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A-level Computing 2009/AQA/Processing and Programming Techniques/Data Representation in Computers

Hexadecimal
As you know, the number system we normally count in is base 10, and the number system that computers use, binary, is base 2. Hexadecimal is a base 16 number system. In hexadecimal, the numbers 0-9 are used, just like in denary, but the letters A-F are also used to represent the numbers 10-15. The table below shows the numbers 0-16 in denary, and their binary and hexadecimal equivalents:
 * Questions

You may notice from the table that one hexadecimal digit can represent exactly 4 binary bits. Hexadecimal is useful to us as a shorthand way of writing binary, and makes it easier to work with long binary numbers.

Converting Between Bases
Since 4 binary bits are represented by one hexadecimal digit, it is simple to convert between the two. You can group binary bits into groups of 4, starting from the right, and adding extra 0's to the left if required, and then convert each group to their hexadecimal equivalent. For example, the number 110110011110101 can be written like this:

0110 1100 1111 0101

and then by using the table above, you can convert each group of 4 bits into hexadecimal:

6 C F 5.

So the binary number 0110110011110101 is 6CF5 in hexadecimal. We can check this by converting both to denary. First we'll convert the binary number, since you already know how to do this:

By multiplying the columns and then adding the results, the answer is 27893.

Notice that the column headings are all 2 raised to a power, $$1 = 2^0$$, $$2 = 2^1$$, $$4 = 2^2$$, $$8 = 2^3$$, and so on. To convert from hexadecimal to denary, we must use column headings that are powers with the base 16, like this:

$$5 \times 1 = 5$$

$$15 \times 16 = 240$$ (You should memorize the values A-F)

$$12 \times 256 = 3072$$

$$6 \times 4096 = 24576$$

Totalling them all up gives us 27893, showing that 0110110011110101 is equal to 6CF5.

To convert from denary to hexadecimal, it is recommended to just convert the number to binary first, and then use the simple method above to convert from binary to hexadecimal.

 * NOTE: Hexadecimal is used as it is easier for people to understand than pure binary. It DOES NOT take up less space in memory, only on paper!

Negative Binary Numbers
A computer works purely in binary. That means that it only uses ones and zeros, and there's no - or + symbol that the computer can use. The computer must represent negative numbers in a different way.
 * Questions

Twos Complement
We can represent a negative number in binary by making the most significant bit a sign bit, which will tell us whether the number is positive or negative. The column headings for an 8 bit number will look like this:

Here, the most significant bit is negative, and the other bits are positive. You start with -128, and add the other bits as normal. The example above is -67 in denary. -1 in binary is 11111111.

Note that you only use the most significant bit as a sign bit if the number is specified as signed. If the number is unsigned, then the msb is positive.

Converting Negative Numbers
To find out the value of a two's complement number we must first make note of its sign bit (the most significant, left most bit). If 0 then the number is positive, if 1 then the number is negative.

0000 0101 (positive) 1111 1011 (negative)

To find the value of the negative number we must find and keep the right most 1 and all bits to its right, and then flip everything to its left. Here is an example:

1111 1011 find the right most one 1111 1011 0000 0101 flip all the bits to its left

We can now work out the value of this new number which is:

128 64  32  16   8   4   2   1    0   0   0   0   0   1   0   1                       4   +   1 = −5   (remember the sign you worked out earlier!)

How about a more complex example?

1111 1100 find the right most one 1111 1100 0000 0100 flip all the bits to its left

128 64  32  16   8   4   2   1    0   0   0   0   0   1   0   0                       4         = −4   (remember the sign you worked out earlier!)

So we know how to work out the value of a negative number that has been given to us. How do we go about working out the negative version of a positive number? Like this, that's how...

Take the binary version of the positive number

0000 0101 (5) 0000 0101 find the right most one 0000 0101 1111 1011 flip all the bits to its left

So now we can see the difference between a positive and a negative number

0000 0101 (5) 1111 1011 (−5)

Binary Subtraction
When it comes to subtracting one number from another in binary things can get very messy. X (82 denary) 0101 0010 Y (78 denary) 0100 1110 −

An easier way to subtract Y from X is to add the negative value of Y to the value of X X−Y = X+(−Y)

To do this we first need to find the negative value of Y

0100 1110 find the right most one 0100 1110 1011 0010 flip all the bits to its left

Now try the sum again 0101 0010    X( 82 denary) 1011 0010 +  Y(−78 denary) 0000 0100 (¹)¹¹¹  ¹       the one carried over the bit 9 is ignored

Which comes out as 128 64  32  16   8   4   2   1 0  0   0   0   0   1   0   0                       4         = 4 = 82-78

Binary Fractions
Up until now, we have only been working with whole numbers, or integers. We need a way to store real numbers on a computer system.
 * Questions

Fixed Point Numbers
First, we should have a look at one of the ways that we can represent fractions in denary:

As you can see, the column headings have been extended to $$10^{-1}=\frac {1}{10}$$ and $$10^{-2}=\frac {1}{100}$$. We can do the same thing in binary with the column headings $$2^{-1}=\frac {1}{2}$$, $$2^{-2}=\frac {1}{4}$$, and so on. The number 12.75 in binary is therefore:

Notice that for the same number of bits after the point, the binary number is less accurate. It can only take 4 different values, whereas the denary number can have 100 different divisions with two digits.

Floating Point Numbers
If you study other subjects such as Physics or Chemistry, you may come across Floating Point numbers like this $$6.63_{10} \times 10^{-34}$$ (Planck's constant) The first bit defines the non-zero part of the number and is called the Mantissa, the second part defines how many positions we want to move the decinal point, this is known as the Exponent and can be positive when moving the decimal point to the right and negative when moving to the left. $$\begin{matrix} \underbrace{6.63} \\ Mantissa \end{matrix} \times \begin{matrix} \underbrace{10^{-34}} \\ Exponent \end{matrix}$$

If you wanted to write out that number in full you would have to move the decimal point in the exponent 34 places to the left, resulting in: $$0.00\;000\;000\;000\;000\;000\;000\;000\;000\;000\;000\;663_{10}$$ Which would take a lot of time to write and is very hard for the human eye to see how many zeros there are. There for, when we can accept a certain level of accuracy (6.63 = 3 significant figures), we can store a many digit number like planks constant in a small number of digits. You are always weighing up the scope (or range) of the number against its accuracy (number of significant bits).

The same is true with binary numbers and is even more important. When you are dealing with numbers and their computational representation you must always be aware of how much space the numbers will take up in memory. As we saw with the above example, the non floating point representation of a number can take up an unfeasible number of digits, imagine how many digits you would need to store. $$0.00\;000\;000\;000\;000\;000\;000\;000\;000\;000\;000\;663_{10}$$ in binary? (don't worry this question is rhetorical)

A binary floating point number may consist of 2, 3 or 4 bytes, however the only ones you need to worry about are the 2 byte (16 bit) variety. The first 10 bits are the Mantissa, the last 6 bits are the exponent.

$$\underbrace{\overbrace{0}^\text{sign bit} \cdot 101010101}_\text{mantissa} \times \underbrace{010101}_\text{exponent}$$

Just like the denary floating point representation, a binary floating point number will have a mantissa and an exponent, though as you are dealing with binary (base 2) you must remember that that instead of having $$\times 10^{xy}$$ you will have to use $$\times 2^{xy}$$

Fixed point binary allows a computer to hold fractions but due to its nature is very limited in its scope. Even using 4 bytes to hold each number, with 8 bits for the fractional part after the point, the largest number that can be held is just over 8 million. Another format is needed for holding very large numbers.

In decimal, very large numbers can be shown with a mantissa and an exponent. i.e. 0.12² Here the 0.12 is the mantissa and the ² is the exponent. the mantissa holds the main digits and the exponents defines where the decimal point should be placed.

The same technique can be used for binary numbers. For example two bytes could be split so that 10 bits are used for the mantissa and the remaining 6 for the exponent. This allows a much greater scope of numbers to be used.

There are several stages to take when working out a floating point number in binary. In fact it is much like a disco dance routine - known on this page as the Noorgat Dance, Kemp variation (but you wont be tested on name but it should help you to remember)
 * 1) Sign - find the sign of the mantissa (make a note of this)
 * 2) Slide - find the value of the exponent and whether it is positive or negative
 * 3) Bounce - move the decimal the distance the exponent asks, left for a negative exponent, right for a positive
 * 4) Flip - If the mantissa is negative perform twos complement on it
 * 5) Swim - starting at the decimal point work out the values of the mantissa. Now make sure you refer back to the sign you recorded on the sign move.

Lets try it out. We are given the following 16 bit floating point number, with 10 bits for the mantissa, and 6 bits for the exponent. Remember the decimal point is between the first and second most significant bits $$0100\;0000\;0000\;0001$$ $$0.100\;0000\;00\;\mid\;00\;0001$$ The first action we need to perform is the sign, find out the sign of the exponent $$\underline{0}.100\;0000\;00\;\mid\;00\;0001$$ It is 0 so the mantissa is positive The second step in the Noorgat dance is the slide, we need to find the value of the exponent, that is the last 6 bits of the number $$0.100\;0000\;00\;\mid\;\underline{00\;0001}$$

$$\begin{matrix} 32 & 16 & 8 & 4 & 2 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{matrix} = 1$$ So we know that the exponent is of size positive one and we will have to move the decimal point one place to the right. The third step in the Noorgat dance is the bounce that is moving the decimal point of the Mantissa the number of positions specified by the slide, which was one position to the right. Like so: $$0.\vec 1 00\;0000\;00\;\mid\;00\;0001$$ $$01.00\;0000\;00\;\mid\;00\;0001$$ The fourth step is the optional flip. Check back to the sign stage and see if the Mantissa is negative. It isn't? Oh well you can skip past this stage then as we only flip the number if the mantissa is negative.

