Topology of the human body. Polygonal character modeling theory

INTRODUCTION

The future explorer is born

not at 30 years old, studying in graduate school,

but much earlier than the time when

his parents will take him to kindergarten for the first time.

Alexander Ilyich Savenkov

doctor of Pedagogical Sciences, Professor of Moscow State Pedagogical University

In the context of the development of new technologies, the demand for people with non-standard thinking, who are able to set and solve new problems has sharply increased. Therefore, the mathematical training of students is becoming more relevant than ever. Here it is appropriate to recall the statement of the great Russian scientist Mikhail Vasilyevich Lomonosov "Mathematics must be taught only then, that it puts the mind in order."

Each person has a visual concept of space, bodies and geometric shapes. In the school geometry course, we will study various bodies and their properties.

But this will be in the future, but for now I was interested in the question: "What is a Mobius strip?" You ask me why I am interested. I will answer. I really love to read. Especially fiction. One of my favorite science fiction writers is Arthur Clarke.

In his story "The Wall of Darkness" one of the heroes travels across an unusual planet bent in the form of a Mobius leaf. I wondered what kind of figure it was and what its properties were.

Having studied the relevant literature and Internet sources, I learned that a separate branch of mathematics - topology - is studying this issue. That is why my work is devoted to solving the simplest research problem in this area.

The purpose of the work can be formulated as getting an idea about one of the most interesting and unusual branches of mathematics, namely topology and the study of the topological properties of some objects.

To achieve this goal, I have solved the following tasks:

understand what this science is studying;

study the history of its occurrence;

consider the topological properties of some objects;

learn about the practical application of topology.

The relevance of the chosen topic lies in the fact that lately this science has increasingly penetrated into such fundamental areas of human knowledge as physics, chemistry, biology. Therefore, knowledge of its foundations becomes significant for a technically educated person living inXXI century.

MAIN PART

Topology as a science and prerequisites for its emergence

Unlike other sections of geometry, where the ratio of lengths, areas, angles and other quantitative characteristics of objects is of great importance, topology is not interested in this, since other, qualitative properties of questions about geometric structures are studied here.

Let's start comprehending the basics of this fascinating science. If we turn to literary sources, then we can find the following definition of this concept.

Topology - a branch of mathematics dealing with the study of the properties of figures (or spaces) that are preserved under continuous deformations, such as, for example, tension, compression or bending.

Let us explain the concept of "continuous deformation" encountered here. Continuous deformation is a deformation of a figure in which there are no breaks (that is, violation of the integrity of the figure) or gluing (that is, the identification of its points).

Each section of mathematics is based on a basic idea. Topology is no exception. The main idea of \u200b\u200btopology is the idea of \u200b\u200bcontinuity, that is, topology studies those properties of geometric objects that are preserved under continuous transformations.

Continuous transformations are characterized by the fact that points located "close to one another" before the transformation remain so after the transformation is completed. During topological transformations, it is allowed to stretch and bend objects, but it is not allowed to tear and break them.

For a visual representation of the definition of topology, it should be said that from the point of view of this science, objects such as a tea cup and a donut are indistinguishable from each other. That is why among scientists there is a catch phrase that says that a mathematician engaged in topology is a person who cannot distinguish a bagel from a teacup. This statement is true because, by squeezing and stretching a piece of rubber from which these objects are made, you can go from one body to the second.

Picture 1 The process of converting a cup to a bagel (torus)

Let's take a historical excursion and return toXVIII century when the foundations of this science were laid.

One of the scientists who stood at the origins of this science is the German mathematician and mechanicXVIII century Leonard Euler. In 1752 he proved Descartes' formula expressing the relationship between the number of vertices, edges and faces of simple polyhedra:

where,.

Euler's next contribution to the development of topology is the solution of the famous bridge problem. It was about an island on the Pregol River in Königsberg (in the place where the river divides into two branches - Old and New Pregol) and seven bridges connecting the island with the banks (Fig. 2).

It was necessary to find out whether it was possible to bypass all seven bridges along a continuous route, having visited each only once and returned to the starting point. Euler replaced land areas with points and bridges with lines. Euler called the resulting schemecount (fig. 3), points are its vertices, and lines are edges.

