Move towards 3D coordinates - GameCreators Forum

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Rudolpho

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Posted: 13th Apr 2013 21:47

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Do anybody know an efficient, purely mathematical way of determining the new position when moving from A(x1, y1, z1) towards B(x2, y2, z2) at a certain speed?
I'd prefer it if it was possible without slow operations such as square roots (distance formula) etc.

As said above I'm looking for the mathematical way to do this, so solutions that make use of point / move object are unfortunately not adequate.

Thanks for any hints

"Why do programmers get Halloween and Christmas mixed up?"

+ Code Snippet

Because Oct(31) = Dec(25)

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Flamertor

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Posted: 14th Apr 2013 01:30 Edited at: 14th Apr 2013 01:32

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Sorry I just relized you didn't want the point command

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Quel

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Posted: 14th Apr 2013 02:41 Edited at: 14th Apr 2013 02:43

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Well then you need two angle checks using atanfull() between the current coordinates and the target coordinates on the X and Y axes, then put the results each in a Sin(), multiplied by the moving speed, and so you get the X movement and Y movement. And i just realized Z is missing... sorry it is 2am here, something similar, i need some sleep...

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Andrew_Neale

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Posted: 14th Apr 2013 02:49 Edited at: 14th Apr 2013 02:57

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This isn't possible. You need the distance and direction to move from one point to another. The speed will be a distance over time, so you need the distance and you'd need to know when you've reached the end. You could do it by creating a unit vector of the target point minus the start point and multiply this by the speed. Whilst this avoids you doing any distance checks though, the normalizing of the vector does the distance check behind the scenes. Why are you trying to avoid it? It is perhaps slow when compared to an addition operation but in real terms on modern hardware it is pretty much negligible. Well, I suppose you could avoid specifically distance and square roots by using some trigonometry to get the angle instead but sin/cos/tan are considerably slower to use than square roots and you would have no way of knowing when you'd reached your target without some kind of distance check anyway, even if a much simpler one. If you just calculate and store once the unit vector and the distance for the movement then you've done one still tiny calculation as a one off and will also know how many steps will be moved before the target is reached without any further distance or bounds checks.

[Edit]
Hastily cobbled together example for you. Hope it helps!

disable escapeKey

#constant A 1
#constant B 2
#constant Movement 3

ignore = make vector3(A)
ignore = make vector3(B)
ignore = make vector3(Movement)

set vector3 A, 0, 0, 0
set vector3 B, 12, 24, 32

set vector3 Movement, x vector3(B) - x vector3(A), y vector3(B) - y vector3(A), z vector3(B) - z vector3(A)
Distance as float : Distance = length vector3(Movement)
normalize vector3 Movement, Movement

make object cube 1, 1
position object 1, x vector3(A), y vector3(A), z vector3(A)

make object cube 2, 1
position object 2, x vector3(B), y vector3(B), z vector3(B)

make object cube 3, 2
position object 3, x vector3(A), y vector3(A), z vector3(A)

position camera 6, 12, -16

Speed as float
Speed = 0.1

sync on
sync rate 60

while (escapeKey() = 0)

if (Distance > 0)
        position object 3, object position x(3) + Speed * x vector3(Movement), object position y(3) + Speed * y vector3(Movement), object position z(3) + Speed * z vector3(Movement)
        point camera object position x(3), object position y(3), object position z(3)
        dec Distance, Speed
    endIf
    
    sync

endWhile

end

+ Code Snippet

disable escapeKey

#constant A 1
#constant B 2
#constant Movement 3

ignore = make vector3(A)
ignore = make vector3(B)
ignore = make vector3(Movement)

set vector3 A, 0, 0, 0
set vector3 B, 12, 24, 32

set vector3 Movement, x vector3(B) - x vector3(A), y vector3(B) - y vector3(A), z vector3(B) - z vector3(A)
Distance as float : Distance = length vector3(Movement)
normalize vector3 Movement, Movement

make object cube 1, 1
position object 1, x vector3(A), y vector3(A), z vector3(A)

make object cube 2, 1
position object 2, x vector3(B), y vector3(B), z vector3(B)

make object cube 3, 2
position object 3, x vector3(A), y vector3(A), z vector3(A)

position camera 6, 12, -16

Speed as float
Speed = 0.1

sync on
sync rate 60

while (escapeKey() = 0)

    if (Distance > 0)
        position object 3, object position x(3) + Speed * x vector3(Movement), object position y(3) + Speed * y vector3(Movement), object position z(3) + Speed * z vector3(Movement)
        point camera object position x(3), object position y(3), object position z(3)
        dec Distance, Speed
    endIf
    
    sync

endWhile

end

[/Edit]

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basjak

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Posted: 14th Apr 2013 15:36 Edited at: 15th Apr 2013 01:38

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moving one object from one point in space to another is better to be independent from object rotation or local direction and must reach its distance with 100% accuracy.

here is a simple code where moving an object is relying on time/speed values.

sync on : sync rate 60

#constant _3Dvector = 1

#constant _floor  1
#constant _box    2 
#constant _sphere 3

#constant _framerate 60   `will help in not creating quick jumpings for small distances.