The fifth and final step is the swim. Taking the mantissa on its own we can now work out the value of the floating point number. Start at the centre and label each number to the left $$1, 2, 4, 8, 16$$ and so on. The each number on the right $$\frac{1}{2}\frac{1}{4}\frac{1}{8}\frac{1}{16}$$ and so on. $$\begin{matrix} 4 & 2 & 1 &. & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} \\ 0 & 0 & 1 &. & 0 & 0 & 0 \end{matrix} = 1 = 0.100\;0000\;00\;\mid\;00\;0001$$ Voila! the answer is 1

Normalising Numbers
When dealing with Floating point numbers in binary you must make sure that the first two bits are different. That is: $$0.1$$ $$1.0$$ And most definitely NOT $$1.1$$ $$0.0$$ This is because we must make sure the space we are using is being used the greatest efficiency. For instance if we take a denary floating point number such as $$6.63_{10} \times 10^{-34}$$ (Planck's constant) If we were to rewrite it as: $$0.0663_{10} \times 10^{-32}$$ (Planck's constant) Then you can see the representation takes up an extra 2 characters, the two extra 0's, even though it represents exactly the same number. This may be acceptable when you are not worried about how many characters a number makes up, but in binary and with computers the space that numbers take up is very important, and we need the most efficient representation we can. With a fixed number of bits, a normalised representation of a number will display the number to the greatest accuracy possible. '''You must make sure that your normalisation does not change the sign of the mantissa. '''Taking a binary floating point number: $$0.010\;0000\;00\;\mid\;00\;0011$$ We can see that the number starts with $$0.01$$. We need to change this to $$0.1$$ for it be normalised. To do this we need to move the decimal place one position to the right, and to retain the same number represented by the unnormalised number we need to change the exponent accordingly. With a movement one place right to normalise the number we need to change the exponent to move the decimal point one place left to compensate. Thus negating one from the current exponent. $$0.010\;0000\;00\;\mid\;00\;0010$$ To make sure you have normalised it correctly, check that $$0.010\;0000\;00\;\mid\;00\;0010 = 0.100\;0000\;00\;\mid\;00\;0011$$ Lets try a more complicated example: $$1.110\;0000\;00\;\mid\;11\;1110$$ To get the mantissa normalised we need to move the decimal point two places to the right. To maintain the same value as the original floating point number we need to adjust the exponent to be two smaller. $$1.000\;0000\;00\;\mid\;11\;1100$$ Now check that the new normalised value has the same value as the original.


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Talk:Abstract Algebra/Category theory

I find it quite surprising that an incorrect definition has survived for the entire lifetime of this document. Of course the supposed function $$ c: C_1 \times C_1 \rightarrow C_1$$ is not a function at all, since it is not well-defined. It was only mentioned later that a pair of maps may only be composed if the source of one is the desination of the other, belying the definition of c. Elroch 16:29, 21 January 2006 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Abstract Algebra/Category theory


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Wings 3D/Tutorials/Box Modelling

'''note: Isn't extrusion modeling and box modeling the same thing? Shouldnt we make an article on other poly modeling techniques like adding components to a main object or cutting detail into geometry? Just putting out ideas here. ...-arquebus'''

title: Wings 3D/Tutorials/Box Modelling


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User talk:JohnDBuell

Hey John...

I agree that my story on the Mac OS X Tiger page wasn't as good as it could have been... no offense taken that you reverted it (I helped write the original one). However, I think the original one has a bit too much info in it. I'm going to write another new one and over the course of a few days, try to get it up to snuff. So don't re-revert it until, say, February.

Thanks, Hyperpasta 16:57, 21 January 2006 (UTC)

Mac OS X Tiger Story
Np. Go ahead and edit the story, but make sure you keep it short and to-the-point. I just want it to be concise, well-balanced, and jargon-free. Hyperpasta 16:34, 29 January 2006 (UTC)

title: User talk:JohnDBuell


text: User talk:85.64.133.65

title: User talk:85.64.133.65


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Developing Learning Objectives

When developing training materials, the critical element is the learning objective. The learning objective defines the outcome or the result of the training or lesson. If you were to think of a course as a bicycle wheel. You have components of it: the tire, the rim, the spokes, and the shaft. All must work together for the wheel to turn. However, everything is centered around the shaft of the wheel. In this analogy, the shaft is the learning objective. No matter how well the other parts work, if the shaft doesn't work then the wheel is ineffective. Much like the bicycle shaft, the learning objective is critical and imperative to the rest of the training. Understanding this, we look at how to develop a learning objective.

Types of Learning Objectives
There are two primary types of learning objectives we will be working with:

 * Terminal Objective: The outcome or the final product. What should the student "look like" when the training is complete? What should they be able to?
 * Enabling Objective: Defines the steps to accomplishing the terminal objective. How is the terminal objective going to be accomplished?

Components and Developing a Learning Objective
Working on the assumption that we are utilizing the Instructional Systems Design model for course development, creating learning objectives does not have to be a complex process. While there are many models to follow, and one should look for one that best suits their style, the simplest to work with is the C-B-S model. The C-B-S model follows the format:

 * (C)Condition- Under what circumstances or conditions should the student perform the task.

 * (B)Behavior- Specifically explains what task the student should be able to do.

 * (S)Standard- To what level of proficiency should the student perform the task.

Utilizing an example from the Fire Officer IV course:

Terminal Objective: Given appropriate community demographic data, appraise the department's human resource demographics to determine if the recruitment, selection, and placement of human resources is effective and consistent with law and current best practices.

Our objective is sectioned as follows:

 * Condition: Given appropriate community demographic data...

 * Behavior: ...appraise the department's human resource demographics...

 * Standard: ...to determine if the recruitment, selection, and placement of human resources is effective and consistent with law and current best practices.

Conclusions
Developing learning objectives does not have to be complex nor a complicated process. However, consistency and comprehension is important.

title: Developing Learning Objectives


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Diplomacy/England

England/British Empire/United Kingdom (English)

 * Leader at 1901: Prime Minister Marquess of Salisbury;
 * Head of State: King Edward VII

Color: Dark Blue or Pink, in some versions (webDiplomacy.net, etc.)

Neighbors: France, Germany, Russia

Home supply centers: London, Liverpool, Edinburgh

England's defensive position is the strongest in the game besides Turkey, and landing an army on the British Isles will usually require at least three units--one convoyed army, one fleet to convoy, and one fleet to support the convoy. England's "back door" in the North Atlantic is, however, much more difficult to defend than Turkey's back door in Syria. England's position as an island means that it will have to maintain a large navy in order to achieve victory. England's position causes a bottleneck similar but less severe than the one Turkey faces, because sea routes can get troops quickly from the home centers to the Mediterranean, to Germany, and to St. Petersburg.

England has a limited choice of centers to make 18. Most simply, three home, Bre and Par, Bel, Hol, Den, Swe, Nwy, StP, Kie, and Ber are the 13 easiest, leaving 5 centers to get out of Spa, Por, Tun, Mun, Mar, Mos, and War. Mos and War are very difficult to get without German or Turkish help, and any centers further south are possible only with an extremely committed French ally.

Opening Strategy
England can choose between commitment to an attack against France or to calmly pick up builds from Norway and possibly Belgium, and wait for 1902 to choose a side.

18 Center Goal
3 home centers, Scandinavia, St. Petersburg, The Low Countries, Kiel, Berlin, Brest, Paris, and Iberia makes 15. Then three out of Munich, Marseilles, Tunis, Moscow, and Warsaw are required to convert to a victory. Any other supply centers are much too far away to be part of a normal victory--although once in a while, England will break into Italy or capture Sevastopol.

England's main choice is where to send her two fleets.

F LON - ENG, F EDI - NTH (Southern Opening)
Provides the best anti-French possibilities.

Wales Variation
A LPL - WAL

Unequivocally anti-French. This move is risky, as failure to acquire the Channel in the spring will make this army useless in the autumn. Useful only when you expect to acquire the Channel, this move provides the strongest set of moves for a French campaign, as the army may be convoyed to Brest or Picardy (usually while NTH acquires Norway) OR may be used in a supported convoy to Belgium.

Yorkshire Variation
A LPL - YOR

A much safer prospect than the Wales Variation, and similarly less profitable as an anti-French maneuver. This opening is the opening of choice for an England only wishing to bounce in the Channel, as the army may then be convoyed to Norway or to Belgium. As an offensive opening, the Channel pressures the French homeland while providing support for a convoy to Belgium... or, perhaps, the opportunity to claim Norway with a convoy and Belgium with a fleet! Using your fleet in NTH to convoy your army also frees up the fleet in English Channel to capture the Mid-Atlantic Ocean in Fall 1901, putting France in an extremely awkward position for 1902.

Yorkshire Variation
A LPL - YOR

The soundest opening from the classical perspective of maximizing minimum gains, this is the only English opening that guarantees a build against all opposition. In brighter times, one may convoy with support to Norway or convoy to Belgium and claim Norway with a fleet; if France, Germany and Russia are determined to stop you, Yorkshire can cover London when France moves to the English Channel, and Norwegian Sea can support North Sea to Norway despite a Russian move Mos -> Stp -> Nor (though a German in this case would seize the North Sea, F Kie -> Den -> NTH; whether or not this is desirable is up for debate).

Edinburgh Variation (AKA "The Churchill Opening")
A LPL - EDI

In this Northern Opening variant, known simply as the Churchill Opening, and named after Sir Winston's plan to invade Norway in World War II, the English army is sent to Edinburgh. This opening sacrifices the ability to cover London for more convoying options in the autumn. For an England looking for two builds in a favorable diplomatic situation, this allows for Norway to be captured with an army and Belgium/Holland/Denmark with a fleet. London may still be covered by the North Sea, but Norway cannot be secured against Russian resistance if this happens. This move is superior to the Yorkshire Variation if and only if one guesses correctly on French intentions; if they go to the Channel, a build isn't guaranteed, but if they don't, England's options are greater.

Wales Variation
A LPL - WAL

The anti-French Split opening. If France goes to the Channel, England is in a very awkward position, having a useless army in Wales and facing the possibility of a German fleet standing it out of the North Sea in the autumn.

