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/*
PL3D.I
Viewing transforms and other aids for 3D plotting.
$Id$
*/
/* Copyright (c) 1996. The Regents of the University of California.
All rights reserved. */
/* General overview:
(1) Viewing transform machinery. Arguably the simplest model
is the CAD/CAM notion that the object you see is oriented
as you see it in the current picture. You can then move
it left, right, up, down, or toward or away from you,
or you can rotate it about any of the three axes (horizontal,
vertical, or out of the screen). The xyz coordinates of the
object remains unchanged throughout all of this, but this
object coordinate system changes relative to the fixed
xyz of the viewer, in which x is always to the right, y is
up, and z is directed out of the screen. Initially, the
two coordinate systems coincide.
rot3, xangle,yangle,zangle
Rotate the object about viewer's x-axis by xangle, then
about viewer's y-axis by yangle, then about viewer's
z-axis by zangle
mov3, xchange,ychange,zchange
Move the object by the specified amounts.
setz3, zcamera
The "camera" is located at (0,0,zcamera) in the viewer's
coordinate system, looking in the minus-z direction.
Initially, zcamera is very large, and the magnification
factor is correspondingly large, giving an isometric view.
Decreasing zcamera makes the perspective more extreme.
If parts of the object are behind the camera, strange things
may happen.
undo3
undo3, n
Undo the last N (default 1) viewpoint commands (rot3, mov3,
or setz3). Up to 100 viewpoint changes are remembered.
viewpoint= save3()
...
restore3, viewpoint
The current viewpoint transformation can be saved and later
restored.
gnomon, on_off
Toggle the gnomon (a simple display showing the orientation
of the xyz axes of the object).
*/
/* ------------------------------------------------------------------------ */
func rot3 (xa,ya,za)
/* DOCUMENT rot3, xa,ya,za
rotate the current 3D plot by XA about viewer's x-axis,
YA about viewer's y-axis, and ZA about viewer's z-axis.
SEE ALSO: orient3, mov3, aim3, setz3, undo3, save3, restore3, light3
*/
{
if (is_void(xa)) xa= 0.;
if (is_void(ya)) ya= 0.;
if (is_void(za)) za= 0.;
x= [1.,0.,0.];
y= [0.,1.,0.];
z= [0.,0.,1.];
_rot3, za, x, y;
_rot3, ya, z, x;
_rot3, xa, y, z;
_setrot3, [x,y,z](,+)*_getrot3()(+,);
}
func _rot3 (a, &x, &y)
{
ca= cos(a);
sa= sin(a);
a= x;
x= ca*a + sa*y;
y= -sa*a + ca*y;
}
func mov3 (xa,ya,za)
/* DOCUMENT mov3, xa,ya,za
move the current 3D plot by XA along viewer's x-axis,
YA along viewer's y-axis, and ZA along viewer's z-axis.
SEE ALSO: rot3, orient3, setz3, undo3, save3, restore3, light3
*/
{
if (is_void(xa)) xa= 0.;
if (is_void(ya)) ya= 0.;
if (is_void(za)) za= 0.;
_setorg3, _getorg3() - _getrot3()(+,)*[xa,ya,za](+);
}
func aim3 (xa,ya,za)
/* DOCUMENT aim3, xa,ya,za
move the current 3D plot to put the point (XA,YA,ZA) in object
coordinates at the point (0,0,0) -- the aim point -- in the
viewer's coordinates. If any of XA, YA, or ZA is nil, it defaults
to zero.
SEE ALSO: mov3, rot3, orient3, setz3, undo3, save3, restore3, light3
*/
{
if (is_void(xa)) xa= 0.;
if (is_void(ya)) ya= 0.;
if (is_void(za)) za= 0.;
_setorg3, [xa,ya,za];
}
func setz3 (zc)
/* DOCUMENT setz3, zc
Set the camera position to z=ZC (x=y=0) in the viewer's coordinate
system. If ZC is nil, set the camera to infinity (default).