Picture 2 Königsberg Bridges Problem

L - left bank , P - right bank ,

Picture 3 Graph

The scientist divided the vertices into even and odd, depending on how many edges go out of the vertex. Euler proved that all edges of a graph can be traversed exactly once along a continuous closed route, only if the graph contains only even vertices.

Since the graph in the problem of Konigsberg bridges contains only odd vertices, the required walk route does not exist.

This problem illustrates the practical application of the concept of "unicursal graph", which appeared in the topology dictionary inXX century. The graph is calledunicursal , if it can be "drawn with one stroke", i.e. go through it all in a continuous movement, without going through the same edge twice.

Thus, the graph of the Königsberg bridge problem is not unique and therefore the problem has no solution.

The term "topology" first occurs in a letter to his school teacher Müller, which the German mathematician and physicist, professor at the University of Göttingen Johann Listing wrote in 1836. General topology, originated inXIX century, finally took shape as an independent mathematical discipline by the second halfXX century. To a large extent, this was facilitated by the works of academician P.S. Alexandrova.

Topological properties of objects

Topology is often referred to in popular science literature as rubber geometry. To understand this, it is necessary to imagine that a geometric object is made of rubber and at the same time has the following properties: it can be compressed, stretched, twisted (that is, subjected to all kinds of deformation), but it cannot be torn and glued.

For example, a small ball can be inflated to the size of a large one, then turned into an ellipse, then deformed into a dumbbell.

Picture 4 Object deformation process

Similarly, you can transform the surface of a ball into the surface of a cube, cone, and other shapes. There are properties in mathematics that are not violated by any continuous deformations. That's what it istopological properties ... One of the topology sections - general topology - deals with these properties.

The properties that are studied in school (Euclidean) geometry are not topological. For example, straightness is not a topological property, since a straight line can be bent and become curvy. Triangularity is also not a topological property, since a triangle can be continuously deformed into a circle.

The lengths of the segments, the values \u200b\u200bof the angles, the areas - all these concepts change with continuous transformations. An example of a topological property is the presence of a "hole" in a torus (donut). Moreover, it is important that the hole is not part of the torus. Whatever continuous deformation the torus undergoes, the hole remains.

One-sided surfaces

Each of us has an idea of \u200b\u200bwhat a "surface" is. We are simply surrounded by different surfaces: the surface of a sheet of paper, the surface of a lake, the surface of the globe ...

As a rule, we imagine a surface with two sides: outer and inner, front and back, etc. Could there be something unexpected and even mysterious in such a common concept? It turns out that it can.

In 1858, the German mathematician and astronomer August Ferdinand Möbius (1790-1868) discovered a surface that later became known as the “Mobius strip”. According to the legend, a maid helped to open her "sheet" to Mobius, who incorrectly sewed the ends of an ordinary ribbon.

The Mobius leaf is the simplest one-sided surface with an edge. You can get from one point of such a surface to another without crossing the edges.

Let's repeat this discovery. Let's create an investigated surface and study its properties.

For work we need an A4 sheet, a ruler, a pencil, scissors and glue.

Picture 5 Tools

Draw two strips 4 cm wide on the sheet and cut them out. These will be the blanks from which we will make our ribbon (sheet).

Picture 6 Create a blank

From one strip we glue an ordinary ring, and from the other - a Mobius strip. To do this, turn the second strip half a turn and glue the ends.

Picture 7 Stages of work

Here's what we should get.

Picture 8 Result of work

Let's start exploring the properties of the resulting shapes. With a Mobius strip, you cannot distinguish the front side from the wrong side. They continuously merge into each other. The task to paint different sides of the ring with different colors will not cause difficulty. Let's see this with a simple example. Take a felt-tip pen, make a dot, and start painting on one side continuously. You will see that only its inner surface is painted over.

Picture 9 Coloring the ring

But will this be true for our second paper object? Let's repeat the experiment, choosing as a test surface not a ring, but a Mobius strip.

Picture 10 Mobius leaf staining

You can see that the entire sheet has become colored. But we were still only guiding with a felt-tip pen on one side. From this we can conclude thatthat the tape from which the Mobius sheet is made has two sides, and the sheet itself has one .

