Please help!

**cyborg** · Jul 22nd, 2003, 06:03 AM

I've searched all over the net and cant find anything!
I've asked in this forum too without any success...

How do i calculate a 3d dot's position on a 2d plane?

x=?
y=?

Could that be so hard?

If you're good at these stuff...please also tell me how to work with vectors!

**Electroman** · Jul 22nd, 2003, 06:11 AM

Didn't the reply I gave work??

**cyborg** · Jul 22nd, 2003, 07:07 AM

well....i didnt get it to work...maybe if i play around alot with it, but there must be someone that has a formula for calculating it.

i went to www.howstuffworks.com and looked it up, but they didnt give me all of the formula...they just said something like this: "now you see how much calculations there is in a 3d scene", then i replied for myself "I DONT CARE! I WANT TO KNOW HOW!" hehe...im getting crazy searching for this! i dont know what to search for. i search for "3d math" and get alot of irrelevant stuff! damn...

**cyborg** · Jul 22nd, 2003, 07:12 AM

this is what i made after reading at howstuffworks.com:

VB Code:

Option Explicit
Const ScreenWidth As Long = 640     'the width of the world we're looking at
Const ScreenHeight As Long = 480    'the height of the "world" we're looking at.
Const Depth As Long = 2     'the depth (front to back) of the world we're looking at
Dim Sy As Double            'height of our window into the world
Dim Sx As Double            'width of our window into the world
Dim Sz As Double            'a depth variable that determines which objects are visible in front of other, hidden objects
Const D As Double = 0.75    'the distance between our eye and the window in this imaginary world.
 
Const Fov As Double = 22    'the total field of view
Const Zn As Double = 1      'the point closest to us where we can no longer see into the imaginary world
Const Zf As Double = 30     'the point farthest from us where we can no longer see into the imaginary world
 
Dim s As Double             'stuff
Dim c As Double             'stuff
Dim Q As Double             'stuff
 
Dim X As Double             'point coords
Dim Y As Double             'point coords
Dim Z As Double             'point coords
Dim W As Double             'point coords
 
Dim X2 As Double            'point coords
Dim Y2 As Double            'point coords
Dim Z2 As Double            'point coords
Dim W2 As Double            'point coords
 
Const PiDiv180 As Double = 1.74532925199433E-02     'Pi / 180
 
 
Private Sub Draw()
    X2 = X * c + ScreenWidth / 2
    Y2 = Y * c + ScreenHeight / 2
    Z2 = s * Zf * ((Z - Zn) / (Zf - Zn))
    W2 = W * s * c
    
    PicDisp.PSet (X2, Y2)
    PicDisp.Refresh
End Sub
 
Private Sub Form_Load()
    PicDisp.Width = ScreenWidth * Screen.TwipsPerPixelX
    PicDisp.Height = ScreenHeight * Screen.TwipsPerPixelY
    
    Sx = ScreenWidth * D / Depth
    Sy = ScreenHeight * D / Depth
    
    s = Sin(Fov / 2 * PiDiv180)
    c = Cos(Fov / 2 * PiDiv180)
    Q = s / (1 - Zn / Zf)
    
    X = -5
    Y = 0
    Z = 0
    
    Draw
End Sub

but theres still something missing! what?

**SLH** · Jul 22nd, 2003, 07:30 AM

What type of 3D are you trying to create? Perspective, isometric....

Also, won't you need a position vector and an angle vector of the camera?

**SLH** · Jul 22nd, 2003, 07:38 AM

Did some googling and fond a few links that may be useful.

For a nice explanatory page click below.

http://www.geocities.com/ResearchTri.../tv_index.html

Not sure how helpful the next page is, but it may be useful.

http://216.239.51.104/search?q=cache...hl=en&ie=UTF-8

BTW, i searched for "3d position 2d plane" on incase you're wondering (without the quotes).

**Electroman** · Jul 22nd, 2003, 08:02 AM

I got a formula for ya, its taken me a while to get their and it still needs a tiny bit more

.

VB Code:

Lander = (nx*(Bx-ax) + ny*(By-ay) + nz*(Bz-az)) / (nx*(cx-ax) + ny*(cy-ay) + nz*(cz-az))
 
X = ax + (cx - ax) * Lander
 
Y = ay + (cy - ay) * Lander
 
Z = az + (cz - az) * Lander

I'll post a pic to tell you what the things all stand for...
(just got to draw it first)

**Electroman** · Jul 22nd, 2003, 08:21 AM

The formula tells you the 3D position on the screen plane(its 3D because if you tilt the camera up it will need the screen plane to work in 3D) that the vector intercepts it. I'll get on to writing something now to change this 3D position into a 2D point on the screen

.

