murrayk@prism.CS.ORST.EDU (04/11/91)
Ok, here we go. First of all I would like to thank all the people that were kind and knowledged enough to reply to my cry for help. I received a lot of mail and postings that helped me to find some new books to look through and some actually sent me some code. I tried to reply to all of you who sent me something or posted something, but I am sure that I missed a few...so if you didn't already hear thanks, then thanks. Next, in most of the replys I got people rehashed just what I have already been doing. Here is my most immediate problem in a lot more detail. I can draw and rotate an object on the screen around the x, y and z-axis all day long. The only problem is that each axis that I rotate around is the corresponding axis of the monitor (what you actually see). Now, what I want to do is to be able to rotate the object around its own three axes (virtual axes). For example, say the object is a tetrehedron with its base in the xy plane (the yz plane is sticking in your face) and its top point in your face. The object is situated so that the z-axis is a line running though the top point and the middle of the base. Now say that I rotate this object around the x axis about 30 degrees so that the point is now partially up the screen. Now if I was to rotate the object about the z-axis as my code now exists, the top point of the tetrehedron would sweep out a circle on the screen. This problem could be solved by doing the rotations in a certain order, but that screws up as soon as you rotate about the third axis. What the object should do if it is rotated about the z-axis (its z-axis) would be to spin along the imaginary line running though its top point and its base. But alas, I cannot get this to happen. In consulting a few graphical technique books, I found out exactly how to do a rotation about an arbitrary line. I figured that if I kept the axes of the object in the data of the object itself and rotated the axes along with the object, then I would be able to do an arbitrary rotation about those axes and voila, it would work. I tried this and have had no luck. My code has been gone over with a fine toothed comb (my own and a friends) and no problem can be found. If anyone has experience in this area of 3D rotation, please keep posting. If I am just missing a small point, don't flame me. I will see it soon enough. I am bound to find out what I am missing eventually. All your help is appreciated. Thanks a lot, Keith Murray -------------------------------------------------------------------------------- CHAOS Software Software for someone... 1360 NW VanBuren Keith Murray a.k.a. Slammer Corvallis, OR 97330 murrayk@prism.cs.orst.edu --------------------------------------------------------------------------------
2fmlcalls@kuhub.cc.ukans.edu (04/11/91)
> If anyone has experience in this area of 3D rotation, please keep posting. > If I am just missing a small point, don't flame me. I will see it soon > enough. I am bound to find out what I am missing eventually. All your > help is appreciated. > > Thanks a lot, Keith Murray I got a bit lost in your process you described. Let me try to explain a process I used as clearly as I can. Lets take a square. We all know its shape and (as opposed to a cube) it has few points. As emntioned in an earlier post, you want an array of 'triples' (the x, y, and z coords for each point) and a sequence to connect the dots. If the points are A,B,C,D then we could come up with values like this: A = (-10, 10, 0) B = (10, 10, 0) C = (10, -10, 0) D = (-10, -10, 0) If you plot these on a piece of graph paper (ignoring the last 'z' component) you get a square 20 x 20 about the origin. Connect A to B to C to D to A. There's the dot-to-dot. These 'local' coordinates are important because they define a simple rotational axis for the shape (you can rotate about any arbitrary point, but putting 0,0,0 as the center of gravity just makes sense). So, the above points might be thought of as the source points. Since you seem to understand transform matrices, I'll skip that rather tedious part. But basically, you pop in sin and cos values for the angle(s) you want to rotate all these points about. The transformation entails putting feeding source points into the matrix and extracting transformed points. If you feed in these original points AS THEY ARE assigned above, the transformation will be about the local origin (say, for example the square is rolling and tumbling about its own axis). The points you get out lets call tA, tB, tC, and tD - small t for the local transformation. Now you do the global transformation (as if the observer is rotating, tumbling etc.). First you need to translate (shift) the points tA, tB, tC, tD by the amount that they are distant from the observer. If the global position of the square is a point P(distX, distY, distZ), then add distX to the x component of tA, tB, tC, tD. Not that we are translating the transformed points and not the original 'raw' source points. All four points of the square have now been: 1) rotated about their own axis and 