If we move along the edge of the Mobius strip, then after a full turn we will find ourselves on the other edge and come from the opposite side.

Let's continue our research and consider the question of how our two figures (a ring and a Mobius strip) will behave when they are cut. If you cut the ring along the midline, you get two narrower rings

Picture 11 Cutting the ring

Picture 12 Ring cut result

If you cut a Mobius strip along the midline, then it does not split into two rings, as it was in the experiment with a ring. We will get one ring, but twice as long (the resulting ring will have a double-sided surface).

Picture 13 Cutting the Mobius strip along the centerline

And what happens if you cut a Mobius strip along a line lying near the edge? To get to the beginning of the cut, we have to travel twice as long as when cutting this sheet along the midline. You will get two interlocking rings, one large and narrow, and the other small and wide. Most interesting fact is that the large ring will have a one-sided surface, and the small one will have a double-sided surface.

If you make a Mobius strip that is twisted 3 half turns (540 degrees), and then cut it in half, you get a Mobius strip twisted in a knot.

Interesting things happen if you fold the paper like an accordion, then make a Mobius sheet out of it and cut it in half or one-third. Before us will appear three interlocked rings.

As researchers of the properties of this figure, we were interested in the question: is it always possible to create a Mobius strip? It turned out that if we take a square sheet of paper and cut a strip out of it, then we will not be able to get the shape we are interested in.

Then a new question arises: what should be the ratio of the length and width of the strip so that it is always possible to obtain a Mobius strip from it? It has been mathematically proven that if we take the width of the strip as 1, then the length should be 1.73.

Practical application of topology

When talking about topology, the Mobius strip is the first thing that comes to mind to a person familiar with this issue. Therefore, in the field of practical application of this science in various branches of human activity, the use of this particular figure is most often encountered.

The amazing properties of the Mobius strip serve as a source of inspiration for writers and poets. As an example, I want to cite a small excerpt from a poem by Natalya Ivanova:

Moebius strip is a symbol of mathematics,

What is the crown of the highest wisdom ...

It is full of unconscious romance:

In it, infinity is rolled up in a ring.

It contains simplicity, and with it - complexity,

which is inaccessible even to the sages:

Here before our eyes the plane has changed

Into a surface without beginning or end.

The classic book about life in two-dimensional space is considered to be "Flatland" by Edwin Abbott and its sequel "Spherland", written by David Burger in 1976.

The Flatlander lives on a planet that has the shape of a two-dimensional surface. If his universe is an infinite plane, then he can travel any distance in any direction. But if the surface on which he lives is closed like a sphere, then it is unlimited and finite.

Whichever direction the Flatlander goes, moving straight and not turning anywhere, he will certainly return to where he began his journey. When a Flatlander travels around the world on a sphere, he seems to be moving along a strip glued into a ring.

But if an inhabitant of this planet travels along the Mobius strip, then returning to the starting point, he will find his heart not on the left, but on the right! A similar situation is described in the science fiction story by H.G. Wells "Plattner's Story." Man, having been in the fourth dimension, returned to Earth with his mirror counterpart - with a heart located on the right.

In production, a belt for a conveyor is made in the form of a Mobius sheet. This design feature makes it possible to increase the service life of the tape, since there is a uniform wear of its surface.

Picture 14 Belt conveyor

Relatively recently, the main device for outputting information from a computer to print was a dot matrix printer. In its print head, the ink ribbon was also laid in the form of a Mobius strip.

Picture 15 Matrix printer

Since we are talking about computers, a computer network is used to connect several machines into a single whole. One of the basic terms of network technology is the concept of network topology.Topology - a general diagram of a computer network, showing the physical location of computers and the connection between them.

Picture 16 Examples of computer network topology

The form of the Mobius strip is quite successfully used in architecture. Here are some examples of this.

Picture 18 Mobius strip logos

There is a hypothesis that the DNA helix itself is a fragment of the Mobius leaf and that is why the genetic code is so difficult to decipher and perceive. In addition, such a structure quite logically explains the reason for the onset of biological death - the spiral closes on itself and self-destruction occurs.

