Need some math help

I should be able to do this but I just can't get it together.

Lets say I have a movement allowance of 30 points.

For each 4 points I move in the Z diraction I will move 1 point in the X direction.Ok - so I can get the angle from the starting point.

But - how do I figure where I end up on the Z axis and where will I end up on the x axis.Must be an easy formula for this.

Appreciate any help.

You have a 'radius' of 30 units and an angle a where Tan a = 1/4


z = 30 * Cos(1/4) ; generally z = radius * Cos(angle)
x = 30 * Sin (1/4) ; generally x = radius * Sin(angle)

{unless I have my axes swapped :-P }

I assume you should be using TranslateEntity with these z and x values each turn, as MoveEntity would depend on which way you are facing and PositionEntity would always place it 30 units from the origin... not updating each turn

Thanks Blackjumper but I don't want to actually move the item.That I can do okay.

I just want to know where it would finish if I did move it.

There are to many items move to sctually move to find out where the end point would be.

Hope this makes sense.

For each total movement of 5 (i.e. 4+1 ) the Z direction gets 4 and X gets 1.

So Z gets 4/5 of the total and X gets 1/5.

Find the vector
easy: (4,1)
Find the magnitude of that vector
M = Sqr(x*x)+(z*z)
M = 4.47213
Divide the vector by the magnitude
X = 4 / M
Z = 1 / M
X = 0.89442
Z = 0.22360
The normalized vector is (.89442,.22360)

So now say you want to move a total of 30 spaces in this direction? Simply use 30 as the magnitude and multiply by the normalized vector.
NewX = NX * M = .89442 * 30
NewZ = NZ * M = .22360 * 30
your new position will be:(26.8326,6.708)

And walla!

Now if you want to move based on an angle, then you must convert the angle into a vector:
Take your angle above (which is 26.5650 degrees)
NVX = cos(A)
NVZ = Sin(A)

This will give you a normalized vector based on the angle (the same vector you have above). To move 30 spaces, use it as the magnitude in the formula above.

So, if I am cathing your drift here, you want to move 30 spaces in an artibrary direction?

What direction, is it an angle? if so, then plug your angle in as A and your 30 spaces in as M into the following for your new position:
NewX = Cos(A) * M
NewZ = Sin(A) * M

Want to know the angle of movement you just went? Then plug in your X and Z values in below (IE you moved X units accross and Z units forward):
M = Sqr(x*x)+(z*z)
Angle = ACos(X/M)

And there you have the angle by which you moved.

Am I off base here?

Yeah, I read the question as taking 30 steps, some in the x direction and some the z direction.

But I think the real question was how to move 30 units in a particular direction, indicated by x changing 4 for each change of 1 in z.

For that I would consider what happens when x changes by 4 and z by 1. The distance traveled is then Sqr( 4*4 + 1*1 ) = Sqr(17).

For each unit of distance the change in x is 4/Sqr(17) and the change in z is 1/Sqr(17).
To get an arbitrary amount of travel, such as 30, just multiply these by the distance.

Graphics 550, 250, 0, 2

x# = 4
z# = 1

dist# = Sqr( x*x + z*z )

dx# = x/dist
dz# = z/dist

; For each unit of distance the x and z step sizes are dx and dz.

; Example, to travel 30 units the x and z changes are

travel# = 30

xStep# = travel * dx
zStep# = travel * dz

Print
Print "To travel while maintaining x,z in a ratio of 4 to 1 we move"
Print dx + " in the x direction and " + dz + " in the z direction"
Print "for each unit of distance."
Print
Print "So to move " + travel + " units we go " + xStep + " in x and " + zStep + " in z."

WaitKey : End

Isn't that Voila! ?

If I had a Germen accent I suppose it would be.

Thanks much guys - just the formula I needed.