transforming vertex normals

chipmunk1886 · 2003-08-19T11:49:27

okay, i need to do a little explaining first. I''m building a simple software rasterizer and an accompanying API that is modeled off of OpenGL (a very basic version of OpenGL). It''s coming along pretty well so far. I have a rotating cube in the screen that''s being lit by three different kinds of lights. It also has point sampled textures applied to it. The front end code looks very very similar to OpenGL. It''s kind of neat! Things left to do with the API are to include the option for bilinear texture filtering, fix some issues with clipping against the near plane, add support for a simple zbuffer, add support for alpha blending... there''s a lot left to do. but i''m having a LOT of fun with the project. And I''m learning a lot too, always a plus. Okay, here''s where I''m having a problem. I am running into a very strange error with this rotating cube demo. I know that I''m dealing with an orthogonal ModelView matrix, so the vertex normals can be transformed by the same matrix used on the vertices themselves (according to Eric Lengyel''s "Mathematics for 3D Game Programming and Computer Graphics", awesome book btw). So rather than go through the trouble of having to create an inverse transpose matrix of the current MV matrix every time it''s modified, i just use the MV matrix. The front, back, left, and right faces are illuminated correctly (with gouraud shading, it''s cool). However, the top and bottom faces are being illuminated. I''ve looked over a printout of the current MV matrix and the current normal the normals for the top and bottom face are not being transformed correctly. Here''s an example of the printout: CurrentNormal=[0.000000, 1.000000, 0.000000, 1.000000, ] MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 -4.000000 0.000000 0.000000 0.000000 1.000000 INV_MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 CurrentNormal=[0.000000, 1.000000, 0.000000, 1.000000, ] MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 0.999550 0.029995 0.000000 0.000000 -0.029995 0.999550 -4.000000 0.000000 0.000000 0.000000 1.000000 INV_MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 0.999550 0.029995 0.000000 0.000000 -0.029995 0.999550 0.000000 0.000000 0.000000 0.000000 1.000000 CurrentNormal=[0.000000, 0.999550, -0.029995, 1.000000, ] MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 0.998201 0.059964 0.000000 0.000000 -0.059964 0.998201 -4.000000 0.000000 0.000000 0.000000 1.000000 INV_MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 0.998201 0.059964 0.000000 0.000000 -0.059964 0.998201 0.000000 0.000000 0.000000 0.000000 1.000000 CurrentNormal=[0.000000, 0.998201, -0.059964, 1.000000, ] MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 0.995953 0.089879 0.000000 0.000000 -0.089879 0.995953 -4.000000 0.000000 0.000000 0.000000 1.000000 INV_MODEL_VIEW= 1.000000 0.000000 0.000000 0.000000 0.000000 0.995953 0.089879 0.000000 0.000000 -0.089879 0.995953 0.000000 0.000000 0.000000 0.000000 1.000000 CurrentNormal=[0.000000, 0.995953, -0.089879, 1.000000, ] Note that the INV_MODEL_VIEW matrix is the same as the modelview except for the translation portion, i just have separate matrices for correctness. In this example, the top face is being rotated forward (out of the screen, so as to become visible). The z-coordinate of the vertex normal should become more positive, which would be the same as pointing out of the screen. But, it''s going in the opposite direction. Note that the transpose of the transformation matrix would transform the normal in the correct way. Well, to make a long story short, i tried using the transpose of the MV matrix and the inverse transpose, but neither technique worked correctly. I''ve poured over all the code and even gone through all the calculations by hand. Everything is mathematically correct but the numbers aren''t what they should be. So there must be something wrong with the technique I''m using? I''m sorry if this post is vague. The problem involves a lot of code and is kind of complicated in and of itself. Thanks in advance for any help or advice you can give me. I''m all out of ideas. -Justin

Graphics and GPU Programming Programming

Started by chipmunk1886 August 17, 2003 02:56 PM

11 comments, last by chipmunk1886 20 years, 8 months ago

Wudan

211

August 19, 2003 08:38 AM

"A normal is a vector representing a plane." <-- we'll use this.

So I take "0.85355, -0.14645, 0.50000", a normal, which is a vector representing a plane. I plug those vector values in to the corresponding x, y, and z spots in an identity matrix (along the right hand side, as above), viola, I have a 4x4 matrix representation of that normal/vector.

Then I can rotate the normal through regular matrix transformation, resulting in a transformed normal. As long as I don't get it confused with regular 'worldspace' vectors, and handle it properly, it should be fine, afaik.

Basically, my thinking is, if it is a vector in any sense, I can transform it like a vector.

As I said, I know there is a better way to do this, but that's for somebody else to tell me.

All tolled, it looks like the method that chipmunk is using is correct.

[edited by - wudan on August 19, 2003 9:43:57 AM]

JuNC

236

August 19, 2003 10:26 AM

I kinda see how you got there, but I'm not sure why.

Transformation of a point P by a 4X4 matrix M:

 P' = M * P [x']       [x] [y'] = M * [y] [z']       [z] [1]        [1]

Transformation of a normal N by (e.g. the same) 4X4 matrix M:

 N' = (MT)-1 * N [x']        [x] [y'] = (MT)-1 * [y] [z']        [z] [0]         [0]

(I might have the T,-1 inside out)

However, if M is orthogonal then MT = M-1
so (MT)-1 = M and you can do

 N' = M * N

Which is what the OP was trying to do.

[edited by - JuNC on August 19, 2003 11:28:36 AM]

browny

139

August 19, 2003 11:49 AM

I haven''t read the whole thing but i guess what you might be doing wrong is transforming the normals using the same MV matrix that you are using for vertex transformationg. That''s wrong... i am sure someone have already mentioned it above... you should not TRANSLATE the normals. Only the rotational components of the MV matrix should be used.. ie. ONLY the top-left 3x3 part of the 4x4 matrix. Just leave out the last column and last row of the 4x4 matrix and use the remaining 3x3 matrix.

in OGL vertex shader this is achieved by

DP3 NormalVector.x NormalVector ModelViewMat[0]
DP3 NormalVector.y NormalVector ModelViewMat[1]
DP3 NormalVector.z NormalVector ModelViewMat[2]

Notice.. we r doing a DP3 (3 component dot product).

transforming vertex normals

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transforming vertex normals

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