**SLH** · Jul 22nd, 2003, 08:29 AM

Originally posted by cyborg
If you're good at these stuff...please also tell me how to work with vectors!

What sort of stuff do you want to know?

Vectors are pretty simple really.

A vector has 3 values, for positions & offsets (velocity) they're usually called x,y and z, for a direction vector you may call them something else (Pitch, Yaw & Roll for instance).

To add them, simply add the x, y and z calues with another vectors x,y and z values respectivly.

The opposite of a vector is simply (-x,-y,-z)

Another thing you'll probably need to know is how to normalize a vector.

This means, given a velocity vector (most common use), make it so that the speed is exactly 1, but the direction remains the same.

Anything else?

**Electroman** · Jul 22nd, 2003, 08:33 AM

He's my works:
Page1

**Electroman** · Jul 22nd, 2003, 08:36 AM

Page2

**Electroman** · Jul 22nd, 2003, 08:38 AM

Page 3

**Electroman** · Jul 22nd, 2003, 08:40 AM

Hehe, didn't realise the pics were so big, soz

**SLH** · Jul 22nd, 2003, 08:43 AM

Originally posted by Electroman
Hehe, didn't realise the pics were so big, soz

Let's hope cyborg isn't a 56ker.

**Electroman** · Jul 22nd, 2003, 08:46 AM

I'm using a 56K at the moment and it didn't take that long(mind the images are less than 100KB each) jpegs are doing some wicked compression, A??

**SLH** · Jul 22nd, 2003, 08:51 AM

BTW, on the first page, shouldn't that 'b' be a 'c', if not where did it come from?

**cyborg** · Jul 22nd, 2003, 10:00 AM

Originally posted by SLH
What sort of stuff do you want to know?

Vectors are pretty simple really.

I really want to use vectors! so i can move and rotate the camera! that would be nice...

Electroman: I'll look into your stuff later...im a bit busy right now!

Thanks for att your help!

**SLH** · Jul 22nd, 2003, 10:09 AM

Originally posted by cyborg
I really want to use vectors! so i can move and rotate the camera! that would be nice...

If you want to do that then your camera would have to have to vetors associated with it. One that was it's position, and one that was the direction it's facing.

To make it move, you'd also want a veolcity vector.

Making the camera move, would simply be camera.positionvector + camera.Velocityvector.

The direction vector would have to be somehow incorperated into the 'graphics engine' (the system to draw your 3D stuf on a 2D screen).

I'll try to write a little module with some common vector functions for you.

**Electroman** · Jul 22nd, 2003, 10:15 AM

SLH: hehe, yea I noticed it just after posting the third page(my bad), it was cos instead of "c" I was using "b" then I changed my mine because "c" for camera, and I wanted to use "B" latter on

.
You'd think the letter "b" in nearly 2cm high text i'd of noticed it

.
I've nearly got the whole last bit done, wooohooo!!!!!

**cyborg** · Jul 22nd, 2003, 10:16 AM

That woul be really nice!

The main problem i have is to write the functons that converts from 3d to a 2d plane...

**Electroman** · Jul 22nd, 2003, 10:19 AM

By 2D plane am I write in assuming you mean Screen coordinates??

**SLH** · Jul 22nd, 2003, 10:37 AM

Originally posted by cyborg
That woul be really nice!

The main problem i have is to write the functons that converts from 3d to a 2d plane...

Did you take a look at the links i suggested?

Below is a few vector functions, they are quite low level, but more powerfull functions could easily be built on top of them.

VB Code:

