This is a continuation tutorial, the second in the wire-frame tutorial series. Here we take the 2D basic house we created on an 2D scatter chart and introduce rotation. These basic tutorials use elementary math/geometry and trigonometry (middle school and high school level). As the series progresses, the tutorials will reach 3D level and the creation of more complex shapes and landscapes (i.e. roller coaster and beyond).

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hello my friends and welcome back today

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we will be continuing our

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introduction in wireframe animation with

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this house this animated two-dimensional

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house

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which

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i saw some comments on the

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on my comment section and they say this

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is for entertainment it’s not for

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entertainment this will lead to a

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roller coaster or more complex 3d pro

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projects in the previous tutorial we

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built this to the house

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and we added some

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scaling

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as you can see here i’m clicking on

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on these buttons

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and i added scaling i added

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i added translation along the x-axis

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and translation along the y-axis

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and also added an animation

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you can see the house moving

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on a pattern resembling number eight

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and again you can adjust these

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parameters to move on a circle or on

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some random curves

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what i did before i started this

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recording is i copied this sheet one

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into an identical sheet sheet2

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right now i just need to readjust

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assign the macro the proper macro

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because when you copy

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the new button that you create

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has the old old macro so associated with

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it so

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right now

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you see is running

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all the buttons work correctly

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and we are trying to do rotation i

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already

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mark here x y the

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label of the columns and rotate it

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and in order to understand the formulas

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i’m going to my website here you can go

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to just anywhere on google type rotation

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formula rotation

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2d rotation stuff like this i

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type the rotation in the search box

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and i hit it return

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and since i use this a lot uh i know

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most of them has

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have this formula here if you if you

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look all of them but there’s a few

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places that have the

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the derivation

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and the derivation is

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the best derivation i think this this

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quite a few

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blog posts they had the derivation but

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the derivation i use is this one you can

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click on pdf view

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and it shows you if you have a

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straight triangle

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not straight triangle or right triangle

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with 190 degree angle right here

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and if you

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label this the length of these

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sides a b and c

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so c is the hypotenuse a and b are the

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catheters

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and the definition of sinus here is

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alpha right here i forgot to put it but

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sine of alpha is equal to b

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so the opposite

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side of triangle

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and divided by hypotenuse the opposite

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cos of alpha is the near catheter a over

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c over the hypotenuse

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and i i did a small derivation here

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and i reached these formulas

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so

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function of the old components

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the old coordinates of a certain point

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if you rotate the point

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keeping the distance to the origin

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constant you get this formula function

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the so the new

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x and y components facts function of the

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old x and y components and function the

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uh

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of the angle alpha rotation

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so i will

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show you this a little bit here

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i open the

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photoshop

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with a blank

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page here

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so

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what i claim is if you have a

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system of coordinates

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x

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y

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x has a unit vector of i okay you need

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vector

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and y

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has a unit vector of

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j

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okay

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j

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if you have a point here right here p

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okay

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and this is a position vector so o

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origin o

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so o p

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is a vector

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let’s call it the p vector position

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vector okay

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if you rotate this clockwise

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in my

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on my blog

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you you see a rotation of

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counterclockwise counterclockwise is the

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standard trigonometric rotation positive

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rotation

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the proper trigonometric sign convention

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rotate rotating clockwise is negative of

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that

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but i use the

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clockwise because excel has a formula

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that

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stands for clockwise rotation

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so it’s very easy to translate between

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the two but

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that’s why i use clockwise

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clockwise rotation okay so you’re

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rotating from from p to p

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prime

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and if this is the

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the coordinate of p

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is equal to x y

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the coordinate of p prime

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with equal will be equal to x prime

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and y prime

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if the angle is small

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x prime is going to be a little bit

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longer than

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larger than x and y prime will be a

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little bit shorter than y

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so

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what i claim is that x prime

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is equal to

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x

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times let’s call this angle of theta

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cos of theta

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is a little bit longer so we need to add

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something plus

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y

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times sine

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of theta

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and y prime

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is equal to

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y cos of theta

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with a plus

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so y

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cos of

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data

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minus this is smaller okay

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x

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sine of theta so having this in mind

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and again you can go to any website any

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anywhere on the internet just type 2d

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rotation formulas the two-dimensional

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rotation formulas

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and you get here so

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sine

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the sine function is like something like

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this

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okay

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and the

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so this is sine

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sine of x

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x

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and cosine

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is exactly like science except except

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these uh

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d phase a little bit is like this

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these are harmonic functions they’re

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very very important so this is

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if this is x

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this is cos of x

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that’s how it looks like

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first we go here at the

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parameters and type

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data

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so angle theta

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or you can say rotation okay

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and let’s put for now zero let’s go in

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developer

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okay

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design mode

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copy this

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ctrl c ctrl v

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and place it right here

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property

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let’s call this

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i wouldn’t call it rotation because

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rotation might be a

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reserved word it is the reserved word so

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let’s call it data

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data

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and let’s go from

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0 to

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it’s 360 degrees

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so from 0 to 36

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and double click on it

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and fill it out so let’s say

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bb1 in square brackets

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b1

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is equal to

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that’s the normal

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engineering convention you put a

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multiplier in front of math convention

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so let’s check if it works we need first

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to get out of design mode by clicking

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here

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or

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clicking right here the same thing

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and

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you see

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it runs from zero

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to

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all the way to

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360.

