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On Thu, 09 May 2002 18:08:14 +0200, "Thorsten Froehlich" <tho### [at] trf de>
wrote:
> Only plain and simple source code, based on the available sphere_sweep code
> that can be found in MegaPOV, if contributed by someone _soon_, will fix the
> problem in the initial 3.5 release. The code was already been broken in the
> original patch :-( Its author apparently did not know a good way how to fix
> it either, so don't expect magic from us!
I have not noticed any announcement that somebody started to code this so I
used some part of my night to prepare code. Some notes:
- I did it completly without parser/compiler so it is not verified for syntax
(in particular I wrote something in C long time ago and I don't remeber
referencing rules)
- I was tired (but enthusiastic about it)
- I hope it isn't too late and used spline equations are correct
- I added some helper functions and made note how it could be improved by
adding Bound union of boxes to additionaly optimize intersection test
- I used MEGAPOV 0.6a source
// *******************************************************************
DBL Compute_B_Spline_Value(DBL t)
{
// should be best to code this using already defined B_Matrix
return 1/6*(-p0+3*p1-3*p2+p3)*t^3
+1/2*(p0-2*p1+p2)*t^2
+1/2*(-p0+p2)*t
+1/6*(p0+4*p1+p2);
}
void Compute_Min_Max_B_Spline(DBL p0,p1,p2,p3,*minp,*maxp)
{
DBL a,b,c,delta;
// first derivative of spline equation is
// 1/2*(-p0+3*p1-3*p2+p3)*t^2+(p0-2*p1+p2)*t-1/2*p0+1/2*p2
a=1/2*(-p0+3*p1-3*p2+p3);
b=p0-2*p1+p2;
c=(-p0+p2)/2;
d=b*b-4*a*c;
if ((d<0)||(a==0)) // for unexpected errors return the biggest bbox
{
t1=0;
t2=1;
}
else
{
// parameter for extremas
t1=(-b-sqrt(d))/(2*a);
t2=(-b+sqrt(d))/(2*a);
// parameter should be clipped to visible part of segment
t1=min(max(t1,0),1);
t2=min(max(t2,0),1);
}
t1 = Compute_B_Spline_Value(t1);
t2 = Compute_B_Spline_Value(t2);
minp = min( t1, t2 );
maxp = max( t1, t2 );
}
DBL Compute_Catmull_Rom_Spline_Value(DBL t)
{
// should be best to code this using already defined Catmull_Rom_Matrix
return ((2*p1)+(-p0+p2)*t+(2*p0-5*p1+4*p2-p3)*t^2+(-p0+3*p1-3*p2+p3)*t^3)/2;
}
void Compute_Min_Max_Catmull_Rom_Spline(DBL p0,p1,p2,p3,*minp,*maxp)
{
DBL a,b,c,delta;
// first derivative of spline equation is
// -1/2*p0+1/2*p2+(2*p0-5*p1+4*p2-p3)*t+3/2*(-p0+3*p1-3*p2+p3)*t^2
a=3*(-p0+3*p1-3*p2+p3)/2;
b=2*p0-5*p1+4*p2-p3;
c=(-p0+p2)/2;
d=b*b-4*a*c;
if ((d<0)||(a==0)) // for unexpected errors return the biggest bbox
{
t1=0;
t2=1;
}
else
{
// parameter for extremas
t1=(-b-sqrt(d))/(2*a);
t2=(-b+sqrt(d))/(2*a);
// parameter should be clipped to visible part of segment
t1=min(max(t1,0),1);
t2=min(max(t2,0),1);
}
t1 = Compute_Catmull_Rom_Spline_Value(t1);
t2 = Compute_Catmull_Rom_Spline_Value(t2);
minp = min( t1, t2 );
maxp = max( t1, t2 );
}
void Compute_Sphere_Sweep_BBox(Sphere_Sweep)
SPHERE_SWEEP *Sphere_Sweep;
{
VECTOR mins,maxs,segmins,segmaxs;
int i,number_of_segments;
DBL min_radius,max_radius;
if( Sphere_Sweep->Interpolation == LINEAR_SPLINE)
number_of_segments=Sphere_Sweep->Num_Modeling_Spheres-1;
else
number_of_segments=Sphere_Sweep->Num_Modeling_Spheres-3;
// set initial value for general bbox extents
// to one of "visible" control points of object
Assign_Vector( mins , Sphere_Sweep->Modeling_Sphere[1].Center );
Assign_Vector( maxs , Sphere_Sweep->Modeling_Sphere[1].Center );
for (i = 0; i < number_of_segments; i++)
{
// set initial value for local bbox extents
// to one of "visible" control points of segment
Assign_Vector( segmins , Sphere_Sweep->Modeling_Sphere[i+1].Center );
Assign_Vector( segmaxs , Sphere_Sweep->Modeling_Sphere[i+1].Center );
