference between a quad, a tris and an N-gon? Well, a quad is a polygon that has 4 sides, a tris is a polygon that has 3 sides, an N-gon is a polygon that has more than 4 sides.
When modeling, it's best to stick to quads or quads. Mainly due to the fact that they divide more predictably, deform better in animation, and textures are distorted the least.
Trises or triangles are best used where they are least visible.
But it’s better to avoid using N-gons altogether, since they can form strange artifacts in the render, and it’s almost impossible to paint a skin with polygons well when rigged.
In addition, in digital sculpting programs such as ZBrush and Mudbox, it is most convenient to work with a model consisting of quadrangles.
The joy of polygons and the sadness of polygons
Uniform-geometry
Uniform geometry means that during the modeling process you try to stick to quads or quads as much as possible, placing them as evenly as possible. It will be a pleasure to rig such geometry; it will deform perfectly during animation. And, despite the fact that good textures largely depend on good UV mapping, they will be distorted even less if the geometry consists of quadrangles.
Maya has a wonderful Sculpt Geometry tool that, if you go into Relax mode, can perfectly smooth out the edges.
Using a toolSculpt Geometry you can smooth out the edges
Topology
At first glance, the location of the edges does not matter. But that's not true.
When modeling realistic characters, it is worth studying human anatomy. In this case, the direction of the edges and topology should correspond to the location of the muscles on the human body, which will create a more correct deformation of the geometry.
In the case of more cartoonish and stylized characters, there is more room for maneuver, however, knowledge of anatomy will not be superfluous even in this case.
For correct deformations, the topology must be appropriate with the necessary edge loops
Non-manifoldgeometry
Non-manifold geometry may contain various errors that arose during the modeling process. These can be hanging edges (without faces); edges, common to three or more faces; normals of adjacent faces directed in opposite directions; the number of faces converging at one vertex may differ from the number of faces emanating from this vertex, etc.
For example, create a cube, select one of its edges and run Edit Mesh > Extrude. So, we have a non-manifold object. If it were a piece of paper, there would be a crease that would be difficult to get rid of. If you perform a Boolean operation on such a cube, then everything will immediately become clear.
Non-manifold geometry can be a pain, so try to avoid it. The Cleanup tool, which is located in the Mesh menu, will help solve many problems associated with non-manifold geometry.
Non-manifold geometry can be a pain
Every edge should be in its place
Ideally, we start the modeling process with a simple primitive, for example, a cube, to which we then add edge loops, extrusion, etc.
It is important to maintain simple complexity, adding details only where it is really needed. Less can be more. Over time you will have a better understanding of how to optimize the model, but for now just keep modeling.
Don't make the model overly complex, add details only where it's really needed
Explore the world around you
Everything that we try to recreate programmatically is a reflection of really existing things. Therefore, the most important advice would be to study the world around you.
And this applies not only to modellers, but also to riggers, animators, lighting designers, etc. Think about how this or that object is structured, how it is illuminated, deformed, etc. Finding answers to such questions will make life much easier.
Want to know more? Come to our
Introduction to Polygons
Polygons are one of the types of geometry used to create 3D models in Autodesk® Maya®. In addition, Maya has two more types of surfaces - NURBS and hierarchical (subdivision).
Polygons are used to create many types of 3D models and are widely used to design 3D objects in films, video games, and the Internet.
Polygon Terminology
Polygons are shapes with straight sides (3 or more sides) defined by points in 3D space ( vertices) and lines connecting these points (edge)). The interior area of the polygon is called face. Edge and face vertices are the basic components of polygons. You can select and modify polygons using basic components.
When creating polygonal models, three-sided (triangles) or four-sided (quadrangles) polygons are most often used. Maya also supports polygons with more sides, but they are used much less frequently.
A single polygon is also called a face and is defined as an area bounded by three or more vertices and their corresponding edges. If many faces are connected to each other, then such an object is called a polygonal mesh (polygon mesh) or polygonal object. A polygon mesh can be created in different ways. For more information on how to create polygon features, see below.
Typically in a polygon mesh, vertices and edges are shared between different faces. In this case they are called shared vertices or shared edges.
Polygon meshes can consist of unconnected parts called shells. The outer edges of the mesh are called border edges.
Applying a texture to a polygonal model
A texture can be applied to polygonal models using UV coordinates. For more information, see the separate tutorial on working with texture coordinates.
Polygon Modeling Overview
There are different techniques for creating polygon models in Maya:
- Primitives are 3D geometric shapes that you can create in Maya. Primitives include, for example, sphere, cube, cylinder, cone, plane and many others. You can change the basic attributes of a primitive to make it more complex. You can also cut, extrude, merge, or remove different components of a primitive to change its shape. Many 3D artists use primitives as a starting point for creating models. This technique is called modeling from a primitive.
- Individual polygons can be created using the Create Polygon Tool. This tool allows you to place vertices in the scene that define the shape of a polygonal face. You can also cut or extrude a polygon face to add new faces to an existing one. This technique is usually used if you need to most accurately build a model along a given contour. For example, you can use the described technique if you need to build a complex 3D logo using an imported 2D image as a reference.
- Polygons can also be created by transforming existing NURBS or subdivision surfaces using the Modify menu.
