Basic Modeling Theory and Technique:
  Perception Theory
  First off, 3D modeling deals with good manipulation of perspective through relationship patterns that is recognized through heuristic thinking. In layman’s terms, the brain uses prior assumptions and experiences of the world to organize patterns of space it perceives through the eyes. Understand that the human eye conveys to the brain a flat upside down colored image. The brain looks for patterns in the image and can extrapolate the space in that image through past interactions and current physical interaction. You know that you can’t interact with your TV show on the TV, but you can interact with the TV and the space around it.

  Since the brain looks for patterns, we can fool it by providing it with a pattern it will follow. A way to establish a pattern is through the use of basic primitives. These basic shapes are what the brain already tries to look for: Square, Circle, and Triangle. Now we also have a natural attraction too arranged facial features, two eyes with a nose and mouth below since we crave human interaction. The type or art discussed in these tutorials at this site is a art form of using visual behaviors that is common among many people and manipulating those visual behaviors to get a visual result. When shapes get too complicated the brain breaks these shapes down in to more simple shapes as elements. A box house is plain and boring but a house that looks like its made up of various sized and shaped boxes looks more interesting as its complex and interesting for the brain to think about. What you the artist has to do is slow this process down and analyze why, think visually and look for patterns.

  Visual Relativity
figure 1-01
  Another pattern is the use of visual relativity. We can use size, position and familiarity to create a spatial relationship pattern between two objects to define a space. Here are two cubic looking objects marked as A and B. Object A is bigger and lower in the space provided than object B.

  Secondary characteristics are used to establish more relative relationships. The letters A and B appear in the same space on the cubes. The letter A is larger than B continuing the size association. The language relationship in the use of A and B is that B follows A. This means we look to A then B for a pattern of sequence observation. Also position matters as object B is to the right of object A and in most cultures we read left to right. The use of color also establishes a relationship on the page. Both cubes are white with black edges. The brain can think these shapes are similar through secondary characteristics even though their size and position vary. Through past experience the brain has learned the “possibility” of that a smaller object can be further away from another similar object on a different parallel plane.

figure 1-02
  The use of color is a great secondary characteristic. Colors that are towards the cooler side like blue, purple, and green have a tendency to recede in to the plane just like objects that are physically further away or forms that curve away shift into the blue end of the spectrum. While the warmer colors like red, yellow, and orange come forward compared to cooler colors. The use of warm and cool colors can create perceived space if it doesn’t exist due to the receding and lifting relationship of these colors.

  Another trick of relativity is to use a interposition object. This is an object that blocks the parts of another object. In the sample with color added to it the extra cube blocks object B, while this new shape is blocked by object A. You can say that this new object is ‘in between’ the two shapes and therefore it occupies the space between the shapes creating a stacking order. This establishes the relationship that object B is “behind” object A since B is behind an object that’s behind object A.

figure 1-03
  The brain will also try to complete patterns based on heuristic thinking. Even though these are just dotted lines, the brain sees the pattern and can fill in the blanks. This completing the visual pattern is something the brain has to do anyways. The truth is the human eye doesn’t see the clean image you think it sees. The brain is able to clean the image and remove loss visual information from blood vessels, floating objects, damage or malfunctioning rods and cones as well as the area in the center of the eye where the optic nerve is.
figure 1-04
  We can also use perspective to manipulate what the viewer sees. The closer the shape gets, the larger in the field of view it will be. Also if a pencil is pointing at you, the tip will appear larger than the eraser if a decrease of the visual angle that’s to a perpendicular object the more foreshortening needs to be applied based on the distance of the object. So the pencil that is eye level needs more foreshortening than the pencil lower from eye level. Also a pencil closer to the eye needs more foreshortening then a pencil that is further away. To see this optical trick better, close one eye as the other eye will correct this effect from happening as much.

  We can force the perspective in a virtual environment by using a technique called visual perspective. This technique creates the illusion of depth perception by using vanishing points. Vanishing points are the points on where a object disappears from visual view. This trick dates back to Giotto di Bondone and then Filippo Brunelleschi’s Perspective demonstration of foreshortening during the Renaissance. By using vanishing point perspective we can make objects appear to receding in to the space of a surface.

figure 1-05
  By carefully orchestrating perception, relativity, and perspective by you the artist, you can create the illusion of what the viewer is seeing. And that’s where this all streams from. Artists are the true illusionists. We create images that you perceive as being real but they are not, by tricking the human eye or at least the recognition processes.