Edinburgh Variation
A LPL - EDI

The pro-French Split opening (or, at least, as pro-French as an opening to the Channel can be). Allows convoy to Norway, with England using the Channel fleet to influence Belgium or pressure Brest.

title: Diplomacy/England


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Diplomacy/France

France/French Third Republic/La Troisième République (French)
Leader at 1901: President of the Council of Ministers Pierre Waldeck-Rousseau

Color: Light Blue

Neighbors: England, Germany, Italy

Home supply centers: Paris, Brest, Marseilles

France is the easiest country to play. While not as defensively sound as England or Turkey, France is able to move troops quickly through Europe without the burden of a long convoy chain required by Turkey or England. France also has better long-term survival prospects than either, since while England and Turkey are often forced into a corner and survive until midgame after a long, hopeless war, if France survives the initial possibility of attack from an England-Germany alliance (or, more rarely, an attack from Italy), they can do very well in the mid- and late-games (France has very high end-survival and draw records, as well as a fair number of wins). Iberia provides two quick and easy builds early, and profitable alliances can be undertaken with either England or Germany, or both. However, England is not suggested, since England has a better chance of stabbing than Germany or Italy does.

18 Center Goal
France has a much greater choice of winning combinations than England. France is also stronger for being able to build fleets on both sides of the MAO bottleneck—although even this is sometimes not enough to break a stalemate in TYS necessary to grab TUN for a victory.

The most common French winning combination is: 3 home centers, Iberia (2), England (3), the Low Countries (2), Germany (3), Scandinavia (3), St. Petersburg, and one of WAR, MOS, and TUN.

However, France also has a good shot at conquering Italy, especially TUN, ROM, NAP, and possibly VEN if he strikes early. This allows France to win without getting STP or SWE, and gives France a good foothold across the major stalemate line.

Opening Strategy
France has more safe and non-committing openings that can almost guarantee quite a few (usually two, sometimes three) builds during the winter of 1901. France is the only power able to reach the centers in Iberia in 1901, and can choose to take them calmly, or expend less effort capturing Spain and Portugal to attack Germany or England.

France's major choice is whether to try for the Channel. If France manages to occupy the Channel, he can almost guarantee himself BEL by force, as long as he has another unit in PIC or BUR. However, forcing one's way into BEL is against most French theory, which says that France can (and should) play as docilely as possibly during the first year, playing England and Germany off each other, and choosing a side in 1902.

F BRE - ENG, The English Attack
This move is more aggressive than the English move to the Channel in S1901, which, although pointing right into French territory, is usually just for support of F NTH C A YOR - BEL.

If you can guarantee a supportive Germany and a relaxed Russia, this move can kill England, who will suffer terribly if the move to the Channel does not work. A French fleet in the Channel can support or be supported by a German fleet in Denmark into the North Sea, quickly ending England.

A MAR - BUR, A PAR - PIC: The Northern Dash
The most aggressive possible opening for France, it leaves Iberia completely untouched if the move succeeds. Obviously anti-English and possibly anti-German, this opening may leave you with no friends in Western Europe, and a very hungry-looking Italy in the east. It provides the maximum possible force on BEL, as well as the possibility of a convoy to WAL or LON.

A MAR - SPA, A PAR - GAS: The English Defense
The opposite of the Northern Dash, this opening guarantees two builds from Iberia, while allowing Germany to make a quick strike into BUR if he so desires.

F BRE - MAO: The Atlantic Opening
The calmer alternative to the Channel is MAO, which allows France great flexibility in befriending either England or Germany. Although it gives up the Channel to England, many times England will try desperately to woo France during the opening years by opening to NWG and NTH. The Mid-Atlantic fleet also gives France a chance for a quick break into the Med by sailing F MAO to Spain's South Coast, which borders WMS. Adding another fleet with F MAR can mount a powerful early attack on Italy, who usually focuses on the East for the first few years.

A PAR - BUR, A MAR S A PAR - BUR: The Maginot Opening
By far the most common French opening, it allows France a finger in each of his three possible neutrals. It protects against an early German incursion, and the three moves are guaranteed to succeed. This is the most anti-German opening in France's repertoire as it guarantees a threat on MUN in the fall. Germany is usually not an early threat to France, and angering him by forcing yourself into BUR may not be the best policy. If England's friendship can be guaranteed, however, this opening can be extremely powerful by getting close to Germany rapidly.

A PAR - BUR, A MAR - SPA: The Burgundy Variation
Second in popularity only to the Maginot Opening is the Burgundy variation. France claims SPA, and can guarantee himself POR, while still having a stake in the argument over BEL or at least keeping Germany out of BUR. The Burgundy bothers England a little over BEL and Germany a little over the move to BUR, but antagonizes neither too strongly. An extremely strong, theoretical opening.

A PAR - GAS, A MAR - BUR: The Vineyard Variation
An alternative to the Burgundy variation, this move order is arguably tactically stronger since standing off Germany in Burgundy with Marseilles rather than Paris gives greater leverage over Iberia in case of an Italian move to Piedmont in Spring 1901. Moving Paris to Gascony also offers the possibility of convoying Gascony to Portugal in Fall 1901, thus maintaining the fleet in Mid-Atlantic. This helps build trust with Germany and affords a stronger footing for an invasion of England or Italy in 1902.

A MAR - BUR, A PAR - PIC: The Belgian Variation
More aggressive than the Burgundy Variation, this opening guarantees France a shot at BEL in the fall, in addition to picking up an Iberian neutral. Somewhat anti-German, this opening aims to get armies to the German border as rapidly as possible.

F BRE - PIC: The Picardy Opening
Though rarely seen, moving the fleet to Picardy gives France the opportunity to influence the fate of Belgium without antagonizing England with a move to the English Channel. However, this move violates the sound strategic principle that fleets should usually be placed in open water rather than on the coastline in order to maximize tactical options.

title: Diplomacy/France


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Talk:Java Programming/Types

What about int? And wouldn't it make more sense to list the integer types in order of size (byte, short, int, long)?

It would also make sense to mention the requirements for attributes other than size. I don't know Java very well, so I won't edit the page myself.

title: Talk:Java Programming/Types


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Talk:Magic: The Gathering

The subscription play link brings me to some fashion website- anyone know the right link? --Gabe Sechan 23:54, 21 January 2006 (UTC)

- Fixed 59.167.87.11 17:16, 2 February 2006 (UTC)

title: Talk:Magic: The Gathering


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General Astronomy/Short History of the Universe

For time immemorial, humans have been intrigued by creation. Where did we, and the universe in which we live, come from? In the Rig Veda, it was proposed that before creation there was "neither existence nor non-existence." The Latin phrase ex nihilo nihil fit ("out of nothing comes nothing") sums up current human beliefs about origins.

The Qur'an contains the following verse regarding the origin of the universe: “Do not the Unbelievers see that the heavens and the earth were joined together (as one unit of Creation), before We clove them asunder?” [Al-Qu’ran 21:30]

Many possibilities have been considered by scientists over the millennia. Did the universe "happen" suddenly?… was it created quickly by God?… has it existed forever?… or is it in a constant state of creation, even now?

Just as we can use size scales to make rough comparisons of the sizes of objects in the universe, we can also use time scales to compare the periods of time over which events occur. For example, Comet Halley takes about 75 years to complete its orbit around the Sun, so we can say that the period of Comet Halley's orbit has about the same time scale as a human lifespan.

The Origin of the Universe according to the Big Bang Theory
The universe is big in space, but it's also big in time. The age of the universe appears to be 13.7 billion years. Like huge space scales, a span of 14 billion years is hard to imagine for a person who will have a much shorter lifespan than that. To better understand very long time scales, we can "compress" long periods of time like the age of the universe into shorter periods such as a human lifetime.

A typical person will live around 80 years. That means that the Earth will go around the Sun eighty times over the course of an average lifetime. The human life time scale and the time scale of human history are far smaller than the time scale of changes in the universe. Astronomers have learned about how the universe as a whole came to be the way it is by studying only an instant of its existence. To get a clearer picture of how the cosmological time scales fit together, let's consider an imaginary astronomer whose life is "stretched out" to fill the entire history of the universe.

If a human lifetime were vastly longer than it is, the orbit of the Earth around the Sun might be too fast to be a useful way to measure age. Instead, it might be more practical measure time from something slower. The Sun takes 230 million years to complete an orbit around the Milky Way Galaxy. That means that a "Milky Way year" will be 230 million times longer than an ordinary year.

Let's suppose our old astronomer has a lifespan of 80 "Milky Way years" instead of 80 normal years. That way, the astronomer will live long enough to see events that happen on cosmological time scales rather than human time scales. The astronomer's life happens in extremely slow motion. His growth and his actions are slowed by a factor of 230 million. At this rate, it takes four normal months for the astronomer just to blink.

Astronomers have theorized that the universe was very small, hot, and dense when it began. Since then, it has expanded and cooled. At first, the universe contained almost entirely hydrogen and helium gas. The universe was very uniform, with no galaxies, stars or planets. We'll place our protagonist's birth at the time of the big bang.

Our astronomer was much too young to remember the early development of the universe after the big bang. By the time the astronomer was only two days old, atoms had formed in the universe and the universe had cooled enough for structure to begin forming in the gas that uniformly filled all of space. Remember, the imaginary long-lived astronomer measures time much more slowly — what the astronomer sees as two days amount to a million years of time on a normal clock. While a million years seems like an extremely long time, that's only a tiny part of the history of the universe.

Our astronomer's earliest memories of childhood will include the first formation of stars and galaxies, which began to occur when the astronomer was around five "Milky Way years" old. Galaxies would continue forming and developing well into the astronomer's teenage years, when the universe was billions of years old. Today, galaxies continue to evolve and change.