SEE ALSO: rot3, orient3, undo3, save3, restore3, light3
*/
{
if (!is_void(zc)) {
if (dimsof(zc)(1)) error, "camera position must be scalar";
zc= double(zc);
}
_setzc3, zc;
}
func orient3 (phi, theta)
/* DOCUMENT orient3, phi, theta
or orient3, phi
or orient3, , theta
or orient3
Set the "orientation" of the object to (PHI,THETA). "Orientations"
are a subset of the possible rotation matrices in which the z-axis
of the object appears vertical on the screen (that is, the object
z-axis projects onto the viewer y-axis). The THETA angle is the
angle from the viewer y-axis to the object z-axis, positive if
the object z-axis is tilted toward you (toward viewer +z). PHI is
zero when the object x-axis coincides with the viewer x-axis. If
neither PHI nor THETA is specified, PHI defaults to -pi/4 and
THETA defaults to pi/6. If only one of PHI or THETA is specified,
the other remains unchanged, unless the current THETA is near pi/2,
in which case THETA returns to pi/6, or unless the current
orientation does not have a vertical z-axis, in which case the
unspecified value returns to its default.
Unlike rot3, orient3 is not a cumulative operation.
SEE ALSO: rot3, mov3, aim3, save3, restore3, light3, limit3
*/
{
if (is_void(theta) && is_void(phi)) {
theta= _orient3_theta;
phi= _orient3_phi;
} else if (is_void(theta) || is_void(phi)) {
z= _getrot3()(,+)*[0.,0.,1.](+);
if (abs(z(1))>1.e-6) {
/* object z-axis not aligned with viewer y-axis */
if (is_void(theta)) theta= _orient3_theta;
else phi= _orient3_phi;
} else if (is_void(theta)) {
if (abs(z(2))<1.e-6) theta= _orient3_theta;
else theta= atan(z(3),z(2));
} else /*if (is_void(phi))*/ {
y= [0.,z(3),-z(2)]; /* in object xy-plane */
x= _getrot3()(,+)*[1.,0.,0.](+);
phi= atan(y(+)*x(+), x(1));
}
}
x= [1.,0.,0.];
y= [0.,1.,0.];
z= [0.,0.,1.];
_rot3, theta, y, z;
_rot3, phi, z, x;
_setrot3, [x,-z,y];
}
/* unless user has supplied alternative defaults, set orient3 defaults */
if (is_void(_orient3_theta)) _orient3_theta= pi/6;
if (is_void(_orient3_phi)) _orient3_phi= -pi/4;
func limit3 (xn,xx,yn,yx,zn,zx,aspect=)
/* DOCUMENT limit3, xmin,xmax, ymin,ymax
or limit3, xmin,xmax, ymin,ymax, zmin,zmax
Set the 3D axis limits for use with the cage.
Use keyword aspect=[ax,ay,az] to set the aspect ratios of the
cage to ax:ay:az -- that is, the ratios of the lengths of the
cage axes will become ax:ay:az.
SEE ALSO: cage3, range3, plwf (include plwf.i), orient3
*/
{
local limits;
eq_nocopy, limits, _car(_draw3_list, _draw3_nll+1);
if (dimsof(xn)(1)>1) {
if (dimsof(xn)(1)!=2 || anyof(dimsof(xn)(2:3)!=3))
error, "bad limit3 arguments";
_setscl3, xn;
return limits;
}
void= [[is_void(xn),is_void(xx)],[is_void(yn),is_void(yx)],
[is_void(zn),is_void(zx)]];
if (nallof(void) || !is_void(aspect)) {
if (is_void(limits)) {
if (anyof(void))
error, "no xyz limits currently set -- you must set all six";
lims= array([0.,1.,1.],3);
} else {
lims= limits;
}
if (!void(1,1)) lims(1,1)= xn;
if (!void(2,1)) lims(2,1)= xx;
if (!void(1,2)) lims(1,2)= yn;
if (!void(2,2)) lims(2,2)= yx;
if (!void(1,3)) lims(1,3)= zn;
if (!void(2,3)) lims(2,3)= zx;
if (!is_void(aspect)) lims(3,)= aspect;
_setscl3, lims;
}
return limits;
}
func range3 (zn,zx,aspect=)
/* DOCUMENT range3, zmin,zmax
Set the 3D axis z limits for use with the cage.