`suggest a speed
#constant _speed 4.5

`set your camera
autocam off
position camera 0,10,-20
point camera 0,0,0

`create environment
makeobjectbox(_floor,50,1,50,0,0,0,0xFF003300)

makeobjectbox(_box,2,2,2,0,2,0,0xFFAA0000)

makeobjectsphere(_sphere,2,10,5,20,0xff00AAAA) : ghost object on _sphere,2

r = make vector3(_3Dvector)

`create vector 3D only to calculate the distance between both objects
Xdistance# = object position x(_sphere)-object position x(_box)
Ydistance# = object position y(_sphere)-object position y(_box)
Zdistance# = object position z(_sphere)-object position z(_box)

set vector3 _3Dvector,Xdistance#,Ydistance#,Zdistance#

distance# = length vector3(_3Dvector)

`how long will it take for the box to reach the sphere.
time# = distance# / _speed

`how many steps we need to move the box to the middle of the sphere.
numberofsteps = ceil(time#*_framerate)

`now lets evaluate steps on each axis 
steponx# = Xdistance# / numberofsteps
stepony# = Ydistance# / numberofsteps
steponz# = Zdistance# / numberofsteps

do
    set cursor 2,2
    print "press space key to start moving the red box into the middle of the sphere"
    
    
    if spacekey() 
        position object _box,0,2,0
        
        repeat until not spacekey()
        
        moveobject(_box, steponx#, stepony#, steponz#, numberofsteps)
    endif
   
   turn object left _box,3
   
   control camera using arrowkeys 0,1,1
   
    sync
LOOP

wait key
end

function moveobject(objno, xstep#, ystep#, zstep#, numberofsteps)
    stepped = 0
    repeat
        turn object left objno,3
        
        position object objno, object position x(objno)+xstep#, object position y(objno)+ystep#, object position z(objno)+zstep#   
        
        inc stepped,1
        sync
    UNTIL stepped = numberofsteps
ENDFUNCTION

function makeobjectbox(objno,width#,height#,depth#,posx#,posy#,posz#,color)
    make object box objno,width#,height#,depth#
    position object objno,posx#,posy#,posz#
    color object objno,color
ENDFUNCTION

function makeobjectsphere(objno,size#,posx#,posy#,posz#,color)
    make object sphere objno,10
    position object objno,posx#,posy#,posz#
    color object objno,color    
ENDFUNCTION

+ Code Snippet

sync on : sync rate 60

#constant _3Dvector = 1

#constant _floor  1
#constant _box    2 
#constant _sphere 3

#constant _framerate 60   `will help in not creating quick jumpings for small distances.


`suggest a speed
#constant _speed 4.5

`set your camera
autocam off
position camera 0,10,-20
point camera 0,0,0

`create environment
makeobjectbox(_floor,50,1,50,0,0,0,0xFF003300)

makeobjectbox(_box,2,2,2,0,2,0,0xFFAA0000)

makeobjectsphere(_sphere,2,10,5,20,0xff00AAAA) : ghost object on _sphere,2

r = make vector3(_3Dvector)

`create vector 3D only to calculate the distance between both objects
Xdistance# = object position x(_sphere)-object position x(_box)
Ydistance# = object position y(_sphere)-object position y(_box)
Zdistance# = object position z(_sphere)-object position z(_box)

set vector3 _3Dvector,Xdistance#,Ydistance#,Zdistance#

distance# = length vector3(_3Dvector)

`how long will it take for the box to reach the sphere.
time# = distance# / _speed

`how many steps we need to move the box to the middle of the sphere.
numberofsteps = ceil(time#*_framerate)

