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

Posted on 2012-04-06
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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
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Question by:Justin_Edmands
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3 Comments
 
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Accepted Solution

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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
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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.
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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.
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