Picture 19 DNA spiral

Artists and graphic artists also paid attention to the topic of interest to us. Illustrative in this regard is the work of the Dutch graphic artistXX century by Maurice Escher. He is known for his lithographs, in which he masterfully explored the plastic aspects of infinity and symmetry.

About his work, he said: "Although I am absolutely ignorant of the exact sciences, it sometimes seems to me that I am closer to mathematicians than to my colleagues - artists."

Picture 20 Lithographs by Maurice Escher

CONCLUSION

Topology is the youngest and most

powerful branch of geometry, clearly

demonstrates fruitful influence

contradictions between intuition and logic.

Richard Courant

american mathematician

A Russian proverb says: "The end is the crown of the work." So my little journey into the fascinating and unusual world of topology has come to an end. It's time to take stock.

In the course of the work, I got acquainted with a new area of \u200b\u200bmathematics for me - topology. Considered some of the simplest concepts used by this science and available for understanding without serious mathematical training.

In practice, he recreated the most famous topological surface - the Möbius strip and investigated its general properties. I also got acquainted with the practical application of topological surfaces in various fields of human activity.

Thus, all the tasks set by me at the beginning of this work were successfully solved. I hope that my acquaintance with this area of \u200b\u200bmathematics will not be so superficial in the future, which gives grounds for continuing to work on the chosen topic as my mathematical baggage accumulates.

BIBLIOGRAPHY

Mathematical encyclopedic Dictionary / Yu.V. Prokhorov [and others]. - M .: Publishing house "Soviet Encyclopedia", 1988. - 340 p.

Boltyansky, V.G. Visual topology / V.G. Boltyansky, V.A. Efremovich - Moscow: Nauka, 1975 .-- 160 p.

Starova, O.A. Topology / O.A. Starova // Mathematics. Everything for the teacher. - 2013. - No. 9. - p.28-34.

Stewart, J. Topology / J. Stewart // Quant. - 1992. - No. 7. - p. 28-30.

Project for Gifted Children: Scarlet Sails [ Electronic resource] - Access mode:http:// nsportal. ru/ ap/ blog/ nauchno- tehnicheskoe- tvorchestvo/ list- myobiusa - access date: 18.01.2017

Prasolov, V.V. Visual topology / V.V. Prasolov. - M .: MTsNMO, 1995 .-- 110 p.

Abbott, E. Flatland / E. Abbott. - M .: Mir, 1976 .-- 130 p.

Topic of conversation: TOPOLOGY.

Topology (from ancient Greek τόπος - place and λόγος - word, doctrine) is a branch of mathematics that studies the phenomenon of continuity in its most general form, in particular, the properties of space that remain unchanged under continuous deformations, for example, connectivity, orientability. Unlike geometry, topology does not consider the metric properties of objects (for example, the distance between a pair of points). For example, in terms of topology, a circle and a donut (solid torus) are indistinguishable.

But this is in mathematics. And what about the characters. I will put it in my own words.
Topology is the ability of a mesh to respond correctly to deformations. Whether it's animation, compression, stretching, or other types of deformation. This is achieved by competently building the polygonal mesh of the character. There are some rules for this. Some of them can be found.

There is also a concept RE-TOPOLOGY... Modification of the topological mesh with maximum preservation of the object's shape. The purpose of retopology is to correct the previous (incorrect) topology and / or reduce the number of polygons.

Almost all modern 3D graphics packages have tools for retopology. I've personally tried it:
1. Maya - both standard tools and plugins.
2. Max - standard tools (horror), plugins and scripts (I liked wrapit, but again, not that much)
3. Zbrush is tight and inconvenient ..
4. Topogun - finally found what I liked ... if I hadn't met
5. 3DCoat .... here I realized that this is still the most convenient for retopology and UV scans ... although it was difficult to figure it out for a start .. but when I understood the principle of the program - everything .. now retopology is only in it. (don't count it as an advertisement.)

