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Monday, April 7, 2008

weekly research ! some MATHS



Summation

reading some research on making car shaders i saw some crazy maths i recognised from high school so i was curious as to what it all meant.

from wikipedia
Summation
is the addition of a set of numbers; the result is their sum or total.


Vetcors

unlike scalars, vectors have more than one component.
they have a direction and a magnitude.

they can be notated with an arrow over the start point and the end point

there are a few methods for addition

a. the end to end method - move one vector to the end of the other one
b. parrallelogram method

in addition they are associative A+B = B + A

negative vectors (5:31)

Subtraction of vectors
A - B = C
A+(-B) = C
(the negative of a vector is pointing in the opposite direction)

when you add scalrs - there is only one answer
but with vectors there could be more than one answer if there is missing information
ie we dont know the direction of a vector - but we kow its magnitude.

with a 3D say vector A vector - we project it onto the xyz axes

the unit vector is like a control
the axes are always pointing in the positive direction
and the magnitiude is always 1 for each axis.
it is noted with little roofs on the vectors to show its a unit vector

decomposition of the vector A:
we break it down into its 3 components


the magnitude is the root of A2 + Y2 + Z2
it is notated with Abs lines / vertical bars around the A (magnitude is a scalar)

Multiplication
there are two methods
dot product / saclar product - notated with a fat dot

the angle method
we project B onto A - then the dot product is |A| |B| cos Theta
the dot product can be pos or neg or = to zero.

it doesnt matter if you take the acute angle of theta or the obtuse angle of theta
their cosines are the same

to be continued !
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