Polygon normals
A normal is an imaginary line perpendicular to the surface of the polygon. In Maya, normals are used to determine the orientation of a polygon face (face normals), or to calculate the shading of faces (vertex normals).
Face Normals
The front side of a polygon's face is represented graphically by a vector perpendicular to it, called the face normal.
The order in which the vertices surrounding a face are listed determines its direction (which way the face is facing, and which way the face is facing). This fact can be important because polygons are only visible from their front side, although Maya by default makes all polygons visible from both sides. You can disable this feature for any polygon mesh.
When shading or rendering polygons, normals determine the reflection of light from the faces, and therefore the color of the polygon model.
Vertex normals
Vertex normals control the smoothness of the shading between polygon faces, as opposed to face normals, which control whether a polygon is visible or invisible.
Vertex normals are represented by lines starting at a vertex, one for each face that uses that vertex.
- If all the normals of one vertex have exactly the same direction (in this case they are called general or soft normals), then the color transition from face to face will be smooth.
- If the vertex normals point in the same direction for each face (in which case they are called hard normals), the color transition between faces will be sharp, creating the effect of a faceted surface.
Advanced users can manually manipulate vertex normals to create the appearance of hard edges (creases) and shadows without using additional geometry. For this operation, use the Vertex Normal Edit Tool item in the Normals menu. If a normal is manually edited, it is frozen. If you unfreeze a previously edited normal, Maya will automatically recalculate its direction and return it to its default position.
This tutorial is a good start for anyone who wants to learn how to model top-notch characters. Famous in his circle, Jahirul Amin will talk about the importance of correct topology, uniform mesh, the importance of quadrangular polygons and much more.
Before diving into the 3D whirlpool, I suggest having a short educational program and splashing around in the shallow water. Below we will touch on the basics of polygonal modeling, without knowledge of which it is pointless to move on.
Introduction
When geometry becomes a modeler's or animator's aid, the ideal mesh layout comes first. After this, a good topology should come into play, reducing the number of defects in character animation. In other words, a correctly (and on time) created polygon will save not only hours but days of your life.
3-gon vs 4-gon vs N-gon
So what's the difference between 3-, 4-, and N-gon polygons? The answer is obvious: the first has 3 sides, the second has 4, the third has any number of them, more than 4. If you are modeling a character for further animation, we recommend use only quadrilaterals. The process of deforming and dividing quadrangular polygons is much easier, and you will encounter less texture distortion.
It is recommended to hide triangles from your own and other people's eyes. For example, in the armpits or in the groin area of the character. In turn, an unspoken ban is imposed on polygons - they should not exist. They cause distortion and cause a lot of trouble when it comes to rigging and editing vertex groups (aka “weight-painting”).
Finally, a model that consists primarily of quad polygons will be easier to export to other modeling programs such as Mudbox.
The joys of four and three-gon polygons and the horror of the N-gon
The contours of the face, which by definition resemble an N-gon, should be brought as close as possible to a quadrangular format. Little of - the location of the polygons should be as uniform as possible in principle. This is what the geometry of the same name calls for. Following these rules will make it easier to go through the rigging stage and will help when deforming the character during the animation process. In addition, the scale of distortion associated with the use of textures will be reduced, although here we should not forget about the importance of the UV scan itself.
To perform the described task, Maya provides the Sculpt Geometry tool.
The Sculpt Geometry tool in Maya will help you “smooth out” your model’s mesh
Responsible for the smooth transition of each individual edge (aka Edge Flow). It may sound simple, but in practice it is a very insidious thing.
If you set out to create a realistic character, it is recommended to study the basics of anatomy before starting work. By following the structure of the human body and the natural movement of muscles, the animator ultimately obtains a copy that is close to the original. This is especially clearly seen during the deformation process. We recommend starting with the process of wrinkle formation and skin stretching.
For stylized and cartoon characters, Edge Flow is much less important. But still, I highly recommend getting at least a basic understanding of human anatomy.
To make the shape realistic, create a good topology and be sure to take into account the smooth direction of the mesh (edges, polygons).
It is also non-manifold. Means that a three-dimensional object cannot be cut and made flat.
Example: Create a cube, select any edge (edge) and extrude it Edit Mesh > Extrude. In front of you is a somewhat shaped object. (Example below on the left) If the cube were made of paper, then when unfolded you would get a cross-shaped figure with broken proportions. Using such an object in Boolean operations is practically impossible.
To fix the situation, use the Cleanup tool.
Violation of the geometry topology can create dozens of problems. Be vigilant and periodically inspect the figure from different angles.
Each loop (edge edge) must have a target
As a rule, modeling begins with a primitive figure (for example, a cube), the structure of which is subsequently complicated by adding edge loops.
It is important that each new element is created with a specific purpose. There are situations in which “less” equals “better.” Understanding the principles of model optimization comes only with experience, so don’t get discouraged and keep working.
Don't complicate your life: detail should be appropriate
Everything we are trying to do on the screen is a reflection of the world around us in its various forms and manifestations. This is why it is so important to get up from the table from time to time. Important not only for developers, but also for animators, riggers, lighting directors, etc.
Take a closer look at the surface, its structure and shadow. How does it reflect light? How does the deformation process occur? The answer to these and other questions will help you make the right decision when modeling any object.