switch (Sphere_Sweep->Interpolation)
{
case B_SPLINE:
Compute_Min_Max_B_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Center[X],
Sphere_Sweep->Modeling_Sphere[i+1].Center[X],
Sphere_Sweep->Modeling_Sphere[i+2].Center[X],
Sphere_Sweep->Modeling_Sphere[i+3].Center[X],
segmins[X],
segmaxs[X]
)
Compute_Min_Max_B_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Center[Y],
Sphere_Sweep->Modeling_Sphere[i+1].Center[Y],
Sphere_Sweep->Modeling_Sphere[i+2].Center[Y],
Sphere_Sweep->Modeling_Sphere[i+3].Center[Y],
segmins[Y],
segmaxs[Y]
)
Compute_Min_Max_B_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Center[Z],
Sphere_Sweep->Modeling_Sphere[i+1].Center[Z],
Sphere_Sweep->Modeling_Sphere[i+2].Center[Z],
Sphere_Sweep->Modeling_Sphere[i+3].Center[Z],
segmins[Z],
segmaxs[Z]
)
Compute_Min_Max_B_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Radius,
Sphere_Sweep->Modeling_Sphere[i+1].Radius,
Sphere_Sweep->Modeling_Sphere[i+2].Radius,
Sphere_Sweep->Modeling_Sphere[i+3].Radius,
min_radius,
max_radius
)
break;
case CATMULL_ROM_SPLINE:
Compute_Min_Max_Catmull_Rom_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Center[X],
Sphere_Sweep->Modeling_Sphere[i+1].Center[X],
Sphere_Sweep->Modeling_Sphere[i+2].Center[X],
Sphere_Sweep->Modeling_Sphere[i+3].Center[X],
segmins[X],
segmaxs[X]
)
Compute_Min_Max_Catmull_Rom_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Center[Y],
Sphere_Sweep->Modeling_Sphere[i+1].Center[Y],
Sphere_Sweep->Modeling_Sphere[i+2].Center[Y],
Sphere_Sweep->Modeling_Sphere[i+3].Center[Y],
segmins[Y],
segmaxs[Y]
)
Compute_Min_Max_Catmull_Rom_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Center[Z],
Sphere_Sweep->Modeling_Sphere[i+1].Center[Z],
Sphere_Sweep->Modeling_Sphere[i+2].Center[Z],
Sphere_Sweep->Modeling_Sphere[i+3].Center[Z],
segmins[Z],
segmaxs[Z]
)
Compute_Min_Max_Catmull_Rom_Spline(
Sphere_Sweep->Modeling_Sphere[I ].Radius,
Sphere_Sweep->Modeling_Sphere[i+1].Radius,
Sphere_Sweep->Modeling_Sphere[i+2].Radius,
Sphere_Sweep->Modeling_Sphere[i+3].Radius,
min_radius,
max_radius
)
break;
case LINEAR_SPLINE:
segmins[X] = min( segmins[X],
Sphere_Sweep->Modeling_Sphere[i].Center[X] );
segmins[Y] = min( segmins[Y],
Sphere_Sweep->Modeling_Sphere[i].Center[Y] );
segmins[Z] = min( segmins[Z],
Sphere_Sweep->Modeling_Sphere[i].Center[Z] );
segmaxs[X] = max( segmins[X],
Sphere_Sweep->Modeling_Sphere[i].Center[X] );
segmaxs[Y] = max( segmins[Y],
Sphere_Sweep->Modeling_Sphere[i].Center[Y] );
segmaxs[Z] = max( segmins[Z],
Sphere_Sweep->Modeling_Sphere[i].Center[Z] );
max_radius = max( Sphere_Sweep->Modeling_Sphere[i].Radius ,
Sphere_Sweep->Modeling_Sphere[i+1].Radius );
break;
}
// consider maximal value of radius
mins[X] = mins[X]-max_radius;
mins[Y] = mins[Y]-max_radius;
mins[Z] = mins[Z]-max_radius;
maxs[X] = maxs[X]+max_radius;
maxs[Y] = maxs[Y]+max_radius;
maxs[Z] = maxs[Z]+max_radius;
// here you can create box{mins maxs} object as bounding object
// of current segment - for further optimization union of bounding
// objects can be used as Bound field of current sphere_sweep
// compare segment extents with object extents
mins[X] = min( segmins[X], mins[X] );
mins[Y] = min( segmins[Y], mins[Y] );
mins[Z] = min( segmins[Z], mins[Z] );
maxs[X] = max( segmins[X], maxs[X] );
maxs[Y] = max( segmins[Y], maxs[Y] );
maxs[Z] = max( segmins[Z], maxs[Z] );
}
Make_BBox_from_min_max(Sphere_Sweep->BBox, mins, maxs);
if (Sphere_Sweep->Trans != NULL)
{
Recompute_BBox(&Sphere_Sweep->BBox, Sphere_Sweep->Trans);
}
}
// *******************************************************************
ABX
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