Solved

Drawing 3D coordinates in 2D screen space using python/pygame?

Posted on 2012-04-06
3
1,220 Views
Last Modified: 2012-04-09
I am drawing 3D coordinates using Python/Pygame.

I KNOW this is meant to be accomplished using OpenGL/DirectX...
and I KNOW these calculations are meant to take place on a GPU...
but I don't care. I'm teaching myself the matrix transformations/projections.

Since I've used XNA/C#, I'm trying to simulate the World*View*Projection Matrix math to calculate screen coordinates for 3D shapes.

Since I have worded the following issue very poorly, I attached my entire source file.

-I'm using numpy, with 4x4 homogenous matrices.
-My vertices all contain a fourth 'w' value of 1

If I have a simple shape, say a diamond, with 6 vertices:

(1, 0, 0), ( -1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1)


World Matrix is just an identity matrix.

vP = (0, 0.0, -2.0)
vR = (1.0, 0.0, 0.0)
vU = (0.0, 1.0, 0.0)
look = (0.0, 0.0, 0.0)
vL = look - vP

v1 = dotProduct(-vP, vR.T)
v2 = dotProduct(-vP, vU.T)
v3 = dotProduct(-vP, vL.T)

VIEW = np.matrix([
        [vR[0,0], vU[0,0], vL[0,0], 0.0],
        [vR[0,1], vU[0,1], vL[0,1], 0.0],
        [vR[0,2], vU[0,2], vL[0,2], 0.0],
        [v1, v2, v3, 1.0]
        ])

width, height = 640, 480
fov = math.pi / 2.0
aspect_ratio = float(width) / float(height)
z_far = 100.0
z_near = 0.1

PROJECTION = np.matrix([
        [1 / tan(fov / 2) * aspect_ratio), 0, 0, 0],
        [0, 1 / tan(fov / 2), 0, 0],
        [0, 0, z_far / (z_far - z_near), 1],
        [0, 0, (-z_near * z_far) / (z_far - z_near), 0]
        ])

(x, y, z, w) = world*view*projection*coordinate

and the final X, Y = x/w, y/w

Long story short, my "diamond" should appear well-formed... however this is what I see:
distorted diamond.It SHOULD look like a symmetric diamond on all axes.
draw3d.py
0
Comment
Question by:Justin_Edmands
  • 2
3 Comments
 
LVL 12

Accepted Solution

by:
satsumo earned 500 total points
ID: 37820006
First of all, well done for actually trying the math.  It's very easy to use a ready made 3D system and it saves a lot of time, but you don't learn anything that way.  People who do that inevitably reach a point where they want to do something that exceeds the system they've been using, and then they don't know how to progress.

In this case everything looks OK at first glance.  The first thing that might be wrong is matrix order.  You do world*view*projection to calculate positions, that depends on whether the matrices are pre or post multiplied, which also depends on them being or row or column order correctly.  If either of these factors is wrong you will get the wrong result.  In this case, it appears to have applied the perspective scaling from right to left, which makes me suspect the matrix order.

Ufnortunately I don't know how the python matrix classes work so I can't be more precise than that.  OpenGL and DirectX use different matrix order and that often confuses people.  The majority of other systems seems to use the OpenGL order rather than the DirectX order.

http://en.wikipedia.org/wiki/Row-major_order
0
 

Author Closing Comment

by:Justin_Edmands
ID: 37825128
Essentially, my problem was the order of matrix multiplication. I read up on the row and column ordering.

In the end, I multiplied the transpose of each of those matrices in reverse... i.e. proj.T * view.T * world.T.

Thanks for the help! Now i'm gonna try drawing some complex shapes.
0
 
LVL 12

Expert Comment

by:satsumo
ID: 37825713
Glad to have helped, thanks for the points.

I've actually had to do this math myself for some jobs, including the clipping and rasterising sometimes.  Not every platform has an OpenGL/Direct X type system.  Sometimes you have to understand the math, so doing this is very useful.
0

Featured Post

Live: Real-Time Solutions, Start Here

Receive instant 1:1 support from technology experts, using our real-time conversation and whiteboard interface. Your first 5 minutes are always free.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
advertisement module in core php 4 159
tidtcpserver connection lost handle 2 83
Hashing Algorithm 5 67
How do sunrise and sunset times change with altitude 14 27
Entering a date in Microsoft Access can be tricky. A typo can cause month and day to be shuffled, entering the day only causes an error, as does entering, say, day 31 in June. This article shows how an inputmask supported by code can help the user a…
Computer science students often experience many of the same frustrations when going through their engineering courses. This article presents seven tips I found useful when completing a bachelors and masters degree in computing which I believe may he…
Viewers will learn how to properly install Eclipse with the necessary JDK, and will take a look at an introductory Java program. Download Eclipse installation zip file: Extract files from zip file: Download and install JDK 8: Open Eclipse and …
In this fourth video of the Xpdf series, we discuss and demonstrate the PDFinfo utility, which retrieves the contents of a PDF's Info Dictionary, as well as some other information, including the page count. We show how to isolate the page count in a…

786 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question