2) shifted in space to represent their distance from the observer. The now shifted points we could call tsA, tsB, tsC, tsD. That is, these are the original points after rotating and then shifting. The last` step is to pop the sines and cosines for the OBSERVERS roll, pitch, and yaw into a transform matrix and run tsA, tsB, tsC, tsD through. What you get out we can call tsTA, tsTB, tsTC, tsTD. These are the final points. Use your similar triangles and clipping on these points. And there it is. For the next frame, add rolls, pitches and yaws to the roll, pitch and yaw of the object and observer. Figure your new distance point P. And run the whole gauntlet again with the source points. A final note. As pointed out in same earlier post, so long as you maintain your original source points and never modify them, you'll get no accumualted round-off errors (read - a parallelogram or rhombus). The points you derive from all the transofroms can be tossed after you draw the scene. In fact, you may have realized that after the first rotation (about the objects axis) you need not keep this copy of points when you translate them and then when you rotate about the observer). Also, rotations and distance are cumulative. If the square is rotated 10 degrees off North and rotates +5 degrees in one loop through the game, you put 15 degrees (not 5) into the transform matrix. john calhoun
meekins@anaconda.cis.ohio-state.edu (timothy lee meekins) (04/11/91)
In article <1991Apr10.191212.5249@lynx.CS.ORST.EDU> murrayk@prism.CS.ORST.EDU writes: <snip!> >I can draw and rotate an object on the screen around the x, y and z-axis >all day long. The only problem is that each axis that I rotate >around is the corresponding axis of the monitor (what you actually see). >Now, what I want to do is to be able to rotate the object around its own >three axes (virtual axes). For example, say the object is a tetrehedron >with its base in the xy plane (the yz plane is sticking in your face) and >its top point in your face. The object is situated so that the z-axis is a >line running though the top point and the middle of the base. Now say that >I rotate this object around the x axis about 30 degrees so that the point >is now partially up the screen. Now if I was to rotate the object about >the z-axis as my code now exists, the top point of the tetrehedron would >sweep out a circle on the screen. This problem could be solved by doing >the rotations in a certain order, but that screws up as soon as you rotate >about the third axis. What the object should do if it is rotated about the >z-axis (its z-axis) would be to spin along the imaginary line running >though its top point and its base. But alas, I cannot get this to happen. > >In consulting a few graphical technique books, I found out exactly how to >do a rotation about an arbitrary line. I figured that if I kept the axes >of the object in the data of the object itself and rotated the axes along >with the object, then I would be able to do an arbitrary rotation about >those axes and voila, it would work. I tried this and have had no luck. >My code has been gone over with a fine toothed comb (my own and a friends) >and no problem can be found. > Rotating about an arbitray axis is a simple thing, but as you have noticed, it is not the solution to your problem. >If anyone has experience in this area of 3D rotation, please keep posting. >If I am just missing a small point, don't flame me. I will see it soon >enough. I am bound to find out what I am missing eventually. All your >help is appreciated. Well, you're not missing a small point. You are most likely experiencing gimbal lock, a term developed in aeronautical engineering (I believe) when using euler angles (x,y,z rotations). Your description of ordering the rotations to make it work about one axis and a different rotation ordering for axis definately sounds a like the euler angle problem. I would suggest that you use Quaternions instead of Euler angles. Basically, you convert your 3 rotations into 4-D space, perform the rotation, then map back. But, a better method would be to learn directly how quaternions work and not even perform the mapping. In which case, you specify the axis of rotation. For more information, see "Animating Rotation with Quaternion Curves" in SIGGRAPH '85 proceedings. Source code for quaternions is provided with Graphics Gems by Andrew Glassner and is available by FTP somewhere. -tim -- +---------------------------S-U-P-P-O-R-T-----------------------------------+ |/ Tim Meekins <<>> Snail Mail: <<>> Apple II \| |> meekins@cis.ohio-state.edu <<>> 8372 Morris Rd. <<>> Forever! <| |\ timm@pro-tcc.cts.com <<>> Hilliard, OH 43026 <<>> /|
minar@reed.edu (04/15/91)
All this talk about how to do 3d rotations is nice. But I'm lazy. Is there source code / a C library that will allow me to do 3d projections? I just want to write the objects up - I don't want to worry with the details on how they get onto the screen. Has someone written 3d projections suitable for real time usage, say if I were to write a game like Battlezone or Elite?