There are two schools of thought on how the Universe formed: "top down" and "bottom up". Top down theorists think that large clusters formed after the Big Bang, which later broke down into stars and galaxies. "Bottom up" theorists instead pose the theory that matter was originally dispersed fairly evenly by the Big Bang, later accumulating into stars and galaxies. Recent data from Hubble Deep Field photographs appear to support "bottom up" theories. The photos show young galaxies from up to 11 billion light-years away. These young, small galaxies, from early in the universe's history, support the theory that large structures formed out of smaller ones. The galaxies appear as faint blue blobs with vague spiral structures, 2000 to 3000 light-years across.

An important necessity for the appearance of life is heavy elements. Since only hydrogen and Helium gas were formed during the big bang, everything heavier than that had to be made in stars later. These other elements — all of the elements on the periodic table — were made in stars.

Stars use light elements like Hydrogen and Helium as their fuel. Like nuclear bombs, they use the power of the atom for energy. Stars are unlike nuclear bombs, however, in that most nuclear bombs get their energy from heavy atoms like Plutonium and Uranium. In a nuclear bomb, the energy comes from converting heavy elements into lighter elements. This process is called fission. In a star, the energy comes from converting the light elements into heavier elements. This process is called fusion. All of the material in the universe heavier than Hydrogen and Helium were made by fusion in a star.

An ordinary star can make many of the elements, especially the most important ones for life. It can't make all of the elements, though; it can't make anything heavier than Iron. The heavier elements were made in supernovae. A supernova occurs when a massive star reaches the end of its life. Supernovae are extremely bright and extremely hot. This is where the heaviest elements in the universe are made.

All of the material needed to make rocky planets was made in stars, and some of it was made in supernovae. This means that planets couldn't exist until there had been enough time for a star to completely go through its life cycle and become a supernova. The material would then be ejected back into space, and would form a new star, possibly with planets. It also means that everything in the world, including you, came from a star. As the astronomer Carl Sagan said, "We are star stuff."

The Sun and the Earth formed about four and a half billion years ago, when our long-lived astronomer was 37 "Milky Way years" old. A solar system forms relatively quickly, and ours probably only took about 100 million years. The Sun and the planets formed from a cloud of sparse gas in the Milky Way, which condensed down and coalesced. After this happened, the Earth was very hot. It was a completely molten ball of rock, and had melted so thoroughly that its consistency was similar to water. Certainly, no life could have existed on the very young Earth.

Soon, however, the conditions on Earth became suitable for life. For our carbon-based type of life to develop, a planet needs to have Earth had all of these fairly early in its history. Scientists aren't sure when life first appeared on Earth, but some evidence dates the earliest life at three and a half billion years ago, when our astronomer was 47 "Milky Way years" old.
 * 1) organic matter (the material from which DNA is made),
 * 2) liquid water,
 * 3) a source of energy, and
 * 4) appropriate temperatures.

Evidence suggests that life appeared almost immediately once the necessary conditions were satisfied on the young Earth, but the first inhabitants of the new planet showed no strong predisposition for evolution to more advanced life forms. More than two billion years passed before primitive, single celled microbial organisms advanced to become multicellular life. Once it did, however, advanced life took rapid hold. This period of rapid development in the complexity of life is called the Cambrian Explosion.

The Cambrian Explosion occurred when our astronomer was 56 "Milky Way years" old. Ten years had passed on our slowed cosmological clock. This period of history was, in some sense, the most profound step in the development of intelligence on Earth.

Since the Cambrian Explosion, things have become very interesting on Earth. The astronomer was barely a year older by the time the primitive multicellular creatures had developed to become the dinosaurs, which were unimaginably more complex and advanced by comparison. We have now come into recent times, as the appearance of the dinosaurs occurred only twelve months before this instant in our astronomer's life.

We can see now that we must occupy a tiny, tiny part of the cosmic timeline. By what standard could the time of the dinosaurs possibly be considered recent? By a cosmological standard. The dinosaurs had a short stay on Earth. They disappeared 65 million years ago, or four months ago by the astronomer's clock. This gave mammals the chance to rise to dominance.

The first humans appeared on Earth only eight hours ago by our astronomer's clock. Civilization accounts for only a small fraction of this time. The first system of writing, and the first evidence of civilization, dates to only 6000 years ago, or fifteen minutes ago by our astronomer's clock. In the lifetime of the universe, all of culture and all of written history could fit into a coffee break!

Periods more similar to the human life span become even smaller in our comparison with the cosmic timescale. It was only very recently that people first endeavored to learn about the world using science in the way we understand it today. These first scientists, who considered observation and experimentation to give the last word on the nature of the universe, lived only about four hundred years ago, or one minute ago on our cosmic clock.

As we come progressively closer to the present, our lives seem progressively more ephemeral and fleeting. How long will our society, our culture, and our ideas endure in the long run? Only time will tell. At the current rate, it does not appear to be long before something must happen to stop the downgrade of society.

We can say little about what might happen on Earth in the next thousand years, let alone the next million years or the next billion years. Meanwhile, the Milky Way will continue on its normal course, a course which happens to be headed straight for a collision with the nearest neighboring galaxy in about 12 "Milky Way years." This is unlikely to be the disaster for Earth it might appear to be — a collision between any stars during a galactic merger is actually extremely improbable. The Solar System will simply take up residence in the new galaxy created in the aftermath of the collision.

Five billion years from now, the Sun will have used up its fuel and will die. At this point, about 20 billion years after the big bang, the long-lived astronomer will be 80 years old. The Earth will no longer be able to support life after the Sun dies, and the Solar System will become rather desolate. The universe as a whole will continue long after the death of both the Sun and our astronomer, but it too will slowly die, eventually becoming cold and empty as it continues to expand.

Looking back over the scales of the universe and seeing humanity's role, unimaginably small in both space and time, one might wonder whether science has painted a bleak, depressing, and hopeless picture for humanity. Some would say so, while others find comfort in the majesty and grandeur of the universe, and the possibilities that the future might bring. For now, the future of humanity in this universe, as chaotic and vast as it is, remains uncertain.


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Tennis

Tennis is a game played between two single players, in the singles game, or two teams of two players each, in the doubles game. To play, the players use a strung racquet to hit the tennis ball and send it over the net into the opponent's court. The purpose of the game is to send the ball fairly into the opponent's court in such a way that the opponent cannot return it fairly into your own court. This would include not being able to return it at all, causing the opponent to return it low and into the net, or returning it outside of the boundaries of your own court. The game is played all over the world, professionally and by amateurs. The simplicity of the game makes it possible for anyone who can hold a racquet, including those in wheelchairs and the very old and very young, to participate.

Table of Contents

 * /The court/
 * /The equipment/
 * /Forehand/
 * /Backhand/
 * /Volley/
 * /Serve/
 * /Spin/
 * /Tennis drills/
 * /Basic rules/
 * /A singles game/
 * /A doubles game/
 * /Local tournaments/
 * /Professional competition/
 * /Terminology/

テニス 테니스

title: Tennis


text:
User:Cjmnyc

See my Wikipedia user page.

title: User:Cjmnyc


text:
Wings 3D/User Manual/The Main Menu

Back to Wings 3D

'''5.1 The Main Menu Figure 33. The main menu bar.'''

The Main Menu consists of logically organized functions that are generally global in nature throughout Wings3D, that is they apply to vertices, edges, faces and objects or general environmental settings such as user preferences and camera manipulation. The exception to this general rule is the Objects Menu, which contains functions relevant to objects only. The Main Menu items include File, Edit, View, Select, Tools, Objects, and Help. Each of these will be covered in this section individually. 5.1.1 The File Menu File Menu – General The File Menu contains file handling options, most of which are common to almost all applications, but some warrant a little discussion. Each option is described in its own section below. File | New (Ctrl-N) Default when starting the program, giving you a clear workspace to work in. When invoked later Wings will ask if you want to save your changes with the standard Yes, No, Cancel options. If you answer No Wings3D will delete all objects in a current workspace. File | Open (Ctrl-O) Will load a previously saved .wings model into the workspace. When invoked, Wings will ask if you want to save your changes with the standard Yes, No, Cancel options. If you answer No Wings3D will present you with a File Open dialog box. You can then navigate to your file and load it by typing in the name or double clicking on it from the list of available models. If you cancel at this point, 46 DRAFT 1.6

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Wings 3D/User Manual/The File Menu

Figure 34: The File Menu. WINGS3D USER MANUAL ==Section 5: The Wings3D Command Reference Guide== Wings will keep what was in your workspace, otherwise all objects in your workspace will

File | Merge... (Ctrl-L) Adds the contents of another .wings file to your current scene. When invoked, the Windows file open dialog appears. By default, it is set to add a .wings file, but the option all files is available. The "All Files" option will only load a native Wings file such as one with the wrong extension (or no extension). Therefore, trying to bring in anything but a wings file returns the error message: 'Read failed: no such file or directory" as this command is for loading native Wings files only. One handy use for the File | Merge command is to load up a previously saved set of lights. If you create a lighting environment you are particularly fond of delete all the non-light objects from the scene and do a Save As. Call it something like lights.wings. Then after doing a file new you can merge the lights into your current scene. Note that File|Import implicitly always merges if you want to add an non-native format model to your scene.

File | Save (Ctrl-S) Saves the current workspace as a .wings file. If the model is new, a Save File dialog box will come up allowing you to specify the path and file name to be saved. If it is a previously existing file, it will save to that file, permanently incorporating any changes you have made since loading it.

File | Save As... (Ctrl-Shift-S)

Allows you to save the current workspace as a .wings file under a new file name. A Save As File dialog box will come up allowing you to specify the path and file name to be saved. This can save hours of labor, being particularly useful whenever you either come to a point where undoing will become a problem if further work does not pan out, or at a point that you want to come back to, for expanding in a different direction altogether.

File | Save Selected...

Allows you to save the currently selected object or objects in the workspace as a .wings file under a new file name. A Save

be deleted before the requested file is opened. dialog box will come up allowing you to specify the path and file name to be saved.