`now lets evaluate steps on each axis 
steponx# = Xdistance# / numberofsteps
stepony# = Ydistance# / numberofsteps
steponz# = Zdistance# / numberofsteps

do
    set cursor 2,2
    print "press space key to start moving the red box into the middle of the sphere"
    
    
    if spacekey() 
        position object _box,0,2,0
        
        repeat until not spacekey()
        
        moveobject(_box, steponx#, stepony#, steponz#, numberofsteps)
    endif
   
   turn object left _box,3
   
   control camera using arrowkeys 0,1,1
   
    sync
LOOP


wait key
end

function moveobject(objno, xstep#, ystep#, zstep#, numberofsteps)
    stepped = 0
    repeat
        turn object left objno,3
        
        position object objno, object position x(objno)+xstep#, object position y(objno)+ystep#, object position z(objno)+zstep#   
        
        inc stepped,1
        sync
    UNTIL stepped = numberofsteps
ENDFUNCTION


function makeobjectbox(objno,width#,height#,depth#,posx#,posy#,posz#,color)
    make object box objno,width#,height#,depth#
    position object objno,posx#,posy#,posz#
    color object objno,color
ENDFUNCTION

function makeobjectsphere(objno,size#,posx#,posy#,posz#,color)
    make object sphere objno,10
    position object objno,posx#,posy#,posz#
    color object objno,color    
ENDFUNCTION

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Rudolpho

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Posted: 15th Apr 2013 03:16 Edited at: 15th Apr 2013 03:16

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Quote: "This isn't possible."

Could've guessed as much but still, thought I'd better ask

Anyhow, thanks for your help Andrew and basjak; got it working and it seems to be running fast and accurately enough

"Why do programmers get Halloween and Christmas mixed up?"

+ Code Snippet

Because Oct(31) = Dec(25)

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Chris Tate

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Posted: 15th Apr 2013 11:12

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Lee created a way, it's a cos/sine shortcut and uses what Quel recommended; you should wrap the two parts into a function similar to what I did:

+ Code Snippet

AngleX# = atanfull(DestY#-CurrentY#,DestZ#-CurrentZ#)
AngleY# = atanfull(DestX#-CurrentX#,DestZ#-CurrentZ#)
x# = NewXValue( CurrentX#, AngleY#, Distance# )
y# = NewYValue( CurrentY#, AngleX#, Distance# )
z# = NewZValue( CurrentZ#, AngleY#, Distance# )

+ Code Snippet

//============================================================
Function CoordToCoordAng( iVec, x1#, y1#, z1#, x2#, y2#, z2# )
	Set Vector3 iVec, atanfull(y2#-y1#,z2#-z1#), atanfull(x2#-x1#,z2#-z1#), Z Vector3(iVec)
Endfunction

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basjak

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Posted: 15th Apr 2013 21:10 Edited at: 15th Apr 2013 21:15

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thank chris for sharing this. much better than my way in getting for to distances.

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Andrew_Neale

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Posted: 15th Apr 2013 21:21 Edited at: 16th Apr 2013 01:40

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The problem with using the NewXValue and NewZValue commands is that they don't take the x angle into account. If you're moving a distance of 1 unit and looking straight forward then you would move forward 1 unit. If you were looking 45 degrees up then you would move 1 unit forward as well as ~0.7 units up making the total distance covered more than the distance you were trying to move at. To handle this properly you would have to do this:

inc x#, sin(AngleY#) * cos(AngleX#) * Distance#
inc y#, sin(AngleX#) * -Distance#
inc z#, cos(AngleY#) * cos(AngleX#) * Distance#

Previously TEH_CODERER.

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Indicium

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Posted: 15th Apr 2013 21:58

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Sorry I might be missing the point here, but this is incredibly simple.

First you work out the direction vector: B-A
Now normalize the vector so it's magnitude becomes one.
Now multiply this vector by the speed and multiply the vector by the time since leaving the initial position to find the total displacement, then add it to the original to find the new position.

They see me coding, they hating. http://indi-indicium.blogspot.co.uk/

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basjak

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Posted: 15th Apr 2013 23:36

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simply use my way if you're doing engineering projects such as what I do but, in computer games, accurate distances can be ignored and chris (or lee's) way is good to handle because you could do more with it.

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TheComet

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Posted: 16th Apr 2013 00:43

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Sorry, but how is this more accurate?