Use keyword aspect=[ax,ay,az] to set the aspect ratios of the
cage to ax:ay:az -- that is, the ratios of the lengths of the
cage axes will become ax:ay:az.
SEE ALSO: cage3, limit3, plwf (include plwf.i), orient3
*/
{
return limit3(,,,,zn,zx,aspect=aspect);
}
func save3 (void)
/* DOCUMENT view= save3()
Save the current 3D viewing transformation and lighting.
SEE ALSO: restore3, rot3, mov3, aim3, light3
*/
{
return _cpy(_draw3_list, _draw3_n);
}
func restore3 (view)
/* DOCUMENT restore3, view
Restore a previously saved 3D viewing transformation and lighting.
If VIEW is nil, rotate object to viewer's coordinate system.
SEE ALSO: restore3, rot3, mov3, aim3, light3
*/
{
if (!is_void(view)) view= _cpy(view);
else view= _cat(_cpy(_draw3_view), _cpy(_light3_list));
_cdr, view, _draw3_n, _cdr(_draw3_list, _draw3_n, []);
_draw3_list= view;
_undo3_set, restore3, old;
}
/* set default viewing direction if user hasn't already done so */
if (is_void(_draw3_view)) _draw3_view= _lst(unit(3), [0.,0.,0.], []);
_draw3_nv= _len(_draw3_view);
/* ------------------------------------------------------------------------ */
func light3 (ambient=,diffuse=,specular=,spower=,sdir=)
/* DOCUMENT light3, ambient=a_level,
diffuse=d_level,
specular=s_level,
spower=n,
sdir=xyz
Sets lighting properties for 3D shading effects.
A surface will be shaded according to its to its orientation
relative to the viewing direction.
The ambient level A_LEVEL is a light level (arbitrary units)
that is added to every surface independent of its orientation.
The diffuse level D_LEVEL is a light level which is proportional
to cos(theta), where theta is the angle between the surface
normal and the viewing direction, so that surfaces directly
facing the viewer are bright, while surfaces viewed edge on are
unlit (and surfaces facing away, if drawn, are shaded as if they
faced the viewer).
The specular level S_LEVEL is a light level proportional to a high
power spower=N of 1+cos(alpha), where alpha is the angle between
the specular reflection angle and the viewing direction. The light
source for the calculation of alpha lies in the direction XYZ (a
3 element vector) in the viewer's coordinate system at infinite
distance. You can have ns light sources by making S_LEVEL, N, and
XYZ (or any combination) be vectors of length ns (3-by-ns in the
case of XYZ). (See source code for specular_hook function
definition if powers of 1+cos(alpha) aren't good enough for you.)
With no arguments, return to the default lighting.
EXAMPLES:
light3, diffuse=.1, specular=1., sdir=[0,0,-1]
(dramatic "tail lighting" effect)
light3, diffuse=.5, specular=1., sdir=[1,.5,1]
(classic "over your right shoulder" lighting)
light3, ambient=.1,diffuse=.1,specular=1.,
sdir=[[0,0,-1],[1,.5,1]],spower=[4,2]
(two light sources combining previous effects)
SEE ALSO: rot3, save3, restore3
*/
{
old= _cpy(_cdr(_draw3_list,_draw3_nv),5);
flags= 0;
if (!is_void(ambient)) {
if (dimsof(ambient)(1)) error, "ambient light level must be scalar";
flags|= 1;
_car, _draw3_list, _draw3_nv+1, double(ambient);
}
if (!is_void(diffuse)) {
if (dimsof(diffuse)(1)) error, "diffuse light level must be scalar";
flags|= 2;
_car, _draw3_list, _draw3_nv+2, double(diffuse);
}
if (!is_void(specular)) flags|= 4;
else specular= _car(_draw3_list, _draw3_nv+3);
if (!is_void(spower)) flags|= 8;
else spower= _car(_draw3_list, _draw3_nv+4);
if (!is_void(sdir)) {
dims= dimsof(sdir);
if (dims(1)<1 || dims(2)!=3)
error, "lighting direction must be 3 vector or 3-by-ns array"
flags|= 16;
} else {
sdir= _car(_draw3_list, _draw3_nv+5);
}
if (flags&28) {
if (is_void(dimsof(specular,spower,sdir(1,..))))