File | Revert

Clears all work done since last save and restores last saved. It does not clear the Undo history. The idea is that you should be able to undo a Revert if did it by mistake. Thus there is no question asking for confirmation.

File | Import

Nendo® (.ndo)

3D Studio (.3ds) [import scale] [export scale] [ok] [cancel]

Adobe® Illustrator (.ai)

Wavefront® (.obj) [import scale] [export scale] [ok] [cancel]

Import files of selected format in current project. Wings supports the importation of Nendo® (.ndo), 3DS Max® (.3ds) Adobe® Illustrator (.ai) and Wavefront® (.obj) format files. Import has no limits on file size other than system resources. Import implicitly always merges therefore you can add nonnative format models to your scene without loosing your current work.

The 3DS Max® and Wavefront® import commands both have option boxes on the right of the menu item. The option boxes allow you to specify an Import Scale. This is useful since many models will be very small or absolutely huge when imported into Wings. By experimentation you can find the right scaling factor and then apply it each time you import models from another program. Simply apply the inverse scale upon export if you wish to take the model back to the originating program.

The Nendo® import works much better than the others because it is a one-to-one translation. This is because both Nendo® and Wings use winged-edge data structures. Import of other formats is trickier. The other formats contains triangle or polygon meshes. To import them, Wings must combine the polygons into one or more closed objects that can be represented by the winged-edge

Section 5.1
The Menus WINGS3D USER MANUAL structure. Combining gets tricky if the mesh contains defects, and many meshes do since the defects usually are not a problem in other modelers or renderers.

Also, if you import a model that has a texture associated with it you may get a Wings message box when attempting to modify it, telling you that the operation can not be performed on a textured model. This is because texture support in Wings is under development. In a future release of Wings, the question will be if you want to convert the texture to colors (just as in Nendo®). But currently, the workaround is to use the Strip Texture command in the Body pop-up menu. Or you can save the model as a Wings file and reload it.

One thing new users may find helpful is the knowledge that Wings and Nendo® work well in tandem since Wings supports both the import and export of .ndo files. So you can model in Wings, take the model into Nendo® to do color assignments, and save the model with colors. Then you can use Wings File | Import (.ndo) and bring the model in with all the color assignments intact. Some Wings operations still cannot work with color assignments but you can smooth the model to a greater degree than is possible in Nendo® for a smoother looking model while still retaining the colors.

Currently, Wings only import textures from the OBJ format, not 3DS. Acceptable file formats for textures are 24 bit BMP, TGA®, and TIFF.

FILE | EXPORT

Nendo® (.ndo) 3D Studio (.3ds) Hash Model (.mdl) Wavefront (.obj) VRML 2.0 (.wrl) YafRay (.xml)) Optional

Saves all objects in workspace in Nendo® (.ndo), 3D Studio (3ds), Animation Master (.mdl), Wavefront (.obj), or VRML 2.0 (.wrl) format. When YafRay rendering software is installed this option will appear. There are option boxes for .3ds, .and obj, exporters

which bring up sub-menus for specifying parameters. The option box for .3ds allows you to enter an export scale. The option box for .obj allows this and a check box to create one group per material. YafRay uses the options setup under the File > Render > Yafray panel.

Quick Tip: Rendering with YafRay

On the PC side you can send a file to render in YafRay right from wings, but on the mac side you are limited to exporting the model and rendering from the command line. See section 7.1 YafRay.

FILE | EXPORT SELECTED

Saves selected elements in one of the export formats (see FILE | EXPORT). Note that the selection can be of any type (e.g. face selection).

FILE | RENDER

Renders the workspace using either the default OpenGL® render routine or YafRay if you have installed it correctly. Support for other rendering engines may be added in the future. The Option Button on the right will bring up a sub-menu for several parameters you can set. Before you can send the file to render in YafRay make sure you have added at least one light or you won’t see anything. The image is rendered from the point of view of the camera

FILE | HISTORY

If you have opened files previously you will see their filenames listed below File | Export. Clicking one will open that file (provided it is still in the same location where you had it at the time). The history list is currently limited to 4 files.

FILE | EXIT (Ctrl-Q) Exits Wings3D. If changes have been made since your last save Wings will ask you if you want to save them before shutting down.

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Wings 3D/User Manual/The View Menu

54 DRAFT 1.6

� WINGS3D USER MANUAL Section 5.1 The Menus 5.1.3 The View Menu Figure 40: The View Menu. VIEW MENU – GENERAL

The View Menu contains functions that set and control how you view your work; i.e.

camera and work environment settings.

VIEW | GROUND PLANE

Toggles the ground plane visibility on/off. Each grid cell of the ground plane represents one "unit" in Wings. A unit can be whatever you want it to be.

VIEW | AXES

Toggles axes visibility on/off.

VIEW | WORKMODE (Tab) Toggles the display between work mode and smoothed mode.

VIEW | SMOOTH PREVIEW (Shift- Tab)

Sets the view mode to shaded and performs one level of smoothing on a temporary basis so that you can see what your model will look like after smoothing. You cannot model in this mode.

VIEW | WIREFRAME

Sets the display mode to wireframe. If you want to extrude a face into the model, set your model to wireframe mode first and you will be able to see how far into the model you are going.

VIEW | SHADE

Sets the display mode to solid flat shading. Toggles between smooth shaded view and solid view on your model. In smooth shaded view the materials being used become visible. This is sometimes referred to as a Wings render.

VIEW | TOGGLE WIREFRAMED/SHADED (W) Toggles between wireframe and shaded

views of the model. This is a handy toggle to use in conjunction with the Tab key. Tab will show you a temporarily smooth-shaded version of your model which you can then overlay with the wireframe by hitting the W key. This wire on smoothed view can be helpful to see how edges affect the overall form of the subject while modeling.

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� Section 5.1 The Menus WINGS3D USER MANUAL VIEW | SHOW SAVED BB

Shows/hides the bounding box set in the Tools Menu. If set on, a dashed wireframe outline shows the extent of the box. Wings can save a single vertex or single edge as a bounding box. Bounding Boxes can be very useful for proportionally scaling and moving a large imported object to a desired volume and position, and can also be used as reference points with vector, magnet, and “snap-to” operations.

VIEW | SHOW EDGES

In flat shaded mode, toggles the edges on/off. This can be useful for very large models, as some otherwise fast graphics cards display edges slowly.

VIEW | SHOW NORMALS

A toggle that shows/hides the normals of every face, edge or vertex (depending on which selection mode you are in) of the model, as a short thick blue line. Handy for planning how things will be moved, as a visual aid if rotating faces around an edge, and to see the normals on an imported model which may have some or all of the normals inverted.

VIEW | SHOW WIREFRAME BACKFACES

Lets you see the wireframe from both front and back in wireframe mode. This can be very useful when trying to position edges to match up on the inside and outside of a wall, for example, prior to using Bridge to cut in a window.

VIEW | RESET VIEW (R) Resets the camera to default location and zoom. Great if you get lost.

VIEW | AIM (A) Points camera directly at selected objects, faces, edges or vertices. Then when you pan and zoom in on the selected the item, it will stay centered in the work space. If there is no selection, the aim point will be reset to the origin (0, 0, 0). This is very handy when doing detailed work and for doing high aspect ratio stuff, such as a giraffe. When working on the head, select a face on the head and Aim. Then all camera movement will be centered on the head. Then when working on the feet select a face there and Aim there, and the point of focus will be on the foot.

VIEW | FRAME (Shift+A) View | Frame works similarly to Aim except that it adjusts the distance to the selection so that the selection will be visible in the Wings window. If there is no selection, the distance will be chosen so that all objects will be visible.

VIEW | ORTHOGRAPHIC VIEW (O) Toggles orthographic/perspective views on/off. Orthographic views are the same as those traditionally used for engineering or technical drawing purposes – i.e. front, side and plan views. Since there is essentially no single point of view (as in perspective) all lines and faces are seen in their true lengths and shapes - provided they lie on a plane that is at right angles to the viewing direction. This can offer an advantage when moving or editing geometry that, for example 'bulges out' towards the viewer. The use of Orthographic View is well married with the use of Move | Free, allowing you to freely move selected items while automatically constraining such movement to only two directions at a time.

VIEW | SCENE LIGHTS

Turns on any lights you may have added to the scene via the Lights primitive.

VIEW | ONE/TWO LIGHTS

Toggles one or two standard lights on in the scene. To avoid confusion consider this menu item as a request. That is, if the menu reads One Light, then two lights are currently on, and vice versa. Note that Scene lights negate the One Light/Two Light option.

VIEW | SHOW COLORS

Vertex colors can be imported on pre-existing models (such as from Nendo®). To see the vertex colors use this option.

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� WINGS3D USER MANUAL Section 5.1 The Menus VIEW | SHOW MATERIALS

Materials can be created and assigned in Wings per face with the Face | Set Material command. They can also be present on models you have imported. To show materials use this option.

VIEW | SHOW TEXTURES

Models with pre-existing textures can be imported into Wings. The textures are retained after import and can be seen via this option.

VIEW | VIEW ALONG (X, Y, Z, Shift-X, Shift-Y, Shift-Z)

+X X

+Y Y

+Z Z

-X Shift+X

-Y Shift+Y

-Z Shift+Z

Sets the camera to view along the selected axis. It is recommended that you look at your model from various angles as you go, to get a good feel for how it is developing. Using the X, Y, Z (etc.) hot keys is a very quick and easy way to do this. It is also very handy to view along a major axis while scaling, as you can scale two vertices along a cross axis to spread them apart or move them towards each other. Useful in conjunction with orthographic mode for certain tasks where precise movement / alignment is required.

VIEW | ALIGN TO SELECTION

Turns the camera to point in same direction as selected elements. Wings then orientates the model such that you are viewing along the selected element's normal. This can be very useful if a single (flat) face is selected and Align to Selection is used. The face is then seen in its true shape, since the viewer is looking at it from a right angle. Selecting geometry forming that face (edges or vertices) and using Move -> Free (for example) allows movement on the same plane as the face. This keeps the face flat, which is required for clean geometry.