`create vector 3D only to calculate the distance between both objects
Xdistance# = object position x(_sphere)-object position x(_box)
Ydistance# = object position y(_sphere)-object position y(_box)
Zdistance# = object position z(_sphere)-object position z(_box)

set vector3 _3Dvector,Xdistance#,Ydistance#,Zdistance#

distance# = length vector3(_3Dvector)

`how long will it take for the box to reach the sphere.
time# = distance# / _speed

`how many steps we need to move the box to the middle of the sphere.
numberofsteps = ceil(time#*_framerate)

`now lets evaluate steps on each axis 
steponx# = Xdistance# / numberofsteps
stepony# = Ydistance# / numberofsteps
steponz# = Zdistance# / numberofsteps

REM --------- SNIP ----------------

function moveobject(objno, xstep#, ystep#, zstep#, numberofsteps)
    stepped = 0
    repeat
        turn object left objno,3
        
        position object objno, object position x(objno)+xstep#, object position y(objno)+ystep#, object position z(objno)+zstep#   
        
        inc stepped,1
        sync
    UNTIL stepped = numberofsteps
ENDFUNCTION

+ Code Snippet

`create vector 3D only to calculate the distance between both objects
Xdistance# = object position x(_sphere)-object position x(_box)
Ydistance# = object position y(_sphere)-object position y(_box)
Zdistance# = object position z(_sphere)-object position z(_box)

set vector3 _3Dvector,Xdistance#,Ydistance#,Zdistance#

distance# = length vector3(_3Dvector)

`how long will it take for the box to reach the sphere.
time# = distance# / _speed

`how many steps we need to move the box to the middle of the sphere.
numberofsteps = ceil(time#*_framerate)

`now lets evaluate steps on each axis 
steponx# = Xdistance# / numberofsteps
stepony# = Ydistance# / numberofsteps
steponz# = Zdistance# / numberofsteps

REM --------- SNIP ----------------

function moveobject(objno, xstep#, ystep#, zstep#, numberofsteps)
    stepped = 0
    repeat
        turn object left objno,3
        
        position object objno, object position x(objno)+xstep#, object position y(objno)+ystep#, object position z(objno)+zstep#   
        
        inc stepped,1
        sync
    UNTIL stepped = numberofsteps
ENDFUNCTION

The inaccuracy of floating point values are ADDED TOGETHER in your while loop, making it far more inaccurate than this:

+ Code Snippet

set vector3 Movement, x vector3(B) - x vector3(A), y vector3(B) - y vector3(A), z vector3(B) - z vector3(A)
Distance as float : Distance = length vector3(Movement)
normalize vector3 Movement, Movement

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Rudolpho

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Posted: 16th Apr 2013 00:53

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Quote: "Sorry I might be missing the point here, but this is incredibly simple."

I suppose it was, I don't use vectors very often though (most code I have that do use those are wrapped up in utility functions that I just call when needed) so yeah. Curiously none (of the first few at least) of the google results I got when searching for seemingly descriptive phrases of the problem suggested that either, the closest I got was something based on trigonometry that was only good for one angle.

"Why do programmers get Halloween and Christmas mixed up?"

+ Code Snippet

Because Oct(31) = Dec(25)

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Chris Tate

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Posted: 16th Apr 2013 01:27 Edited at: 16th Apr 2013 01:32

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Quote: "The problem with using the NewXValue and NewZValue commands is that they don't take the x angle into account."

Why don't you think the New value commands wouldn't consider the X angle?

+ Code Snippet

AngleY# = 90.0
AngleX# = 45.0
Distance# = 100.0
x# = 0
y# = 0
z# = 0
inc x#, sin(AngleY#) * cos(AngleX#) * Distance#
inc y#, sin(AngleY#) * -Distance#
inc z#, cos(AngleY#) * cos(AngleX#) * Distance#
Print "Position 1: "; Str$(x#,4); ", "; Str$(y#,4); ", ";  Str$(z#,4)

x# = 0
y# = 0
z# = 0
x# = NewXValue( x#, AngleY#, Distance# )
y# = NewYValue( y#, AngleX#, Distance# )
z# = NewZValue( z#, AngleY#, Distance# )
Print "Position 2: "; Str$(x#,4); ", "; Str$(y#,4); ", ";  Str$(z#,4)

Wait Key

Quote: "To handle this properly you would have to do this:

inc x#, sin(AngleY#) * cos(AngleX#) * Distance#
inc y#, sin(AngleY#) * -Distance#
inc z#, cos(AngleY#) * cos(AngleX#) * Distance#"

How would this work? You can't use the Y angle to influence the Y axis; unless you use the third angle dimension (Z); meaning the object would have to roll in order for its Y rotation to affect anything other than the X and Z axis. But then... there is no object, just two coordinates.