Well, since such a booze has gone, I'll post a couple of my images on the topic of topology.
Head and face

found an old render of this head.

topology of the face of a humanoid character. from him you can make both a woman and a child ... not to mention a man.
and here's the proof. done quickly, but clearly.
so. a man, an elf, a creature, a woman, and a girl of about 15 ...
I am not saying that this is the only competent topology, and that it is necessary to do ONLY THIS.
in some studios, characters are modeled with their eyes closed. This allows you to get rid of some problems when closing the eye, and avoid deformities of the eyelid with deformation of the cheek.

wrist.

I draw your attention to the fact that there are vertices to which 6 edges fit ... but in these places there are no problems because the deformations are minimal. Naturally, from this brush you can make a hand for a woman and a man and a child .. yes anyone ..
Skull.

male skull. there are many differences between the male and female skulls.

the differences are as follows:
The male and female skulls have a number of differences. Namely:
1. The male skull is more massive than the female and has a rather square shape. The woman's skull is slightly pointed towards the crown and more rounded.
2. The upper edge of the orbit is slightly sharpened in the female skull, while in the male it has a smoother curve
3. As a result of evolution, the muscles of the face have received a stronger development. Consequently, the place of muscle attachment to the skull is much more noticeable in men. After all, a warrior and a hunter need powerful jaws for battle and struggle.
4. The strong lower jaw of a man is square in shape and that of a woman is rounded.
5. The depth of the skull of men is greater than that of women. This provides relative safety.
6. The brow ridges on the male skull protrude noticeably more. They protect the eyes from direct sunlight.
7. Canines in men are much larger than in women. The warrior and the hunter were forced to eat in field conditions, and, therefore, actively chew food and do it quickly enough.
Hand and body.
If the body is female or without pronounced muscles, then the loupes forming the muscles can be ignored. This applies to the hands. I draw your attention to white polygons. they go from under the pectoral muscle and bend around the deltoid.

Topology - a rather beautiful, sonorous word, very popular in some non-mathematical circles, interested me in the 9th grade. Of course, I did not have an exact idea, however, I suspected that everything was tied to geometry.

Words and text were chosen in such a way that everything was "intuitively clear". As a result - a complete lack of mathematical literacy.

What is topology ? I must say right away that there are at least two terms "Topology" - one of them simply denotes a certain mathematical structure, the second carries with it a whole science. This science consists in the study of the properties of an object that will not change when it is deformed.

Illustrative example 1. A cup of bagel.

We see that the circle is transformed by continuous deformations into a donut (in the common people "two-dimensional torus"). It has been observed that topology studies what remains unchanged under such deformations. In this case, the number of "holes" in the object remains unchanged - it is one. Let's leave it as it is for now, we'll figure it out a little later)

Illustrative example 2. Topological man.

With continuous deformations, a person (see figure) can untangle his fingers - a fact. Not immediately obvious, but you can guess. And if our topological man prudently put the watch on one hand, then our task will become impossible.

Let's be clear

So, I hope a couple of examples have brought some clarity to what is happening.
Let's try to formalize it all childishly.
We will assume that we are working with plasticine figures, and plasticine can stretch, squeeze, while gluing different points and gaps are prohibited... Homeomorphic figures are figures that are translated into each other by continuous deformations described a little earlier.

A very useful case is a sphere with handles. A sphere can have 0 handles - then it's just a sphere, maybe one - then it's a donut (in the common people "two-dimensional torus"), etc.
So why is the sphere with handles isolated from other shapes? It's very simple - any figure is homeomorphic to a sphere with a number of handles. That is, in fact, we have nothing else O_o Any volumetric object is arranged as a sphere with a number of handles. Whether it's a cup, a spoon, a fork (spoon \u003d fork!), A computer mouse, a person.

Such a sufficiently meaningful theorem has been proved. Not by us and not now. More precisely, it has been proven for a much more general situation. Let me explain: we limited ourselves to considering figures molded from plasticine and without cavities. This leads to the following troubles:
1) we cannot get a non-orientable surface in any way (Klein bottle, Möbius strip, projective plane),
2) we restrict ourselves to two-dimensional surfaces (n / a: sphere - two-dimensional surface),
3) we cannot get surfaces, figures extending to infinity (you can of course imagine this, but no plasticine will be enough).