  Computer graphics is just another medium that artists use to create art much like the traditional paint on canvas. Based on mathematics use of measuring space we can describe an image by its height and width. This is referred to as 2D as its two dimensions of measurement of space. Three dimensions of measurement is achieved when you apply a depth measurement to the height and width so that you can move back in to the space creating several planes of height and width.
figure 1-06
  For all present purposes, 3D modeling is the function of plotting points (vertices) within a Three-dimensional (x, y, and z axis) measured area of space. We then connect the points with lines and create a ‘simple polygon’ in that space. By creating enough polygons we can create a shape that’s just beyond the plain polygon like a cube. A graphics engine (programming code that creates a displayed image) translates these polygons in to sprites, which is actually in computer terms a 2D object with only a height and width. The computer can then calculate and place the corners of the sprite in a 3D space by treating the corners as vertices. A ‘complex polygon’ may not have a well-defined plane of space and can create triangles out of four-pointed sprite by having the plane crossover itself to meet the vertices warping the plane unnaturally. To solve this, the computer breaks the squared sprite down in to two triangles at render time. As a 3D modeler you need to make ‘simple polygon’ shapes or work in triangles to avoid warping the plane unnaturally.

  In math, a primitive in geometry is a point, line, plane, and spline curve. An artist will take these to make a shape that is similar in nature to that of the basic shapes discussed earlier in the Perception section. So in order to create these basic shapes in a 3D enviroment we add depth to them of equal shape. 3D applications list these as basic geometric primitives though in truth they’re geometric shapes. What I call extended shapes is a basic shape that composes of another type of geometric shape. Notice that a tetrahedron that is a triangular base pyramid is not a standard shape in 3d applications. To get this shape in 3ds Max create a Geosphere, drop the Segments to 1 and select Geodesic base as Tetra.

Symmetrical geometric shapes:
figure 1-07
Extended geometric shapes:
figure 1-08
  3D Modeling Theory
  As an artist you want to convey to the viewer the shape using simple polygons plotted in 3D space to make a geometric mesh. These shapes can arrange from a simple table to a complex shape of a car. You define the shape through the use of space much like a sculptor makes a sculpture. You can achieve this through a computer application by editing geometric shapes or a 3D scanner that uses lasers to determine vertices.

  When trying to convey a complex shape using a geometric shape, look for the elements of basic geometric shapes shown above. A car is relatively a complex shaped Euler brick with cylinders for wheels. Breaking complex shapes down in to relative basic shapes can help you figure out the starting point of a model if you're box modeling. A good test to see if you can do this is the following challenge.

  By folding the shapes below mentally in your mind at the edges, what type of shapes will you create? (answer at bottom of page)

figure 1-09
  Important factor of making geometric meshes look like the shape you want them to look like has everything to do with reference material and research. The best way to model a object is to be looking right at the object and matching the contours of the object. This may be hard as you can’t go out and actually get a Stealth Bomber. Pictures will help and the higher the resolution the better your model will be, as you will see everything. As will having knowledge on how the object works and was built will help as you can add in the detail and imperfection that can be found in the object through construction or moving parts. But like all art repetition is master. Keep modeling and eventually you will get better. Tricking everyday people is easy. Trick a master at their job like a gun enthusiast is hard.

  Modeling a Table
I prefer to work in 3DS Max with Editable Polygon and switching back and forth to Editable Mesh and back again. 3DS Max toolset for either is sadly light years ahead of Maya, but there are features in Maya I like such as the channel box. I could argue all day over the disadvantages and advantages of either program. But knowing what they are makes you better at your job. To plainly go out and say it sucks like a brand of car is childish if you know nothing about or have a good reason to back it up without using what someone else said.
figure 1-10
Lets model a simple table.

This is not a lesson in using 3DS Max, but a lesson in creating a low polygon model. Unfortunately something’s will have to be shown or talk you through in the use of 3DS Max.

Now I use the basic shapes like boxes, cylinder, geospheres, and torus. The last two I use rarely but every once and a while I use them.

figure 1-11
Step 1: Create a simple Box in the Top view port with the following attributes: length: 130, width:10, height: 260, all segments set to 1. Each program is slightly different. Max favors the top down view which is based off it cousin program AutoCad. There for the xyz coordinate system is a little screwy. It takes a bit getting used to but for the most part just remember that 3DS Max coordinate system is based on a top down orthographic view.

Step 2: For 3DS Max you need to convert it in to editable polygon shape. So right click anywheres on the box to get its quad menu. Move your mouse pointer over the 'Convert To' and another menu pops out. Then select 'Editable Polygon' from the menu and the Command Panel will change to the Modify panel automatically.

figure 1-12
Step 3: In the Modifier Panel you have several sub menus. They are Vertex, Edge, Border, Polygon (face), and Element.

