Hello Friends
 I have been part of the news gruop for some time as a silent reader but
this is my first post. I have not been able to find a satisfactory answer
to a technical problem I'm having within previous posts in the newsgroup.
 Can any math wizz out there tell me what the formula would look like that
would describe the motion of a camera that looked at one spot in space
continually as it gradually began to move in a circular and expanding
spiral, steadily gaining speed and steadily rising above what it is looking
at?
 If this motion could be visualized by a single curved line, it would
probably appear to be a very symetrical and conical tornado.
 Also; how would a mathematical formula discribing the above motion be
worded in POVray?

                                    Thanx

Post a reply to this message

How about:

#declare Initial_Position=<5,3,0>;
#declare Radius_Increase=5;
#declare Revolvements=1;
#declare
Cam_Location=vrotate(Initial_Position+x*clock*Radius_Increase,y*360*Revolvem
ents*clock);

This would get you a path beginning at Initial_Position,
looking from positive x axis, and encircle the origin while
increasing the distance (but not the height) to the object.

To increase the height as well, you'd have to add another
+y*clock*Some_Value before the "," of the vrotate (look
that one up in the Docs). For more rotations, increase
Revolvements.
If you want to begin from in front of the object (I think
left-handed, -z is front), exchanget the Initial_Position
with <0,3,-5> and the "+x" in vrotate with "-z".

When you dissect that, you should understand the concept.

Regards,
Tim

-- 
Tim Nikias v2.0
Homepage: http://www.digitaltwilight.de/no_lights

> Hello Friends
>  I have been part of the news gruop for some time as a silent reader but
> this is my first post. I have not been able to find a satisfactory answer
> to a technical problem I'm having within previous posts in the newsgroup.
>  Can any math wizz out there tell me what the formula would look like that
> would describe the motion of a camera that looked at one spot in space
> continually as it gradually began to move in a circular and expanding
> spiral, steadily gaining speed and steadily rising above what it is
looking
> at?
>  If this motion could be visualized by a single curved line, it would
> probably appear to be a very symetrical and conical tornado.
>  Also; how would a mathematical formula discribing the above motion be
> worded in POVray?
>
>                                     Thanx
>
>
>


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"Tim Nikias v2.0" wrote:
> 
> How about:
> 
> #declare Initial_Position=<5,3,0>;
> #declare Radius_Increase=5;
> #declare Revolvements=1;
> #declare
> Cam_Location=vrotate(Initial_Position+x*clock*Radius_Increase,y*360*Revolvem
> ents*clock);
> 
> This would get you a path beginning at Initial_Position,
> looking from positive x axis, and encircle the origin while
> increasing the distance (but not the height) to the object.
> 
> To increase the height as well, you'd have to add another
> +y*clock*Some_Value before the "," of the vrotate (look
> that one up in the Docs). For more rotations, increase
> Revolvements.
> If you want to begin from in front of the object (I think
> left-handed, -z is front), exchanget the Initial_Position
> with <0,3,-5> and the "+x" in vrotate with "-z".
> 
> When you dissect that, you should understand the concept.
> 
> Regards,
> Tim
> 
> --
> Tim Nikias v2.0
> Homepage: http://www.digitaltwilight.de/no_lights
> 

Then you may also want the distance between the camera position in the
frames to be a constant. This complicates things a bit.
I've done just that, a while ago, but I wanted the camera direction to
move along. It turned out to be more complicated then I thought. When I
finally figured it out I thought it looked awfull and changed it...

Remco

Post a reply to this message

Try this sequence to produce a spiral motion of the camera:

  plane { <0, 1, 0>, -2
    pigment {
      checker color White, color Green
    }
  }

#declare center_object =            // whatever object you have
     box {<-.5,-.5,-.5>,<.5,.5,.5> pigment {checker color Red,color
lue }  }

     object {center_object}

// adjust any or all of these 3 to change the spiral
#declare revolutions = 10 ;
#declare constant_a = 0.05 ;
#declare constant_b = 1 ;

#declare theta = revolutions*360*clock ;
#declare spiral_radius = constant_b*exp(constant_a*radians(theta)) ;   //
logarithmic spiral (equiangular)
#declare ex = spiral_radius*cos(theta) ;
#declare zee = spiral_radius*sin(theta) ;

camera {angle 100
        location  <ex,spiral_radius,-zee>
        look_at   <0,0,0>        // or wherever your object is located
       }



"tgl" <tgl### [at] canadacom> wrote in message
news:web.3f507d5f85bbe1cfe331e8d30@news.povray.org...
> Hello Friends
>  I have been part of the news gruop for some time as a silent reader but
> this is my first post. I have not been able to find a satisfactory answer
> to a technical problem I'm having within previous posts in the newsgroup.
>  Can any math wizz out there tell me what the formula would look like that
> would describe the motion of a camera that looked at one spot in space
> continually as it gradually began to move in a circular and expanding
> spiral, steadily gaining speed and steadily rising above what it is
looking
> at?
>  If this motion could be visualized by a single curved line, it would
> probably appear to be a very symetrical and conical tornado.
>  Also; how would a mathematical formula discribing the above motion be
> worded in POVray?
>
>                                     Thanx
>
>
>

Post a reply to this message