Will this 3d plotting procedure work?

[richcash]

Well, I've been trying to figure out the best way to plot 3d points on a 2d screen, and I was directed to this page by Delos and [Gandalf].
http://freespace.virgin.net/hugo.elias/routines/3d_to_2d.htm
(I'm not really working on this right now, but it's good to know for when I do.)
Well, there were some variable names used on that web site that I didn't really understand, and no one could seem to explain them to me. (For my original topic and more background info : http://www.compsci.ca/v2/viewtopic.php?t=13184)

However, looking at Catalyst's 3d particle engine, I derived this procedure from it and it seems to work for plotting 3d points. I'm not too sure if it works accurately though, so if anyone can tell me if this works or not (maybe it doesn't always work?).

code:

var Camx, Camy, Camz, CamzFrame : int proc DrawParticle (x, y, z : int)     var xD, yD : int     if z < Camz then         xD := round ((CamzFrame - (z - (((z - Camz) / ((x - Camx) + 0.001)) * x))             / ((z - Camz) / ((x - Camx) + 0.001))))         yD := round ((CamzFrame * ((y - Camy) / ((z - Camz) + 0.001))) + (y -             (((y - Camy) / ((z - Camz) + 0.001)) * z)))     end if     drawdot (xD, yD, 7) end DrawParticle

Also, on an unrelated note, if I have 3d structures connected by points, how can I avoid drawing everything behind the structure (for optimization).

[Windsurfer]

It does work, but it's very complex. Start off from the simple stuff first. The basis of this type of 3D -> 3D proc is this:

code:

var draw_x : int := x div z var draw_y : int := y div z

Yes, it's that simple. Divide X and Y by Z.
Well, to begin with.
Then you have to add everyhting else in, like making the camera centered, rotating it, adjustments for Field-of-view, ect.

For a slightly more simplified version of this (and perhaps more usable? i don't know) I came up with a function that converts 3D stuff. I created all this from scratch, btw, so it may be wrong in some ways.

code:

%this is the size of the screen % i suppose i could have used maxx and maxy instead. const X_SCREEN := 1024 const Y_SCREEN := 768 %middle of the screen in the X and Y axis so that the camera is centered     const SCR_W := X_SCREEN div 2     const SCR_H := Y_SCREEN div 2     %this is the "key dividor" amount... it makes something at a z coordinate     %perfectly align with the screen... just don't touch it     %I got to this value by experimentation     const Z_KEY_DIV := 350 var rotate_x, rotate_y, rotate_z : real := 0 var camera_pan_x, camera_pan_y, camera_pan_z : real := 0 %this rotates a 3D point( x1, y1, z1) around another point (origin) by a cetain number of degrees in each axis (xy, zy, zx). %Keep in mind that this modifies the point. (uses var)     procedure Rotate_Point_3D (var x1 : real, var y1 : real, var z1 : real,             origin_x, origin_y, origin_z, xy, zy, zx : real)         var temp_x : real := x1 - origin_x         var temp_y : real := y1 - origin_y         var temp_z : real := z1 - origin_z         % zx plane         x1 := temp_x * cosd (zx) - temp_z * sind (zx) + origin_x         z1 := temp_x * sind (zx) + temp_z * cosd (zx) + origin_z         temp_x := x1 - origin_x         temp_z := z1 - origin_z         % zy plane         z1 := temp_z * cosd (zy) - temp_y * sind (zy) + origin_z         y1 := temp_z * sind (zy) + temp_y * cosd (zy) + origin_y         temp_z := z1 - origin_z         temp_y := y1 - origin_y         % xy plane         x1 := temp_x * cosd (xy) - temp_y * sind (xy) + origin_x         y1 := temp_x * sind (xy) + temp_y * cosd (xy) + origin_y     end Rotate_Point_3D %this converts a 3D point into a 2D one and returns true if the conversion was successful %xt and yt are the 2D coordinates     function Make3D (x1, y1, z1 : real, var xt, yt : int) : boolean %create duplicate variables of the point and pan it         var x2 : real := x1 + camera_pan_x         var y2 : real := y1 + camera_pan_y         var z2 : real := z1 + camera_pan_z         Rotate_Point_3D (x2, y2, z2, SCR_W, SCR_H, 0, rotate_x, rotate_y, rotate_z)         if z2 > 1 then             xt := round ((x2 - SCR_W) / (z2 / Z_KEY_DIV) + SCR_W)             yt := round ((y2 - SCR_H) / (z2 / Z_KEY_DIV) + SCR_H)             result true %3d was successful         else             xt := 100             yt := 100             result false %3d was not successful         end if     end Make3D

This is fun because if you want to draw a black dot at a point, say 500,500,0, you just make a proc that does this:

code:

var temp_x, temp_y : int if Make_3D(500,500,0, temp_x, temp_y) then drawdot(temp_x, temp_y, black) end if

note: untested.

Simple, no? All rotations and panning is taken care of. Of course, there is then dealing with madifying the values accociated with that... maybe i should make a tutorial on this, considering so many people are interested... or maybe there already is one? hmm.....

[richcash]

Thanks, Windsurfer, you explained it very well. It seems to work great. Now, when I need to use 3d I'll just have to learn how to use your system to rotate and move the camera. As I said, I'm not really working on this just yet.

A tutorial would be great if we don't already have one, I think 3d is an interesting thing that is possible in Turing, but not too many people end up working with it!

[iker]

I've found this semi-simple algorithm to rotate a point in Zylums 3D engine, but had to refine it a bit to work for the 3d project I'm working on. This rotates the points from the camera's POV. pntX, pntY and pntZ are the original xyz points, then rotX, rotY, rotZ are the xyz points. xR yR and zR are the angles of rotation (0 .. 359). I haven't 100% figured out whats going on, but what I do know is that Zylum used 3D addition. Hopefully this helps, maby if someone wanted to expand on it a bit.

code:

rotY := pntY  * cosd (yR) - pntZ * sind (yR) rotZ := pntZ  * cosd (yR) + pntY  * sind (yR) temp := rotZ rotZ := temp * cosd (xR) - pntX * sind (xR) rotX := pntX * cosd (xR) + temp * sind (xR) temp := rotX rotX := temp * cosd (zR) - rotY * sind (zR) rotY := rotY * cosd (zR) + temp * sind (zR) pntX := rotX pntY := rotY pntZ := rotZ

[richcash]

That's a fairly good algorithm, iker, I really like how you're rotating in 3 dimensions (or at least I think so). Perhaps I could combine yours and Windsurfer's, though they are very similar. I didn't even know zylum made a 3d particle engine, now I have more resources! I think I'm finally understanding these types of systems and the mathematics behind them, thanks for your input!

[Windsurfer]

richcash wrote:

That's a fairly good algorithm, iker, I really like how you're rotating in 3 dimensions (or at least I think so). Perhaps I could combine yours and Windsurfer's, though they are very similar.

Yes, they are very similar... in fact, i think they're the same, apart from the fact that mine rotates around an origin, and not just (0,0,0).