Type TVector
    X As Single
    Y As Single
    Z As Single
End Type
 
Public Function VAdd(V1 As TVector, V2 As TVector) As TVector
    VAdd.X = V1.X + V2.X
    VAdd.Y = V1.Y + V2.Y
    VAdd.Z = V1.Z + V2.Z
End Function
Public Function VNormalize(V As TVector, Optional Length As Single = 1) As TVector
    Dim Mag As Single
    Mag = VMagnitude(V)
    VNormalize.X = V.X * Length / Mag
    VNormalize.Y = V.Y * Length / Mag
    VNormalize.Z = V.Z * Length / Mag
End Function
Public Function VEqual(V1 As TVector, V2 As TVector) As Boolean
    VEqual = V1.X = V2.X And V1.Y = V2.Y And V1.Z = V2.Z
End Function
Public Function VMagnitude(V As TVector) As Single
    VMagnitude = Sqr(V.X ^ 2 + V.Y ^ 2 + V.Z ^ 2)
End Function
Public Function VScale(V As TVector, Factor As Single) As TVector
    VScale.X = V.X * Factor
    VScale.Y = V.Y * Factor
    VScale.Z = V.Z * Factor
End Function
Public Function VDotProduct(V1 As TVector, V2 As TVector) As TVector
    VDotProduct.X = V1.X * V2.X
    VDotProduct.X = V1.Y * V2.Y
    VDotProduct.X = V1.Z * V2.Z
End Function
Public Function VIsZero(V As TVector) As Boolean
    VIsZero = V.X = 0 And V.Y = 0 And V.Z = 0
End Function

**cyborg** · Jul 22nd, 2003, 10:48 AM

Yes i did look at the links, but they allready showed me some stuff i've seen before that didnt help me much...

Thanks for those functions!
btw, whats does the normalization do?

**SLH** · Jul 22nd, 2003, 10:53 AM

Here's an updated version, with a new function:

VB Code:

Type TVector
    X As Single
    Y As Single
    Z As Single
End Type
 
Public Function VAdd(V1 As TVector, V2 As TVector) As TVector
    VAdd.X = V1.X + V2.X
    VAdd.Y = V1.Y + V2.Y
    VAdd.Z = V1.Z + V2.Z
End Function
Public Function VNormalize(V As TVector, Optional Length As Single = 1) As TVector
    Dim Mag As Single
    Mag = VMagnitude(V)
    VNormalize.X = V.X * Length / Mag
    VNormalize.Y = V.Y * Length / Mag
    VNormalize.Z = V.Z * Length / Mag
End Function
Public Function VEqual(V1 As TVector, V2 As TVector) As Boolean
    VEqual = V1.X = V2.X And V1.Y = V2.Y And V1.Z = V2.Z
End Function
Public Function VMagnitude(V As TVector) As Single
    VMagnitude = Sqr(V.X ^ 2 + V.Y ^ 2 + V.Z ^ 2)
End Function
Public Function VScale(V As TVector, Factor As Single) As TVector
    VScale.X = V.X * Factor
    VScale.Y = V.Y * Factor
    VScale.Z = V.Z * Factor
End Function
Public Function VDotProduct(V1 As TVector, V2 As TVector) As Single
    VDotProduct.X = V1.X * V2.X + V1.Y * V2.Z + V1.Z * V2.Z
End Function
Public Function VIsZero(V As TVector) As Boolean
    VIsZero = V.X = 0 And V.Y = 0 And V.Z = 0
End Function
Public Function VCrossProduct(V1 As TVector, V2 As TVector) As TVector
    'Direction of VCrossProduct(V1,V2) is perpendicular to plane with vectors V1 and V2 on it,
    'magnitude is VMagnitude(V1)*VMagnitude(V2)
    VCrossProduct.X = V1.Y * V2.Z - V2.Y * V1.Z
    VCrossProduct.Y = V1.Z * V2.X - V2.Z * V1.X
    VCrossProduct.Z = V1.X * V2.Y - V2.X * V1.Y
End Function

The easiest way to think about the norm. function is by example.

If the vector V was a velocity vector. Then it's magnitude is it's speed (how fast it's moving, ignoreing direction).

If you want the speed to be reduced to 1, but keep the object moving in the same direction, you'd normalize it's velocity vector.

Hope that was an adiquate explanation.

**SLH** · Jul 22nd, 2003, 10:57 AM

I'll see what i can do with the 3D stuff now....

**cyborg** · Jul 22nd, 2003, 11:06 AM

Thanks alot! You've been really helpful!

**SLH** · Jul 22nd, 2003, 11:30 AM

I think this will work, but i havn't tested it properly yet though...