This is also useful in situations where you want to maintain a reference face, so that other geometry not linked to that reference

face can easily be moved on planes parallel to the reference face. To accomplish further editing of this 'external' geometry, select the reference face, use Align To Selection, and the model re-aligns to the correct position. For example, Align To Selection can be used on a flat face, then an edge can be Cut by 2 to create a new vertex. It is then possible to 'slide' the new vertex along the edge to a new position. The edge can either be kept straight via vector moves (discussed later) or 'distorted' by moving the vertex accordingly to form a new apex. In either case, by first using Align To Selection, the face will remain flat. Similar operations can be preformed via other methods as well, such as the Slide plug-in which will be discussed later.

VIEW | AUTO ROTATE (U) This will fly your camera around the model, so that it appears to rotate. The angle and speed of rotation can be set via the Edit | Preferences menu. Rotating gives you a good overall view of the model, and can be used in conjunction with screen capture software to create an AVI to show off your model. Left click to stop the rotation. You can change the aspect of the camera with the middle mouse button during rotation and the rotation will continue.

Quick Tip: View Orthographic in Wireframe Mode.

Sometimes it is not all that obvious what the difference between Orthographic and Perspective views do for you. To see this graphically, create a cube and hit the X key to look at it straight on. Then hit the O key a couple of times. It does not seem to do much other than change sizes, right? Now hit the W key to put the cube into Wireframe Mode and repeat the exercise. You can definitely see the effects of perspective now, even when looking dead on. Now use the marquee select function (drag a box) to select the top left vertex of the cube while still in perspective view. You get one vertex selected. Clear the selection and go into Orthographic View. Select the top left vertex via marquee drag. Rotate the camera a little and you will see that you got both the front and back vertices because you were in Orthographic view. This can be very useful

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� Section 5.1 The Menus WINGS3D USER MANUAL when you are working on a complex but thumb, as an example, you can go into symmetrical, or nearly symmetrical model. Orthographic view and use a marquee select To get the vertices of the left and right to get both sets at once.

Image by Mentat7 (www.sargentgfx.com) Rendered in Cinema4D

title: Wings 3D/User Manual/The View Menu


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Wings 3D/User Manual/The Select Menu

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� WINGS3D USER MANUAL Section 5.1 The Menus 5.1.4 The Select Menu Figure 41: The Select Menu. SELECT MENU – GENERAL

The Select Menu is one of the most important items in Wings3D as it contains many operations that lead to fast and efficient modeling. By being able to quickly select the elements you need to work with, and even combine (or subtract) that selection with another selection set you can quickly achieve the results you desire.

SELECT | DESELECT (Space) Deselect all selected items.

SELECT | MORE (+) Grows the selection set to include all the adjacent items (vertices, edges, or faces) of

the same type on a given object. For example, if a face is selected all adjacent faces will become selected as well. If there are multiple objects in a scene, it will not cause more objects to be selected, however, each object with a selection set active will have it's selection set grow.

SELECT | LESS (-) Shrinks the selection set in reverse order of it's growth. If working with an initial selection set, this will cause nothing to be selected. As with More, selection sets on multiple objects can be manipulated at the same time.

SELECT | REGION (Shift-L) Select | Region works in conjunction with a properly selected closed edge loop. Given a properly selected edge loop, Select | Region will then select all the faces contained by that loop. If a single edge is selected, or if the loop is not closed, then all the faces become selected. Select|Region will also handle multiple loops. For instance, you can select both hands or both legs. Select|Region and Select|Edge Loop are the inverse of each other.

SELECT | EDGE LOOP (L) Selects edges that flow in a line until a pole is encountered. A pole is a non-4way intersection (i.e. it has 3 edges or 5 or more edges joining at a single vertex).

SELECT | EDGE RING (G) Selects a set of edges that run between two edge loops. These cross edges are sometimes referred to as "struts". If you think of the lines of latitude on a globe as edge loops, then the lines of longitude between any two parallels would constitute an Edge Ring. In Wings, simply select one such "strut" then Select | Edge Ring, and the entire set of edges will become selected, until the model is completely encircled, or until a pole is encountered. This can result in big time savings when modeling.

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� Section 5.1 The Menus WINGS3D USER MANUAL SELECT | PREVIOUS EDGE LOOP

(F3)

This will "step" down the model from one closed edge loop to the next, deselecting the originally selected loop in favor of the next one it encounters. Repeated use of F3 continues on down the model until it no longer finds another loop to select, then it reverses order and comes back up the model. This is very powerful and when used in conjunction with other functions (such as Scale, Move, Rotate, etc.) and can greatly increase the efficiency of your modeling work flow.

SELECT | NEXT EDGE LOOP (F4) This will "step" up the model from one closed edge loop to the next, deselecting the originally selected loop in favor of the next one it encounters. Works just like F3, except it goes in the opposite direction, so that you can use the two function keys to toggle back and forth between two edge loops, or change directions at will.

SELECT | SIMILAR (I) Selects items similar to the currently selected item. Select | Similar is not that useful for organic modeling. Its main strength is in what Jakob Cederlund calls geometric art (i.e. objects that are highly symmetrical). It is good for selecting faces widely apart. The rules for similarity are as follows.

Faces - Same number of edges. Sum of edge lengths approximately equal. Sum of angles between each pair of edges approximately equal.

Edges -Approximate length of edge equal. Angle and length of the nearest four edges approximately equal.

Vertices - Angle and length of edges going out from the vertex approximately equal. This may be the least useful of the bunch, as it seldom finds many hits.

Note that Less does not deselect items selected via Similar; i.e. it does not revert to the original selection set.

SELECT | ADJACENT

VERTICES – selects vertices adjacent to the currently selected vertex/vertices.

EDGES – selects edges adjacent to the currently selected edge(s).

FACES – selects faces adjacent to the currently selected face(s). If you press the same key several times, the selection will grow each time. In vertex selection mode, pressing the "v" will grow the selection in exactly the same way as does SELECT | MORE. However, in edge selection mode, pressing "e" will grow the selection by selecting the four edges nearest each edge. SELECT | MORE, on the other hand, will select all edges that share a vertex with a selected edge. To see the difference, select one edge on an icosahedron or a grid and try both commands. In face selection mode, all faces that share an edge with a selected face will become selected. SELECT | MORE, on the other hand, will select all faces that share a vertex with a selected face. Try it out on a grid to understand the difference.

Note that if there is no current selection set the keys v, e, f (and b) simply change selection mode to vertex, edge, face and body, respectively.

Model by Mr. Christopher. Rendered in Strata Studio 60 DRAFT 1.6

� WINGS3D USER MANUAL Section 5.1 The Menus SELECT | BY

Hard Edges

Vertices with

2 Edges

3 Edges

4 Edges

5 Edges

Faces With

2 Edges

3 Edges

4 Edges

5 Or More (F5)

Material

Default

Hole

Random

10%

20%

...

90%

Short Edges [] Click on the box to the right to specify how short.

Id

Select | By offers a wide variety of methodology to choose selection sets. These selections can be stored (as discussed later) and then used in conjunction with other selection sets via Union, Subtract, and Intersection (also discussed later).

Hard Edges selects all Hard Edges in the selected object.

Vertices with (2, 3, 4, and 5) selects faces that have the given number of vertices as designated by the number. This is helpful in trying to maintain quads.

Select | By | Faces With | 5 Or More has a hot key, F5, so that you can quickly find any non quad or tri sided polygons. Such polygons can cause problems in some 3D modeling and rendering packages and should therefore be resolved.

Material is used to select faces by their assigned materials. Any user-defined material will automatically be added to the Material sub-menu and become available for selection.

Random (10 – 90%) selects a random subset of the current selection type (vertices, edges, faces or objects) for manipulation.

Short Edges selects any edges that are too short, as determined by the option box to the right of the command. Short edges are often responsible for display anomalies and difficulties in continued modeling. Often these edges will be so short and located such that you can not see them, even after selecting them. You can Extrude them to find them, or simply Collapse them to eliminate them.

Id. You can also select any item (vertex, edge, or face) by its ID number, which can be gleaned from the Wings status bar when the item is selected. So, if you record an ID number you know you want to come back to, you can later Select it then Aim at it to continue working in that area.

SELECT | LIGHTS

Will select all the lights in your scene.

SELECT | ALL [Vertices, Edges, Faces, Objects] (Ctrl+A) Selects all the vertices, edges, faces, or

objects, dependent on the current selection mode. For objects, it selects all within the scene that have not been hidden or locked (via Object | [object name] | Hide or Lock (to be discussed later)).

SELECT | INVERSE (Ctrl-Shift-I) Inverts the selected set. That which was selected becomes unselected and vice versa.

SELECT | STORE SELECTION

Stores a selection set so that it can be used in conjunction with other selection sets.

SELECT | RECALL SELECTION

Recalls a selection set so that it can be used in conjunction with other selection sets.

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� Section 5.1 The Menus WINGS3D USER MANUAL SELECT | EXCHANGE SELECTION

Exchanges a selection set so that it can be used in conjunction with other selection sets. The current selection set becomes the stored selection set while the stored selection set becomes the active one.

SELECT | UNION WITH STORED

Creates a new selection set by combining the current selection set with one that has been stored.

SELECT | SUBTRACT WITH STORED

Creates a new selection set by subtracting the stored selection set from the current selection set. That is, all items in common

between the two sets are deselected from the current selection set.

SELECT | INTERSECTION WITH STORED

Creates a new selection set intersecting the current and stored selection sets. That is, only those items that are common to both sets remain selected. This can be used very effectively to add noise to an organic model. You can store all the vertices on a tree trunk, for example, then Select | By | Random | 30% which will select vertices on trunk, branches and leaves. Then do a Intersection With Stored and only random vertices on the trunk will remain selected which you can then Move | Normal to make knobs.