error, "specular, spower, and sdir not conformable";
if (flags&4) _car, _draw3_list, _draw3_nv+3, double(specular);
if (flags&8) _car, _draw3_list, _draw3_nv+4, spower;
if (flags&16) _car, _draw3_list, _draw3_nv+5, double(sdir);
}
if (!flags) {
for (i=1 ; i<=5 ; ++i)
_car, _draw3_list, _draw3_nv+i, _car(_light3_list,i);
}
_undo3_set, _light3, old;
}
func _light3 (arg)
{
for (i=1 ; i<=5 ; ++i)
_car, _draw3_list, _draw3_nv+i, _car(arg,i);
}
/* set default values if user hasn't already done so */
if (is_void(_light3_ambient)) _light3_ambient= 0.2;
if (is_void(_light3_diffuse)) _light3_diffuse= 1.0;
if (is_void(_light3_specular)) _light3_specular= 0.0;
if (is_void(_light3_spower)) _light3_spower= 2;
if (is_void(_light3_sdir)) _light3_sdir= [1.0, 0.5, 1.0]/sqrt(2.25);
_light3_list= _lst(_light3_ambient,_light3_diffuse,_light3_specular,
_light3_spower,_light3_sdir);
func get3_light (xyz, nxyz)
/* DOCUMENT get3_light(xyz, nxyz)
or get3_light(xyz)
return 3D lighting for polygons with vertices XYZ. If NXYZ is
specified, XYZ should be 3-by-sum(nxyz), with NXYZ being the
list of numbers of vertices for each polygon (as for the plfp
function). If NXYZ is not specified, XYZ should be a quadrilateral
mesh, 3-by-ni-by-nj (as for the plf function). In the first case,
the return value is numberof(NXYZ); in the second case, the
return value is (ni-1)-by-(nj-1).
The parameters of the lighting calculation are set by the
light3 function.
SEE ALSO: light3, set3_object, get3_normal, get3_centroid
*/
{
list= _cdr(_draw3_list, _draw3_nv);
ambient= _nxt(list);
diffuse= _nxt(list);
specular= _nxt(list);
spower= _nxt(list);
sdir= _nxt(list);
/* get normal */
normal= get3_normal(xyz, nxyz);
/* get direction to viewer's eye (camera) */
zc= _getzc3();
if (is_void(zc)) {
view= [0.,0.,1.];
} else {
view= [0.,0.,zc]-get3_centroid(xyz, nxyz);
m1= abs(view(1,..),view(2,..),view(3,..))(-,..);
m1= m1 + (m1==0.0);
view/= m1;
}
/* do lighting calculation */
nv= (normal*view)(sum,..);
light= ambient + diffuse*abs(nv);
if (anyof(specular)) {
sdir= sdir(,*);
sdir/= abs(sdir(1,),sdir(2,),sdir(3,))(-,);
sv= sdir(+,*)*view(+,..);
sn= sdir(+,*)*normal(+,..);
m1= max(sn*nv(-,) - 0.5*sv + 0.5, 1.e-30); /* max(1+cos(alpha),0) */
if (is_func(specular_hook))
m1= specular_hook(m1, abs(nv)(-,..), spower);
else
m1= m1^spower;
light+= (specular(*)*m1)(sum,..);
}
return light;
}
func get3_normal (xyz, nxyz)
/* DOCUMENT get3_normal(xyz, nxyz)
or get3_normal(xyz)
return 3D normals for polygons with vertices XYZ. If NXYZ is
specified, XYZ should be 3-by-sum(nxyz), with NXYZ being the
list of numbers of vertices for each polygon (as for the plfp
function). If NXYZ is not specified, XYZ should be a quadrilateral
mesh, 3-by-ni-by-nj (as for the plf function). In the first case,
the return value is 3-by-numberof(NXYZ); in the second case, the
return value is 3-by-(ni-1)-by-(nj-1).
The normals are constructed from the cross product of the lines
joining the midpoints of two edges which as nearly quarter the
polygon as possible (the medians for a quadrilateral). No check
is made that these not be parallel; the returned "normal" is
[0,0,0] in that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
coplanar, that case. Also, if the polygon vertices are not
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