VB Code:

Public Function Pos2Cord(DotPosition As TVector, CamPosition As TVector, CamPanning As TVector) As TCord
    Dim PanPos As TVector
    Dim DotPos As TVector
    DotPos.X = DotPosition.X + CamPosition.X
    DotPos.Y = DotPosition.Y + CamPosition.Y
    DotPos.Z = DotPosition.Z + CamPosition.Z
    
    PanPos.X = DotPos.X * Cos(CamPanning.X) - PanPos.Z * Sin(CamPanning.X)
    PanPos.Z = DotPos.X * Sin(CamPanning.X) + PanPos.Z * Cos(CamPanning.X)
    PanPos.Y = DotPos.Y * Cos(CamPanning.Y) - PanPos.Z * Sin(CamPanning.Y)
    
    DotPos.Z = PanPos.Y * Cos(CamPanning.Y) - PanPos.Z * Sin(CamPanning.Y)
    DotPos.X = PanPos.X * Cos(CamPanning.Z) - PanPos.Y * Sin(CamPanning.Z)
    DotPos.Y = PanPos.X * Sin(CamPanning.Z) + PanPos.Y * Cos(CamPanning.Z)
    
    If DotPos.Z > CamPosition.Z Then
        Pos2Cord.X = DotPos.X / DotPos.Z * Zoom + Form1.Width / 2
        Pos2Cord.Y = DotPos.Y / DotPos.Z * Zoom + Form1.Height / 2
    End If
End Function

i gtg soon, but i'll keep puzzling over it until i do.

**SLH** · Jul 22nd, 2003, 11:45 AM

Try http://freespace.virgin.net/hugo.eli...s/3d_to_2d.htm

**Electroman** · Jul 22nd, 2003, 02:45 PM

Here we go agin:

VB Code:

d= Sqr(((X-Bx)^2) + ((Y-By)^2) + ((Z-Bz)^2))
Theta = InverseCos((ux*dx + uy*dy + uz*dz) / u*d)
 
'Now to find the (X,Y) screen co-ordinate:
XOffSet = d*Sin(Theta)
YOffSet = d*Cos(Theta)
'These OffSet values are from the center of the screen

I'm goging to write a class to hold all this because these a lot of these things that will only change if the camera is adjusted so a Class could handle it very easily.
Another diagram to describe the new stuff:

**Electroman** · Jul 22nd, 2003, 04:16 PM

Check out the files attached, I used a couple of your vector functions SLH to keep the codeshort in the class

.

**SLH** · Jul 22nd, 2003, 07:23 PM

Originally posted by Electroman
I used a couple of your vector functions SLH to keep the codeshort in the class.

Glad they helped.

**cyborg** · Jul 23rd, 2003, 08:59 AM

I cant get the class file to work...I get all kinds of error messages about the UTS's and functions..like this one for example:

"Only public user defined types defined in public object modules can be used as parameters or return types for public procedures of class modules or as fields of public user defined types"

**Electroman** · Jul 23rd, 2003, 09:07 AM

try just throwing it into a normal code module then because I got that error and just had to use it sepratly, I don't get the error becasue I did decalare the "Type" in a public module

**Electroman** · Jul 23rd, 2003, 09:14 AM

You'll also need to change the params to ByRef cos there user-defined type, opps.

**cyborg** · Jul 23rd, 2003, 09:37 AM

ok i'll try that!

btw, what does ByRef mean?

**Electroman** · Jul 23rd, 2003, 09:45 AM

ByRef is instead of ByVal, When you use ByVal only the Value of the parameter is sent to the sub, but when you use ByRef a pointer is sent that points to the variable that you used as a parameter so if in the sub the parameter is edited the variable you gave the procedure will also be edited. I'm sure someone could give you a better definition, I can't say what I mean if you get me??

Try this example project, I can't seem to get it to work perfectly but it does display the points, just there all together

:

**Electroman** · Jul 23rd, 2003, 09:48 AM

I spoke too soon, change the FOV to about half what I set it to and move the cam pos to:

VB Code:

CamPos.X = 50
CamPos.Y = 50
CamPos.Z = 50

**Electroman** · Jul 23rd, 2003, 12:06 PM

heres what I have now, I found a typo in the ConvertVetor Procedure and I've fixed that, apart from that theres seems to be something up with the X and Z axis if the camera is set so LookAt.X = LookAt.Y

I'm trying to fix that now but can't be sure if its actually just perspective?? Anyway take a look at the attachment, I also fixed a problem that caused the screen to be upside down, in my diagrams the vector u should be the oposite way round, my bad

. I feel victory near

.

**cyborg** · Jul 23rd, 2003, 01:58 PM

yes, you're probably really close. i cant check anything right now cus the whole family is here visiting so i must be with them all the time. Lots of small kids

**cyborg** · Jul 23rd, 2003, 02:05 PM

this one looks pretty good, but its without vectors.
maybe it will help you a bit

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