Perhaps there is a typo... In the code snippet all that happens is the Y velocity uses the reverse of the Z velocity. Or perhaps I am missing something. Why doesn't it work?

Quote: "this is incredibly simple.

First you work out the direction vector: B-A
Now normalize the vector so it's magnitude becomes one.
Now multiply this vector by the speed and multiply the vector by the time since leaving the initial position to find the total displacement, then add it to the original to find the new position."

Hehe, that wouldn't sound simple to a learner.

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Andrew_Neale

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Posted: 16th Apr 2013 01:42

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Quote: "
First you work out the direction vector: B-A
Now normalize the vector so it's magnitude becomes one.
Now multiply this vector by the speed and multiply the vector by the time since leaving the initial position to find the total displacement, then add it to the original to find the new position.
"

Indeed, that is exactly what I did in my first post.

Quote: "Why don't you think the New value commands wouldn't consider the X angle?"

Because the x angle is never supplied to those commands.

Quote: "Perhaps there is a typo..."

Yep, sorry, fixed. Other than that though it was correct. With an adjust version of your code:

+ Code Snippet

AngleY# = 90.0
AngleX# = 45.0
Distance# = 100.0
x# = 0
y# = 0
z# = 0
inc x#, sin(AngleY#) * cos(AngleX#) * Distance#
inc y#, sin(AngleX#) * -Distance#
inc z#, cos(AngleY#) * cos(AngleX#) * Distance#
Print "Position 1: "; Str$(x#,4); ", "; Str$(y#,4); ", ";  Str$(z#,4)

x# = 0
y# = 0
z# = 0
x# = NewXValue( x#, AngleY#, Distance# )
y# = NewYValue( y#, AngleX#, Distance# )
z# = NewZValue( z#, AngleY#, Distance# )
Print "Position 2: "; Str$(x#,4); ", "; Str$(y#,4); ", ";  Str$(z#,4)

Wait Key

The first option gives the correct values and the second option is incorrect as the total distance moved is more than the specified distance because of the x angle not being taken into consideration.

Previously TEH_CODERER.

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Phaelax

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Posted: 16th Apr 2013 10:13

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Quote: "I suppose it was, I don't use vectors very often though"

Time to start using them!

D = B - A
D = normalize(D)
A = A + D*speed

The square root would only be used once when normalizing the vector, which you only need to calculate when the direction changes (if B moves before you reach it).

"You're all wrong. You're all idiots." ~Fluffy Rabbit

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Chris Tate

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Posted: 16th Apr 2013 13:26

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Quote: "Because the x angle is never supplied to those commands."

OK got it now; got lost there. Here is a demo that shows how Andrew is right; the distance in the second method is accurate because the X angle is not being considered.

+ Code Snippet

`%Project Title%
`%Source File Name%
`======================
AngleY# = 90.0
AngleX# = 45.0
Distance# = 100.0
x# = 0
y# = 0
z# = 0
inc x#, sin(AngleY#) * cos(AngleX#) * Distance#
inc y#, sin(AngleX#) * -Distance#
inc z#, cos(AngleY#) * cos(AngleX#) * Distance#
Print "Position 1: "; Str$(x#,4); ", "; Str$(y#,4); ", ";  Str$(z#,4)
Print "Distance 1: "; Dist#( x#,y#,z#,0,0,0)
x# = 0
y# = 0
z# = 0
x# = NewXValue( x#, AngleY#, Distance# )
y# = NewYValue( y#, AngleX#, Distance# )
z# = NewZValue( z#, AngleY#, Distance# )
Print "Position 2: "; Str$(x#,4); ", "; Str$(y#,4); ", ";  Str$(z#,4)
Print "Distance 2: "; Dist#( x#,y#,z#,0,0,0)
wait key

//============================================================
Function Dist#( x1#,y1#,z1#,x2#,y2#,z2#)
   fDist_X# = X1# - X2#
   fDist_Y# = Y1# - Y2#
   fDist_Z# = Z1# - Z2#
	 // TODO Use faster method
   fDistance# = Sqrt(fDist_X# * fDist_X# + fDist_Y# * fDist_Y# + fDist_Z# * fDist_Z#)
EndFunction fDistance#

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basjak

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Posted: 16th Apr 2013 14:28

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@The commet:

sorry, I didn't understand your question !!!.
it seems that there are different ways, if we comeback to the top question, rdolpho is looking to control the seed#. my formula (i don't think i invented it

) will give high point reaching accurancy based on adding floting points together.

however, am open to all solution and chris suggestion is amazing.

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