Thursday, November 22, 2012

Square Area....


Square
*click to make bigger*

Definition:

 A Square is a flat shape with 4 equal sides and every angle is a right angle (90°) and opposite sides are parallel.


Diagonals...


A square has two diagonals, they are equal in length and intersect at the middle point.

Diagonal square

The Diagonal is the side length(a) times the square root of 2:
*side length = a = the length between A and D* (see image at top)

Diagonal "d" = a × √2
 

Perimeter...


The Perimeter is 4 times the side length:
Perimeter Square

Perimeter "p" = 4a

Area...


The Area is the side length squared:

Area Square
Area = a2 = a × a

....or half of the diagonal squared:

Area Square 
Area = d2/2


What this looks like in ICE ....



Side length

To work out the side length of the square shown below.....

square side length in softimage ICE

..... Subtract the corner point (-1,-1,0) with corner point (-1,1,0). Then simply get the length of the vector between the them.

side lentgh of a square softimage

 

Perimeter

The light green perimeter value is worked out with the math sum shown below, while the darker green value shows the curve length attribute in ICE, they are both the same.


p = 4.a

calculate perimeter of a square in ICE

Diagonal

The diagonal length as shown by the blue value below was got by....

Daigonal of a square in softimage ICE


d = a .  √2

calculate diagonal of a square in ICE


Area

 Area can be calculated two ways, by multiplying the side lengths or by the diagonal....

Area of a square in ICE

..... here are what those calculations look like in ICE.

Calculate area of a square in ICE


The end :D




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