Model by Mr. Christopher.

title: Wings 3D/User Manual/The Select Menu


text:
Wings 3D/User Manual/The Tools Menu

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� WINGS3D USER MANUAL Section 5.1 The Menus 5.1.5 The Tools Menu Figure 42: The Tools Menu. Tools Menu – General

The tools menu contains some functions that will interact with other Wings commands.

TOOLS | ALIGN

All

X Y Z Radial X (YZ) Radial Y (XZ) Radial Z (XY)

Aligns all selected objects based on the bounding box of the selection for each element. This can be useful to line things up once they have gotten off center. For example by using a series of Aligns, you could get wheels on a model that have become misaligned back into proper positions relative to each other. It does not align vertices, edges or faces to an axis on the same model.

TOOLS | CENTER

All

X Y Z Radial X (YZ) Radial Y (XZ) Radial Z (XY)

Centers objects in the workspace based on the bounding box of all selected items. If you work on a large model that has sort of "grown" off in one direction, you can quickly center it in the workspace again. Also, if you have multiple objects in a complex model, and you've lost track of one of them, you can select it (via the Objects Menu – to be discussed latter) and then Center to find it again.

TOOLS | SAVE BOUNDING BOX

Saves the bonding box of selected items, from one or more objects, for later use. Use Save Bounding Box without any selection to clear the bounding box. An outline of the current bounding box is displayed if so chosen in the users' preferences.

TOOLS | SCALE TO SAVED BB

All

X

Y

Z

Radial X (YZ)

Radial Y (XZ)

Radial Z (XY) Scales the selected object(s) to the bounding box that has been previously saved. This command will scale each selected object, along one, two, or three axes. The amount to scale could be different along each axis, meaning that this command can distort the proportions of the objects (i.e. a cube might no longer remain a cube). The scale factor for each axis is computed by comparing the saved bounding box with the bounding box for

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� Section 5.1 The Menus WINGS3D USER MANUAL the selection. To avoid distorting the objects, use Scale to Saved BB Proportionally.

TOOLS | SAVE TO SAVED BB PROPORTIONALLY

All

X

Y

Z

Radial X (YZ)

Radial Y (XZ)

Radial Z (XY) Similar to Scale to Saved Bounding Box, but the idea with this one is that it should preserve the proportions of the selected objects, i.e. all axes will be scaled the same amount. This command will keep the scaled objects inside the saved bounding box.

TOOLS | MOVE TO SAVED BB

All

X

Y

Z Will move the selected object(s) based on the center of their aggregate bounding box to the center of the saved bounding box.

TOOLS | SET DEFAULT AXIS

Sets the default axis for vertex commands.

TOOLS | VIRTUAL MIRROR

The Virtual Mirror tool puts you into a special modeling mode for creating perfectly symmetrical models. To use it select a face to mirror around and then select Virtual Mirror. The model will be mirrored from the selected face so that as you make changes on either side of the model they will be reflected on the other side of the model. This has the potential for cutting your modeling time in half and can be used to do some things that are otherwise sometimes difficult to achieve, such as rotating two surfaces in opposite directions. Note that if you want your model to stay centered in the workspace it is best to loop cut the model down the middle, delete half the model,

select the resulting face, and then start Virtual Mirror.

Create – Creates the virtual half of the model which mirrors the real half. Note that you can work with either the virtual or real half and actions will be reflected on the counterpart.

Break – Destroys the virtual mirror so that only the real half of the model remains.

Freeze – Makes the virtual half of the model into real geometry, thus creating a perfectly symmetrical full model.

TOOLS | TWEAK

Tweak is a special modeling mode that allows you to drag vertices freely for fine movements. It is a very useful and powerful tool that warrants getting used to. Most of the controls are clearly explained on the status bar at the bottom of the workspace, as outlined here:

(L) – Left mouse button; Drag vertices freely (R) – Right mouse button; Exit tweak mode (M) – Middle mouse button; Tumble (Shift-M) – Shift plus the middle mouse button; Track (Ctrl-Shift-M) – Control plus Shift plus the Middle mouse button; Dolly

(1) – Turns the magnets on or off. You can use Tweak with standard moves, or with magnetic moves. To turn on the magnets press the 1 (the number 1) key. Doing so will cause the status bar to change. While in magnet mode L will drag and R will exit Tweak mode. The + key will increase the fall-off zone while the – (minus) key will decrease the fall-off zone. The 2, 3, and 4 keys will change the type of magnet in use. Pressing the 1 key will turn the magnets off again.

These controls effectively turn Tweak into an interactive magnet with the area of influence for the magnet defined by the fall-off zone. Tweak was originally a plug-in designed by Howard Trickey and has since been incorporated into the Wings3D core.

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� WINGS3D USER MANUAL Section 5.1 The Menus Quick Tip: Additional Tools

Note that some very useful tools for Wings will appear in the Tools Menu if you have installed the available plug-ins. These include Draw Loop, Locked, Slide, and Tweak_s from Clacos. They are available at:

http://members.lycos.co.uk/clacos/

I highly recommend them. Apologies to any other tool makers if I'm missing any.

Quick Tip: Bounding Boxes

Don't overlook the usefulness of bounding boxes. You can use them to place an object at any given location, such as putting a hat on a hat rack. To do so select a vertex on the hook of the hat rack and do a Save Bounding Box. Then select a vertex on the inside of the hat and do a Move To Saved BB. The hat will snap right into place.

Image by Mentat7 (www.sargentgfx.com) Rendered in Cinema4D

title: Wings 3D/User Manual/The Tools Menu


text:
Wings 3D/User Manual/The Objects Menu

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� Section 5.1 The Menus WINGS3D USER MANUAL 5.1.6 The Objects Menu Figure 43: The Object Menu. Objects Menu – General

The Objects Menu presents you with options limited specifically to whole objects.

OBJECTS | SHOW AND UNLOCK ALL

Pretty self explanatory. It shows all objects in the workspace, and if any of them were locked, unlocks them, making all objects eligible for further manipulation.

OBJECTS | HIDE SELECTED

Hides any object or multiple objects that are currently selected. This is handy to hide a large, easily selected object, so as to be able to get to and manipulated a smaller object that his mostly or completely obscured by the larger object. Once hidden, the objects are locked and therefore protected from any changes.

OBJECTS | HIDE UNSELECTED

Hides any object that is not currently selected. Hidden objects are automatically locked and protected from any geometry/orientation changes.

OBJECTS | LOCK UNSELECTED

Locks unselected objects, but leaves them visible in the workspace as reference objects.

OBJECTS | {OBJECT LIST} (object1 would be cube1 for the example shown above.) [] object1

Select

Hide

Hide Others

Lock

Rename [] object2

Select

Hide

Hide Others

Lock

Rename [] object3

Select

Hide

Hide Others

Lock

Rename and so on...

The bottom part of the Objects Menu shows a list of all the current objects in the workspace. They will initially have default names based on how they were created. For example, when a cube primitive is added to the workspace when Wings is first started, it will be named cube1. Note that if you do a File | New, the item numbers are not reinitialized. So if you then added a cube to the new workspace it would be listed as cube2. The open eye icon to the left of the name (represented in this document as [] brackets) will show if it is currently visible and change to a closed eye icon if it is hidden. Each object in the list has a sidebar menu from which you can do many handy things. From this menu an object can be Selected/Deselected, Hidden/Shown (note, if hidden Show is the only option in the side bar menu), Locked/Unlocked, and Renamed.

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� WINGS3D USER MANUAL Section 5.1 The Menus Objects retain the name assigned to them upon Save and Export, which is very useful in texture mapping applications later on. Hide Others (the middle option in the menu) does not work on the selected object. Rather, it hides all the rest of them. This is very useful when working in a multi object scene. As mentioned elsewhere, the Object Menu can be used to find objects you've lost track of, or

to recenter around a specific object. To do this simply choose Object | Select and then use Tools | Center | All to find/recenter on the elusive object. Currently this is a single column, non-scrollable list, so if your scene has a lot of objects in it, they may not all be accessible via this menu.

Model by Mike Gleason. Rendered in Strata Studio

title: Wings 3D/User Manual/The Objects Menu


text:
Wings 3D/User Manual/The Help Menu

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� Section 5.1 The Menus WINGS3D USER MANUAL 5.1.7 The Help Menu Figure 44. The Help Menu. Help Menu – General

The Help Menu contains some general information on selected topics. They are pretty self explanatory, and new users would be advised to read through them. They are brief, so it won't take very long.

HELP | GETTING STARTED

Basics on program navigation.

HELP | USING A MOUSE WITH ONE OR TWO BUTTONS

Explains how to tell Wings what type of mouse you are using.

HELP | FRENCH AND GERMAN KEYBOARDS

Explains how keyboard mapping differ for French and German keyboards.

HELP | LIGHT BASICS

Tells you how to create, manipulate, and use lights in Wings.

HELP | ASSIGNING HOTKEYS

Explains how to assign and delete hot keys in Wings3D. Figure 44. The Help Menu.

HELP | ADVANCED MENUS

Tells you how to turn on the advanced menus and why you would want to.

HELP | OPENGL INFO

Tells you some basic information about your graphics card and how it handles some of the OpenGL® properties. Could be useful information to include if you report a bug that deals with how Wings displays things on your system.

HELP | ABOUT

Displays the current revision number for Wings3D.

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� WINGS3D USER MANUAL Section 5.2 6The Context Sensitive Menus 5.2 The Context Sensitive Menus The key to the Wings3D user interface is the use of context sensitive pop-up menus. These menus are accessed by right clicking in the workspace. There are a total of five context sensitive menus; the Primitives Menu, the Vertex Menu, the Edge Menu, the Face Menu and the Object Menu, not to be confused with the Objects Menu on the Main

Menu). Depending on what is selected, different menus will pop up presenting the user with operations that are applicable to the current situation only. In this way the interface is kept clean and simple, a joy to work with compared to many overly complex user interfaces found in some graphics and modeling packages.

