Math Terms - Visually Described ?

SuperLynx · 2010-08-04 10:40:01

Trying to find a site that describes things as the following in visual diagrams if possible.

- Clamp
- Matrix
- Modulo
- Absolute Value
- Floor
- Quaternion Interpolate
- InRange
- Transpose
- 3X3 and 4X4 Matrix
- Dot Product
- Cross Product
etc

bobbym · 2010-08-04 10:45:22

Hi SuperLynx;

Haven't seen you in a while.

This is a example of a 3 x 3 matrix:

An example of a 4 x 4 matrix:

This is a example of a dot product of 2 vectors, it returns a scalar.

This is an example of a cross product of 2 vectors:

This is what a transpose operation looks lie:

Example of a floor function:

Here is an example of an absolute value:

This is a modulo operator:

Quaternion interpolation no easy example!

InRange, I don't know what that is!

I only know one usage for clamp. It is a math function implemented in some languages.

If number < = low return low

If number > = high return high
else return number.

clamp( number, low, high )

clamp( 21, 2 , 10 ) returns 10

clamp( 11, 5, 17) returns 11

Just showing you what they look like and their notation. Ask if you need more.

SuperLynx · 2010-08-04 11:49:37

Hi, yeah I've been learning some stuff and doing some designing changing around my site and such and have had a really bad summer so far from the Heat and a lot of personal issues.

What does Transpose do ? And how did you calculate Modulo ?
That is my first of a few set of questions

bobbym · 2010-08-04 11:57:36

Hi;

Transpose makes the rows of a matrix into it's columns. The first row 1 , 2 became the first column 1 , 2.

Modulo is easy, basically it is the remainder, or whats left over when you divide by some number.

39 mod 6 is 3 because 39 / 6 is 6 with a remainder of 3.

SuperLynx · 2010-08-04 11:59:55

Ohh what would be the purpose of that in Computer Graphics?

bobbym · 2010-08-04 12:02:20

Hi;

See the above post for the first answers. Matrix operations are responsible for the translations you see in graphics programs. That's what the human eye sees as motion on the screen. Mods are clock arithmetic.

SuperLynx · 2010-08-04 12:12:03

39 mod 6 is 3 because 39 / 6 is 6 with a remainder of 3.

39/6 = 6.5 where do you get a remainder of 3 ?

Transpose turns a rows into columns, I still don't understand besides that

bobbym · 2010-08-04 12:15:49

Transpose turns rows into columns, I still don't understand besides that

That's what the transpose operator does.

If you had to split 39 cents among 6 kids how would you do it? You can't give them 6.5 cents. You would give each kid 6 cents , 6 * 6 = 36 and you have 3 cents left over. That's modular arithmetic. So 39 mod 6 = 3.

SuperLynx · 2010-08-04 13:02:31

I still don't get how you get 3 cents remainder ? When it's 6.5 cents, something I'm missing

And the Floor function is calculated how [3.2]=3 ??

bobbym · 2010-08-04 13:18:33

Hi;

Yes, 6.5 cents is the exact answer, but we are talking about whole numbers. You can't cut a penny in half, now can you? You can't give every kid 7 cents because you don't have enough. You can give them 6 cents, but when you do you will have 3 cents left over.

SuperLynx wrote:

And the Floor function is calculated how [3.2]=3 ??

The floor function rounds down it's argument to the nearest integer. 3.2 is not an integer. 3 is an integer or whole number.

SuperLynx · 2010-08-04 23:08:15

Alright I understand Floor it rounds the number to the nearest Integer (aka 4.6 = 5). Although I still don't understand Modulo how you got a 3 remainder ???

How do you figure out a cross product of two vectors, the math ?

bobbym · 2010-08-05 08:22:26

Hi SuperLynx;

Hold it! Floor does not round 4.6 to 5. It rounds down to the nearest integer.

.

How do you figure out a cross product of two vectors, the math ?

These are all mechanical. You can learn how to perform these operations with little or no understanding. I will show you how. First, let us stick to the modulo problem. 1 thing at a time!

still smile don't understand Modulo how you got a 3 remainder

It is an integer division. Before I go any further can you tell me what you would do with the 6 kids and the 39 pennies? Can you explain your solution? It is the key to what I am doing.

SuperLynx · 2010-08-05 13:06:16

4.6 = 5
Nearest Integer you can't round up because .6 is closes to making it a round number, you have to use the number on the left which is 4. [8.4]=8 ???

If I had 39 cents and had to give it to 6 gives I'd give each kid 6 cents and have 3 left over, Ohhhhh

Last edited by SuperLynx (2010-08-05 13:08:19)

bobbym · 2010-08-05 15:53:21

Hi SuperLynx;

Correct!

If I had 39 cents and had to give it to 6 kids I'd give each kid 6 cents and have 3 left over, Ohhhhh

That is exacly right, so:

Which is the same as saying 39 is congruent to 3 mod 6 or dividing 39 by 6 leaves a remainder of 3.

SuperLynx · 2010-08-05 22:18:50

47=7 Mod 5? Correct ?

How do you figure out the Cross Product of two Vectors ?
How does a Matrix work?

bobbym · 2010-08-05 22:21:52

Hi;

We will get to matrices and cross products. First you are still having trouble with the modulo operator.

47=7 Mod 5? Correct ?

Not exactly.

If you had 7 left over, couldn't you take another 5 out of that?

Try the kids and pennies model if you get stuck. If you have 47 pennies and 5 kids, how would you share the pennies? What would you have left over? That is what 47 mod 5 is.

SuperLynx · 2010-08-05 23:24:37

47/5 = 9.4
9 * 5 = 45 with 2 Remainder

bobbym · 2010-08-06 09:41:52

Hi SuperLynx;

Correcta Mundo! You say,

Read 47 is congruent to 2 mod 5 or 47 divided by 5 leaves a remainder of 2.

SuperLynx · 2010-08-06 10:22:10

81=6 Mod 9 ??

If so onto the question in Post #15

bobbym · 2010-08-06 10:26:57

Hi SuperLynx;

Nope. 81 does not leave a remainder of 6 when divided by 9.

SuperLynx · 2010-08-06 11:20:08

0.6

SuperLynx · 2010-08-06 11:23:08

I have 81 cents and I want to split it up amongst 6 kids = 0.07

bobbym · 2010-08-06 11:33:11

Hi SuperLynx;

You are not using that right. If you had 9 kids and you wanted to split 81 cents how would that work out?

SuperLynx · 2010-08-06 12:19:33

87 cents amongst 4 kids = 21.75 * 4

87=0 Mod 4 ???

bobbym · 2010-08-06 12:27:12

Hi;

Hold on you are jumping ahead. First get this one.

If you had 9 kids and you wanted to split 81 cents how would that work out?

Math Is Fun Forum

#1 2010-08-04 10:40:01

Math Terms - Visually Described ?

#2 2010-08-04 10:45:22

Re: Math Terms - Visually Described ?

#3 2010-08-04 11:49:37

Re: Math Terms - Visually Described ?

#4 2010-08-04 11:57:36

Re: Math Terms - Visually Described ?

#5 2010-08-04 11:59:55

Re: Math Terms - Visually Described ?

#6 2010-08-04 12:02:20

Re: Math Terms - Visually Described ?

#7 2010-08-04 12:12:03

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#8 2010-08-04 12:15:49

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#9 2010-08-04 13:02:31

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#10 2010-08-04 13:18:33

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#11 2010-08-04 23:08:15

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#12 2010-08-05 08:22:26

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