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and i want to do a how do you say

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uh rollover feature add the role of the

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feature but for now let’s just implement

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formulas here

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this one x

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we open photoshop here

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x is equal to x the old x x prime is

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equal to

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let’s uh label this x prime and y prime

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okay

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prime

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and y prime

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yeah my my keyboard is

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it’s dark i cannot see

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so

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so this is equal to

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x

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times

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cos

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of

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pick up this value and absolute

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reference it okay absolute reference it

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so hit f4 once and you get dollar sign

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in front of the

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uh column and in front of the row

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so now we need when we copy right and

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right or left or down or up

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this will be firmly

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fixed there

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another thing i want to do is

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um

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these functions accept don’t accept

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degrees they accept radians so okay so

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the

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radians

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of that

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okay

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okay so is radiance a function

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okay

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it’s not i made a typo here

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so now it’s good so copy this here

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and let’s change something what

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oh wait um

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we need to add something here

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plus y sine of

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theta

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so we go

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here

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copy i’m sorry

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copy this

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ctrl c

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plus

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ctrl v

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so d11 is gonna be e11 here okay

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e11 and here’s sine

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okay

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let’s now copy this to the right

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we need to move this reference here or

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we could have put dollar sign in front

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of the column

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hit return to save this and then go here

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and say let’s look at

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formula

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minus sine plus cos okay so

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where is it

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this is

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with minus

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and here plus cos

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and

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now

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first i want to add

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another data

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series

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add

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let’s take

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this

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for x

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and take

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this

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for y

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let me see

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40

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40 40 okay

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and let’s copy this down

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and see if it if it’s correct

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yeah it looks right

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i tell you why

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if i go and

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let’s make it green

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so go here to feel

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and

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make it a nice green let’s say maybe

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this is too light

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let’s make it darker like

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like this green okay

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and i think the thickness is three

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i’m not sure how much it is

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two and a half maybe

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let me see

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click on this

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three right so

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let’s make it three

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okay and now let’s copy down

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so we saw in the previous tutorial that

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we need to delete certain uh

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points in the data otherwise we get

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artifacts

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so we delete just like the other ones

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wherever we see black here in the

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previous formulas in the previous

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columns we deleted okay

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check out all the artifacts disappear

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we can increase the angle check this out

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okay let’s do let’s continue deleting

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these artifacts

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okay so now

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okay

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so it goes from zero

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to

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360.

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i would like to implement a rollover

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feature

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so

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in order to implement this rollover

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i will first go to developer

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visual basic

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and

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actually

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go in design mode

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properties

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let’s go between uh decrease the zero by

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minus one

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okay

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by one so instead of zero to 36 it goes

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to minus -1

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the maximum is good usually we have to

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increase it but

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since 36 is equal to zero so 360 degrees

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and zero are the same thing we leave it

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like this and we go then to

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double click on this we go here

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and say

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if

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data

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is eq

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is greater than

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let me see greater

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than

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35

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then

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data

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is equal to zero

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actually let’s put it in the data is

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greater than 36

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or equal i think is like this

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equal or greater than 36 then theta is

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zero oh if theta is smaller than

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zero

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then theta is going to be

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35

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okay

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and check this out now

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before it was limiting be between 0 to

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35 between 0 the rotation because we

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multiply by 10 between 0 and 3

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160

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so now exit design mode we can use the

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button check this out go go go go go go

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go we are at 340 350

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click again goes to zero

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so we can just hold this button

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and describe

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circles after circle of the circle or

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hold the other button

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and go

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down i mean decreasing and when it goes

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to

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10 0 instead of going to negative number

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or staying there it goes to 350.

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so we can

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rotate over and over as many times as we

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want

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for angles i always add

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this rollover feature and i will say

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go over go to google

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and type how to rotate or rotation

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formula for two dimensional

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so 2d rotation formulas or you go to my

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blog

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and again type rotation and follow the

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tutorials derive the equation

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the the the system of equations

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these are the first steps in order to

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build a roller coaster like you guys

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asked me i want to learn how to

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how to do that

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so follow these tutorials if you are

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beside i i bet

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99 of people are not interested they

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just

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throw a look here at the channel the

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video

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this is not meant to be entertaining

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about subscription everybody says

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subscribe to my channel i’ll say do not

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subscribe to my channel unless you’re

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highly interested

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i would advise that you if you’re mildly

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interested visit occasionally okay

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it’s better to for somebody to to have

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the attitude why didn’t i visit this

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more often than the attitude hey i’m

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getting all these

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alerts why did i subscribe to this guy

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so i prefer to have fewer people but

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more enthusiastic

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again feel free to subscribe if you want

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but definitely i would not advise you to

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hit the notification bell

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because then you’re going to be annoyed

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every time i post something you’re going

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to be annoyed i will say

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once in a while not

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youtube will not notify you okay

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we’ll give you an alert but if you don’t

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hit the notification bell

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you’re not going to be bothered i mean

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nagged by this repeated

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over and over notification so

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let’s uh play a little bit more with

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this

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i will say

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see while i’m running the macro

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i rotate

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the house

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we can go in

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the macro itself

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and

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here sheet two

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and b1

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b1

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is equal to

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let’s copy one of these

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ctrl c

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i would like to rotate it uh sine sine

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goes between zero minus one to one

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so let’s rotate this by um

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180

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so it goes from minus 180 to plus 180 so

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and this is a little bit slower rotation

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so let’s put here 7 instead of 20.

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check this out now

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let’s also add add some automation to

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the scale

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so this is b3 maybe yeah b3

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b3 from -1 to 1 that’s okay

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um

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[Music]

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let’s put 12 here

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so now you have everything you have

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translation rotation

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scaling and

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yeah two different translations one

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rotation one scaling

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so that’s how the coaster is done i mean

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the formulas are a little bit more

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advanced

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we will get to them pretty soon

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in a few tutorials i would say probably

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in

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5 10 tutorials maximum we get straight

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to the roller coaster maybe not even

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that much 5 not 10.

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and this being said thank you for your

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attention