The Mobius strip

Klein bottle

With this article, I begin a series of tutorials on organic 3D modeling. This article is specifically about the principles of modeling, i.e. absolutely independent of the features of your (any) 3D package. This series of articles will cover the following topics:

• the form,
• proportions,
• poles,
• topology
• and much more.

There are a huge number of modeling methods and all of them have their own advantages and disadvantages, so there is no such thing as "The best modeling method".

The reason why I went exactly the way shape - she works. I also always wanted to be a sculptor. Before getting into details, I like to sketch out the rough shape. It is because of this that I have achieved so much and that is why I decided to write this article to help beginners with organic 3D modeling and show them the shape before they start doing anything.

I started with the head shape first and ran into frustration as I tried to do it without any background information (without references - from the English reference), just using your imagination. Instead of sketching out a rough shape, my brain was preoccupied with questions such as "How many cuts are needed? Why? Where and When?"

I was worried not only about the head, but also about the eyes, nose and mouth (and I haven't even gotten to them yet). My brain was confused and I was completely at a loss how to create this head ... until one day when I contrived to sketch a basic boxing head and see ... behold the moment of truth! I was so excited that I decided to do it again! And then again and again, until I was tired of it and I was not exhausted.

Looking back, it seems so elementary and simple to me. All that was needed was to create a box and make a couple of cuts and edits!

However, if it is that simple, then why did I suffer for so long over it? Can we all do this without the problems I experienced? Well my answer is YES! But only if you have it the right mindset... For example, I didn't when I first started.

What I understand now is that when we study 3D modelingthen we just don't teach 3D at all! What we really do is look for the right mindset. So when you are experiencing difficulties in some business, it does not mean that you do not have enough skills or knowledge. This is because you do not have the right mindset to do what you are trying to do.

Once you realign your mind, your reason will take over and you will begin to do things naturally. So this is the first thing we should try to rebuild - the mindset.

Mentality

Drawing a profile (outline): connecting points

This little example will help you rebuild your mindset.

First, just look at this image. Now we will draw a profile using points and connect them. If you only had two points (on the forehead and chin) to connect them. How would you do it? Answer: from the forehead to the chin, because there is simply no other way.

However, if you increase the number of points, then they will not only allow you shape the profile more exactly, but also let you do it in many ways, and this already leads to style formation (artistic).

This is very important to keep in mind when you need to make cuts or know where to complete them.

Key Incision (KP) and Fill Incision (ZR).

At first, it was very difficult for me to understand where and how many cuts I should make when creating one shape or another. So I was looking for an analogy to this process. This analogy turned out to be Animation.

Animation has a concept Key Frames (QC). In short, it is characteristic poses character in a certain moment of time... This concept also includes Intermediate Frames (PrK), which fill the time intervals between Key Personnel.

This not only speeds up the process, but also makes it easier. The more Interframes (fill cuts) you have, the smoother and more accurate the movement will be.

If you are an animator, then it is in your power to control the number of PCs. This is very similar to cutting polygons in 3D.

Drawing a large number of PCs and managing them all is a very tedious job. The same goes for moving a lot of vertices in 3D - it's very time consuming.

The idea behind CR is joints. When the modeler sketches out the rough shape, he always starts with the RCs, which always look rough. If the editor you are using supports bones, then use them to figure it out. Flex / twist the bones at the joints to see your rough shape in poses.

After all the RCs are ready, you have two options:

1. Flatten the model.
   Sometimes I create a CD, and then I just let the code responsible for dividing the model into a larger number of polygons (subdivision) draw all the CPs for me. The downside is that it doesn't look realistic. So the next step is to use a soft selection to touch up the shape. This can sometimes save you a ton of time (but it depends on what you are modeling).
2. Add RR manually.
   In most cases, I prefer manual work, since this way I can control the number of ZR and their location.

Please note that this concept with Key and Fill Cuts is not only useful for creating shapes, but also for detailing your mesh. The KR and RR created with the partitioning is one way to optimize the mesh (glutes, thighs, etc.) Also, sometimes the Fill Cut can become the Key Cut depending on how you look at it. You are a creator, therefore everything is in your power.

