point rotation

[PZ]

Is there a way to rotate a point around a given axis in a 3d space? Example: point=P(3,4,5) and the axis is a line from (2,7,6) to (2,8,12). I can't find a way to make point P rotate around that axis! Please help me!<br><br>Thanx in advance! <p> Alex<br><a href=mailtoizzapz@libero.it>pizzapz@libero.it</a><br><a href= > </a><br>*** Q(uick)BASIC RULEZ! ***

 

[Karl Blessing]

Perhaps, I feel that when you got two Axis, X and a Y its pretty eazy, your Z Axis may be a bit slightly harder. If we look at the Axis, you'll notice X and Y make a cross:<br><br><FONT FACE=monospace><br>&nbsp;&nbsp;¦<br>&nbsp;&nbsp;¦<br>-----<br>&nbsp;&nbsp;¦<br>&nbsp;&nbsp;¦<br></font><br><br>to add a Z Axis, would be to similate depth, in this example, I'm going to make it the Slope of X and Y<br><br><FONT FACE=monospace><br>\ ¦<br>&nbsp;\¦<br>-----<br>&nbsp;&nbsp;¦\<br>&nbsp;&nbsp;¦ \<br></font><br><br>if you can cacluate how to move up and down that third axis (like Y - some Number, and X - some number) I dont know off the top of my head, but you should be able to get a perfect diagonal if you pratice, so then your X,Y,Z is really, an X,Y,(Some Formula to place it similated on an XY Graph)<br><br>did this help somewhat? <p>Karl<br><a href=mailto:kb244@kb244.com>kb244@kb244.com</a><br><a href=

http://kb244.com>

</a><br>Experienced in : C++(both VC++ and Borland),VB1(dos) thru VB6, Delphi 3 pro, HTML, Visual InterDev 6(ASP(WebProgramming/Vbscript)<br>

http://www.brainbench.com/transcript.jsp?pid=629151

 

[PZ]

I think I didn't explain myself fully, sorry. I'll try again:<br>this is my sub:<br><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;zoom = 200<br> depth = 40<br> x2! = (x3d! * COS(rotZ!)) - (y3d! * SIN(rotZ!))<br> y2! = (x3d! * SIN(rotZ!)) + (y3d! * COS(rotZ!))<br> x3! = (x2! * COS(rotY!)) - (z3d! * SIN(rotY!))<br> z2! = (x2! * SIN(rotY!)) + (z3d! * COS(rotY!))<br> y3! = (y2! * COS(rotX!)) - (z2! * SIN(rotX!))<br> z3! = (y2! * SIN(rotX!)) + (z2! * COS(rotX!))<br> x2d% = zoom * (x3! / (z3! + depth)) + (screenwide/2)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y2d% = zoom * (y3! / (z3! + depth)) + (screenhigh/2)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;pset (x2d%, y2d%), col%<br><br>By modifing rotx!,roty! or rotz! I can rotate a point around the x, y or z axis, but what about an axis that ISN'T x, y or z? <p> Alex<br><a href=mailtoizzapz@libero.it>pizzapz@libero.it</a><br><a href= > </a><br>*** Q(uick)BASIC RULEZ! ***

 

[Karl Blessing]

you mean how to rotate around only X,y cordinate?, if thats the case, the situation still stands true, you just use zero for the Z Depth, then go from there. <p>Karl<br><a href=mailto:kb244@kb244.com>kb244@kb244.com</a><br><a href=

http://kb244.com>

</a><br>Experienced in : C++(both VC++ and Borland),VB1(dos) thru VB6, Delphi 3 pro, HTML, Visual InterDev 6(ASP(WebProgramming/Vbscript)<br>

http://www.brainbench.com/transcript.jsp?pid=629151

 

[Guest_imported]

Here's a reply from comp.graphics.algorithms on 5 Aug 2000<br>on the same question, which gets asked often.<br><br>The derivation involves quaternions or <br>the definition of 4x4 matrices raised to the nth power.<br>I learned it in school as the 'Rodrigues Formula' and<br>it is briefly mentioned in Computer_Graphics: Principles_and_Practice.<br><br><br>&nbsp;co=cos(alpha) ; si=sin(alpha) ; c1 = 1-cos(alpha)<br>&nbsp;e=(e1,e2,e3) unit vector of the rotation axis<br>&nbsp;&nbsp;<br>&nbsp;&nbsp;<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c1.e1.e1+co&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c1.e1.e2-si.e3&nbsp;&nbsp;&nbsp;&nbsp;c1.e1.e3+si.e2<br>&nbsp;M(alpha,e) =&nbsp;&nbsp;&nbsp;&nbsp;c1.e2.e1+si.e3&nbsp;&nbsp;&nbsp;&nbsp;c1.e2.e2+co&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c1.e2.e3-si.e1<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c1.e3.e1-si.e2&nbsp;&nbsp;&nbsp;&nbsp;c1.e3.e2+si.e1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;c1.e3.e3+co <br>&nbsp;&nbsp;<br>&nbsp;&nbsp;<br>&nbsp;The quaternion representing this rotation is<br>&nbsp;&nbsp;<br>&nbsp;c = cos(alpha/2)&nbsp;&nbsp;s = sin(alpha/2)<br>&nbsp;&nbsp;<br>&nbsp;q(alpha,e) =&nbsp;&nbsp;( c , s.e1, s.e2, s.e3 )