These Modes as I call them, allow you to manipulate only the vertex or only the edges of the shape that is selected. Each Mode has its own toolset (commands) under each roll out tab. To expand the roll out tabs all you need to do is click on the plus sign to pop out the rest of its commands. Clicking the minus closes the rollouts. In Maya the commands you need are on the shelf or buried up in the menu.

figure 1-12
Step 4: Now go back to the Create Panel (the arrow pointer icon) next to the Modify icon. Create a Cylinder in the Top view port with the attributes of radius:10, height: -140, Height segments: 8, Cap segments: 1, Sides: 8. Position the shape where one of the legs is supposed to go and convert it to a Polygon shape.

Step 5: First toggle on the Draw Edges by hitting the 'F4' key. Now you can see the cylinders edges.

figure 1-14
Select the polygon cylinder and go in to the Command Panel. Select Edge mode and select one of the lines in the second row from the bottom (line in red) away from the box. Then hit the Loop command (highlighted in yellow in the animated gif to the right) and it will select all the lines going around the object saving you time from manually picking each line by tumbling around the object. Then move the selected loop up to form the correct spacing for the peg like shape by moving it only on the y-axis in the Front view port. Then position the others in roughly in same place shown in picture.
figure 1-15
Step 6: Switch to the scale command (short cut is ‘R’) and scale down the two loops of edges in the cylinder and the bottom cap. Scale them uniformly like in the animated gif.

To select the lines indicated, just click on one line of the row and use the loop command. You can also add to the selection by 'Ctrl +Left Click', or minus from selection by 'Alt +Left Click' if the loop command doesn't work. Like on the cap’s edges. Or you can use the face mode like in the animated gif.

Step 7: Now tumble to the bottom of the leg in the Perspective view port and right click on the Editable Poly shape and convert it in to an Editable Mesh. Go to the Edge mode and create a selection box marquee around the whole object so you get what is being shown. Though the dotted lines are hard to see in this image you should see them once you select all the lines in the object.
figure 1-16
Step 8: In the command Panel go to the Surface Properties roll-out in the Editable Mesh Modifier and hit the Visible command (found at the bottom of the edge mode rollout). This forces the tessellation of the 4-sided or more edge faces in to their triangular shapes.

Step 9: Under the Edit Geometry rollout turn on the Turn tool by clicking on it. Now every line you select will turn the opposite way by connecting the opposite vertexes. Now change your model edge flow so that it matches the image in the last frame. This average things out a bit, though right now it makes no difference but when it comes time to texture this it will make a huge difference.

figure 1-17
Step 10: Tumble to the other end of the cylinder (the top) and delete all these faces. The reason is that you can float the geometry as long as you don’t see the open edge.

An open edge is a spot on the geometry that when rendered will allow you to see through a shape that is to appear solid. This is not a fault as this saves the Shader code time by not rendering a backside to all the faces of a shape. Three solutions are available to stop this ability to see through a solid shape. The first one is a cheap way by forcing two side rendering which increases the polygon count at render time killing efforts to reduce polygon count. Another is to place faces in the hole by filling it in. Or set the gap up where the camera can’t see it inside another shape that has no open edges. That is what we will be doing.

Since we’re modeling a table, we'll place the open edge of the leg inside the solid tabletop. Making the open edge only viewable inside the tabletop, which the end viewer will never be able to go. Well, unless the programmers can't set up a good collision code. But that's not our fault, so we can get away with this floating technique.

Now why do this technique? Believe it or not it cuts polygons. Look below at the samples.

figure 1-18   figure 1-19
The table on the right is where the table is made of continues geometric shape with a poly count of 460. While table on the left is where the table is made of floating geometry with a poly count of 420. Ohh, 40 triangles, but that’s forty that can be used somewhere else. That can be 40 more to define the table legs with a little more grooved out edges to make the round bumps on the leg. Or they can go to another model that will share the room with this table.
figure 1-20
Step 11: Now copy the leg three times and move them in to the corners of the tabletop box like in the image to the right. Floating geometry works when you have faces meet at 90° angles and you place the open edge way inside past the face of another geometric side.

Step 12: Select the table top box. Under the Edit Geometry Roll-out is the command Attach. Just like Turn when you click it, it turns on and you can click on one of the legs to file that shape under the shape you currently have selected. Click on all the objects to file them under one shape. The color of the shape should change to match the color of the tabletop to indicated that it has been attached.

Step 13: In the Name box on the top of the Command Panel while in the Modify mode change the name to anything like Table. This will allow you to merge this object or other objects with this table file without a hitch.

  Now we have made a simple table with only a Poly count of 420. You could lower the Poly count drastically by lowering the sides of the cylinders on creation. Go with 6 instead of 8. The less sides you have, the less rounder the object will appear. Organic shapes require to appear round so they will always need more polygons. But with static none organic mesh you can go with a tall skinny box with only four sides for the table legs. Which would give your table a Poly count of 52. Nevertheless, you should have the hang of it and dependent on your poly count you can make some intricate furniture or simplistic models.

  The answers are: Cube and a four-based Pyramid.
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