More importantly, this concept also works great for topology / loops (Key and Fill Loops).

Basic and Fill is a very interesting concept as it can be applied to almost anything! The next time you look at the topology mesh, try to find a Key Loop, since every head has at least one.

Based on what I've seen there are head topologies like this:

• C-loop
• X-loop
• E-loop
• And a bunch of others

I'll talk about all this later, but for now let's focus on the form.

Rounding

This is the most common mistake all newbies make. They create Key Cuts and then Fill between them and leave it all unchanged. If you don't round your RR, then the result will be square (unnatural, inorganic) and then you have to sweat a lot to fix it. If you, every time you create the next Fill Section, you will correctly fit it to the shape, then you will save yourself from constant reworking of the mesh.

Following shape lines (body lines, smooth lines).

Another common mistake is NOT following the smooth lines of an object. Remember that this is organic modeling, so try to think organically. When sketching body parts such as a tail or a body that bends, try to imagine a bending cylinder. And create blocks accordingly.

Fear, haste and doubt

This is the mental level of the problem when you are just starting out with 3D modeling.

Every time you do something for the first time, you experience great difficulty. The bottom line is you don't have to give up! Everybody goes through it... It is rare to find a person who has passed this first stage and does not tell how he suffered.

So here's my advice: easier, slow down, there's nowhere to rush. Try spending a month or two playing with shapes. Start with objects that allow you to make a bunch of mistakes, such as creatures. And just practice. If it turned out shitty - delete and start over.

At first, you will get things slowly, but as you do similar tasks, your speed will increase all the time. This is why we need practice to do everything better and faster.

When you create a model for the first time, it can be a very fun process. All because of the "look at the whole".

Take a human figure, for example. Let's say you start with a torso and extrude it. If you don't have legs and arms / head yet, then it all looks very comical. To make "it" look like a human, you must complete all the remaining body parts.

So there is no need to lose interest due to a terrible result without having all the parts in place. You just need to extrude all parts of the body and place them in the right places, only then "it" will start to look like a human figure.

Practice

Modeling subject

First, let's talk about the subject of modeling.

If you are doing character modelingthen you will obviously start from the head and go down. Simplified head, torso, and then arms and legs. After a few weeks, you will realize that the head is the simplest part of the body, since it is just one block, completely visible from one point. And all you need to model is to zoom in and out (the head).

Other parts of the body (arms, legs) will be more difficult, since it requires you to rotate and scale (zoom) the model in the viewport. And since you are new to 3D, there is a good chance that you are not used to full use of rotation, flying (spin), panning (pan) and zooming in viewports.

Use references to avoid unnecessary difficulties at first. And when you get your hands on it, try to model from memory.

To create a hand for the first time from memory is difficult. So try to use reference images / photographs first and memory later.

Why do it from memory at all? Just to see if your understanding of the shape of the hand (or whatever object you are creating) has improved.

If you modeling different creatures, then the situation is the same. Start with the head, then the body, and then everything below. Don't limit yourself to modeling only one part. Jump from one part to another (I, for example, do this), so you (thanks to the change in the type of activity) will constantly maintain an interest in this process.

Extruding (Extrude).

Before you start extruding parts such as arms and legs, you should know that there are only two ways to do this. This has to do with how to model the corner.

Method A is, of course, faster, but you still, sooner or later, you will come to method B. You can also convert A to B using the Polarity method (more on that later). Also pay attention to shape line (red).

I have seen many variations of Method A for creating realistic human hand... While Method B is suitable for unrealistic characters, for example, cartoons and the like.

If you find it difficult to rotate every time you extrude, then use method A. But it doesn't really matter (which method you choose) as you can convert one topology to another on the fly.

This concludes the first part of the article. You can ask questions if something is unclear.

Here are a few the best.

This is my translation of an excellent series of posts by SomeArtist on subdivisionmodeling.com (which have been removed since the forum has ceased to exist).

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P.S. The turtle barbarian in the title picture is by American Jesse Sandifer. The modeling was done entirely in Mudbox, then the whole scene was collected in 3ds Max and visualized by the forces Vray. Photoshop used for texturing and post-processing. Other types of character, as well as a discussion of the work, read