Btw, it would be perfectly possible to create a POV-Ray macro which takes
a 2-dimensional array of 3D points (ie. basically a grid of points) and
which would then generate a smooth surface which goes through all these
points, by creating a bicubic patch for each group of four adjacent points
in the grid. The tangential control points can be easily calculated in such
a way that the resulting group of bicubic patches form a smooth surface
which goes through all the given points.

  I actually once started writing such a macro, but I never finished it.

-- 
                                                          - Warp

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I attempted a calculation of normal vectors for this mesh2 object.
--------------------------------------------
camera {location <0,0,-5> look_at 0}
light_source {<-10,20,-50>, rgb 1}

#declare GridSize = 7;
#declare PointCount = pow(GridSize,2);
#declare NumberOfFaces = 2*pow(GridSize-1,2);
#declare use_normal_vectors = 1;

#declare XCoord =
   array[PointCount] {
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5,
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5,
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5,
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5,
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5,
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5,
     -1.5, -1.0, -0.5, 0,  0.5,   1.0,  1.5
   }

#declare YCoord =
   array[PointCount] {
     -1.5, -1.5, -1.5, -1.5, -1.5,  -1.5, -1.5,
     -1.0, -1.0, -1.0, -1.0, -1.0,  -1.0, -1.0,
     -0.5, -0.5, -0.5, -0.5, -0.5,  -0.5, -0.5,
     0,   0,   0,   0,    0,    0 ,   0,
     0.5,  0.5,  0.5,  0.5,  0.5,   0.5,  0.5,
     1.0,  1.0,  1.0,  1.0,  1.0,   1.0,  1.0,
     1.5,  1.5,  1.5,  1.5,  1.5,   1.5,  1.5
   }

#declare ZCoord =
   array[PointCount] {
     0.7781,  0.9975,  0.6816, 0, -0.6816,  -0.9975, -0.7781,
     0.9975,  0.8415,  0.4794, 0, -0.4794,  -0.8415, -0.9975,
     0.6816,  0.4794,  0.2474, 0, -0.2474,  -0.4794, -0.6816,
     0,       0,       0,      0,       0,  0,       0,
     -0.6816, -0.4794, -0.2474, 0,  0.2474,   0.4794,  0.6816,
     -0.9975, -0.8415, -0.4794, 0,  0.4794,   0.8415,  0.9975,
     -0.7781, -0.9975, -0.6816, 0,  0.6816,   0.9975,   0.7781
   }

mesh2 {
   vertex_vectors {
     PointCount,
     #local I = 0;
     #while (I < PointCount)
       #if (I != PointCount-1)
	<XCoord[I],YCoord[I],ZCoord[I]>,
       #else
	<XCoord[I],YCoord[I],ZCoord[I]>
       #end
       #local I = I + 1;
     #end
   }
   #if (use_normal_vectors)
     normal_vectors {
       PointCount,
       #local I = 0;
       #while (I < GridSize)
	#local I1 = ((I = 0) ? 0 : I - 1);
	#local I2 = ((I = GridSize - 1) ? I : I + 1);

	#local J = 0;
	#while (J < GridSize)
	  #local J1  = ((J = 0) ? 0 : J - 1);
	  #local J2  = ((J = GridSize - 1) ? J : J + 1);

	  #local dx  = XCoord[I2 + J * GridSize] - XCoord[I1 + J * GridSize];
	  #local dy  = YCoord[I + J2 * GridSize] - YCoord[I + J1 * GridSize];
	  #local dzx = ZCoord[I2 + J * GridSize] - ZCoord[I1 + J * GridSize];
	  #local dzy = ZCoord[I + J2 * GridSize] - ZCoord[I + J1 * GridSize];
	  #local vnorm = vnormalize( vcross(<dx, 0, dzx>, <0, dy, dzy>) );
	  #if ((J < GridSize - 1) | (I < GridSize - 1))
	    vnorm,
	  #else
	    vnorm
	  #end
	  #local J = J + 1;
	#end
	#local I = I + 1;
       #end
     }
   #end
   face_indices {
     NumberOfFaces
     #local I = 0;
     #while (I<GridSize-1)
       #local J = 0;
       #while (J<GridSize-1)
	#local K = I*(GridSize)+J;
	<K,K+1,K+GridSize>,
	#if (K!=NumberOfFaces-1)
	  <K+1,K+GridSize+1,K+GridSize>,
	#else
	  <K+1,K+GridSize+1,K+GridSize>
	#end
	#local J = J + 1;
       #end
       #local I = I + 1;
     #end
   }
   pigment {rgb 1}
}

Post a reply to this message

"Dan Connelly" <djc### [at] yahoocom> wrote in message 
news:48f6195e@news.povray.org...
>I attempted a calculation of normal vectors for this mesh2 object.

You just beat me to it :o)

We've both used very similar techniques. I was just investigating some dark 
lines that I get along the edges of the grid and light lines along the 
diagonals of the triangles (I notice you got them too), but I've concluded 
that it's just due to the fact that the z distances are relatively large.

Regards,
Chris B.

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Warp wrote:
>   Btw, it would be perfectly possible to create a POV-Ray macro which takes
> a 2-dimensional array of 3D points (ie. basically a grid of points) and
> which would then generate a smooth surface which goes through all these
> points, by creating a bicubic patch for each group of four adjacent points
> in the grid. The tangential control points can be easily calculated in such
> a way that the resulting group of bicubic patches form a smooth surface
> which goes through all the given points.
> 
>   I actually once started writing such a macro, but I never finished it.

I once made a set of macros that handles this.
Here are some images made with it:

http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patches_Torus.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patches_UV-mapped.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patchwork.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patchwork_Ctrl_Grid.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patchwork_Top_View.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patches_Stitched.jpg
http://home.online.no/~t-o-k/POV-Ray_Images/Bezier_Patches_Stitched_.jpg

-- 
Tor Olav
http://subcube.com

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