5.2.1 The Primitives Menu Primitives Menu – General

Figure 45: The Primitives pop-up menu. To bring up the Primitives Menu, right click on the empty

workspace, or on a workspace where nothing is selected. You will be presented with a list of available primitives to add to your workspace. Left click on one of the primitives to add it. It will be added to the center of the scene as an unselected object at it's default size. You may need to turn other objects' visibility off (via the Objects Menu) in order to find the newly added object. The complete list of standard primitives is given below. Notice that some primitives have a little box icon to the right of their name. This is the Options Box for that primitive. If you click on the primitive name you will add a default primitive, whereas, if you click on the options icon you will be presented with some options (number of sections, number of slices, etc.) that you can change.

Tetrahedron – a four sided object; a triangular pyramid. Octrahedron – an eight sided object. Octotoad – A twenty-six sided object, unique to Wings. Designed by Mike (roadtoad), the host of the Wings discussion forum, and added to the Wings primitives as a tribute to the great service this board provided in the further development of Wings3D. Dodecahedron – a solid object with twelve faces. Icosahedron – a solid object with twenty faces. Cube – Plain and simple. What most models start out as. Cylinder – Click on the options button (the little box on the right) for the Sections option. A Windows dialog box will come up showing the number of sections in the cylinder (16 by default). You may change this and then click OK, or click Cancel. If you do not click on the options button, but simply click on the name Cylinder, then a default cylinder will be added (with 16 sides). Cone – Sections (16 by default). Sphere – Sections (16 by default) and Slices (8 by default). Torus – Sections (16 by default) and Slices (8 by default).

title: Wings 3D/User Manual/The Help Menu


text:
Wings 3D/User Manual/User Interface/The Title Bar

The Title Bar

 * The Title Bar along the top of the application window identifies the program's name (Wings 3D). At the far right of the Title Bar are the standard GUI widgets for Minimize, Restore, and Close.  If a previously saved file is open in Wings 3D,  the Title Bar will display its file name.  When a file is Auto-Saved the title bar displays that the file has been auto-saved.

 * The Auto-Save feature can be turned on and set to the number of minutes the user desires between auto-saves and can be found in Edit|Preferences|Misc. The default setting is 10 minutes between auto-saves.  Auto-save will only save that has been previously saved.  Auto-save creates a separate file from the one the user saved and overwriting the auto-save file for each iteration.  If Wings is closed during an auto-save session without the user saving changes manually, the next time Wings is asked to opens that file may prompt the query: [[Image:Auto_Save_Open.png|frame|left]]


text:
Wings 3D/User Manual/User Interface/The Menu Bar

The Menu Bar
Below the Title Bar and inside the Geometry window is the Menu Bar. Here you will find options more common to Wings in general such as settings and tools that are not specific to any one Selection Mode.

 * Edit, File, View, Select, Tools, Windows, Help.

Each Menu item will be discussed fully in Section 5, The Wings3D Command Reference Guide.


text:
Wings 3D/User Manual/User Interface/The Icon Bar

2.4 The Toolbar

There are three sets of Icons above the workspace as illustrated here.

The two on the left determine what Display Mode your model is in. They are, from left to right, Wire-shaded on/off, and Perspective on/off. These are used to toggle on and off these features as you work. Perspective off, also called Orthogonal view, is useful for lining an object up to a reference image plane.

The next four icons display what Edit/Selection Mode you are in. They are Vertex, Edge, Face and Body. The red highlighting gives you a quick visual key as to just what elements are affected in each mode and the white outline box indicate which mode you are currently in. In the above illustration we are in Face selection mode. Your Edit Mode will be important when it comes to using any of the modeling tools, since most tools are presented in context sensitive menus within the Workspace. The context of those menus is determined by the current Edit Mode.

The last two are Ground Plane and Reference Axes. These icons are used to quickly toggle on or off these features as needed.


text:
Wings 3D/User Manual/The Edge Operations Menu

Commands
This section lists commands as they appear with advanced menus enabled. With advanced menus disabled, some options and commands are not available.  .Move.  Normal Free X Y Z Last Axis
Default Axis

Absolute

.Rotate.

.Normal.

.Free.

.X.

.Y.

.Z.

.Last Axis.

.Default Axis.

.Scale Uniform.

.Scale Axis.

.X.

.Y.

.Z.

.Last Axis.

.Default Axis.

.Scale Radial.

.Radial X.

.Radial Y.

.Radial Z.

.Radial Last Axis.

.Radial Default Axis.

.Extrude.

Normal

Free

X

Y

Z

Last Axis

Default Axis

.Cut.

2

3

4

5

10

Enter Number

Connect

Bevel

Dissolve

Collapse

Hardness

Soft

Hard

Loop Cut

Vertex Color

.Intersect.

Reference
To use the commands in the menu, select one or more edges and press RMB.

Axes
Many commands require that you select an axis from the menu. This axis defines the direction or orientation for the command.

In addition to the three world axes—X, Y and Z—many commands work with edge normals, custom axes, default axes and most recently used axes.

If you specify edge normals as the axis (by selecting Normal), each group of connected edges uses the average normal of its vertices.

Custom axes can be specified only when advanced menus are enabled. For details about this feature, see Advanced Menus.

A default axis is an axis that you define in advance to use later. To define the default axis, use the Tools | Set Default Axis in the main menu. This is done in two stages: first you specify the actual axis, and then the point of origin for that axis. A default axis is stored until you redefine it. To recall the default axis for an edge operation, such as Move, select Default Axis from the edge operations menu.

The Last Axis menu item recalls the axis you used during your most recent operation.

Move, Rotate and Scale
Moving, rotating or scaling are straightforward operations.

To move the selection, specify the axis you want to move it along. For details about axes, see above.

To rotate the selection, specify the pivot axis. If you use custom axes, the pivot point (center of rotation) is set automatically as well.

Scale Uniform scales the selection in all directions at once. If you right-click the command, the secondary selection specifies the pivot point (scaling center).

Scale Axis scales the selection along the axis you specify.

Scale Radial scales sideways around the axis you specify, but not along it. Each vertex in the selection of stays on the plane perpendicular to the specified axis.

The effect of edge rotation and scaling depends on whether you let Wings set the center automatically or specify it with a secondary selection.

By default, each isolated edge and group of connected edges gets its own transformation center. This means, for example, that default scaling of multiple isolated edges is different from scaling their vertices. To see the difference, try scaling an edge ring, then undoing, converting the selection to vertices and scaling the vertices.

Slide
Slides the selected edges, shifting the border between the edges that they connect.

Extrude
Creates an edge loop that runs around the selected edges, and moves the selection along the axis you specify, creating a "ridge". Use the + and - numpad keys to slide the new edges.

Cut
Splits the selected edges by creating vertices along their length. Click Cut to select a predefined number of divisions (2, 3, 4, 5 or 10) or specify a custom number. If advanced menus are enabled, you can right-click Cut to perform a precise split.

Connect
Creates edges that connect the centers of the selected edges.

Bevel
Creates a face in place of the selected edges, putting the vertices of the new face on the edges that were connected to the original edge. Drag the mouse to slide the face along those edges.

Dissolve
Removes the edge or edges and joins the faces that shared them.

Collapse
Collapses each isolated edge or group of connected edges to a single vertex; switches to vertex selection mode. This command can be used very effectively in conjunction with Select | By | Short Edges to remove microscopic edges that are interfering with your modeling.

Hardness
Makes the selected edge or edges Hard or Soft. Edge hardness affects two things: the way edges appear in the geometry window and the way the model is smoothed.

Soft Edges are smooth by default. Soft edges do not look sharp in preview mode (when you toggle off work mode with Tab). In other words, Gouraud shading is used for soft edges—the normals of connected faces are interpolated smoothly across the edge. Soft edges are fully affected by the Smooth operation.

Hard Hard edges look sharp in preview mode, as if the faces they connect belong to different models.

The Smooth operation in Wings produces different results on smooth and hard edges. Smoothing actually happens in two stages: first, the model is subdivided; then the resulting vertices are displaced to make a smooth shape. Edge hardness does not affect the subdivision, but has an effect on the displacement.

Smoothing considers the surrounding geometry when vertices are displaced after subdivision. Hard edges mark boundaries for displacement. After a face is subdivided, displacement calculations ignore geometry beyond a hard edge.

You can use edge hardness as a modeling aid to retain sharp features when you perform smoothing. The effect is most pronounced when you harden edges that form a closed shape.

Note that it doesn't normally make sense to leave hard edges in your finished model. Not all file formats and renderers support hard edges, and they don't look natural when rendered. It's generally better to replace them with small bevels.

Loop Cut
Use this command when the selected edges form one or more closed shapes on the surface of the model. Loop Cut splits the model into as many objects as these shapes divide the model into.

One obvious use case is to loop cut an asymmetrical model in half and mirror it.

Vertex Color
Opens a dialog box where you can specify a color for the vertices belonging to the selected edges. The specified color is strongest at the target vertices and fades out towards surrounding vertices.

Note: A vertex cannot have a color and a UV coordinate at the same time.

Intersect
Extends the selected edge or edges to the points where they intersect the specified plane. Requires advanced menus.

Intersect has three modes depending on which mouse button you click the command with:

LMB—Intersect standard planes

RMB—Pick plane

MMB—Pick plane and ref point on plane

Intersect standard planes
Extend the edges till they intersect with the plane perpendicular to one of the following axes:

X

Y

Z

Last Axis

DefaultAxis

 For details on axes, see above.

Clicking an axis label with LMB specifies that the plane passes through the world origin. Clicking with RMB lets you specify the point that this plane passes through.

Pick plane
Extend the edges till they intersect with a custom plane. Specify the plane by selecting the components that define it.

Pick plane and ref point on plane
Extend the edges till they intersect with a custom plane passing through a custom point. First specify the direction of the plane's normal, and then the point that the plane passes through. This mode is a step forward from the RMB mode. It is useful when some components conveniently specify the direction of the normal, but the plane must pass elsewhere.