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|
/* $XConsortium: miNurbs.c,v 5.4 93/09/03 15:06:20 hersh Exp $ */
/*
Copyright (c) 1989, 1990, 1991 X Consortium
Permission is hereby granted, free of charge, to any person obtaining
a copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE X CONSORTIUM BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.
Except as contained in this notice, the name of the X Consortium shall
not be used in advertising or otherwise to promote the sale, use or
other dealings in this Software without prior written authorization
from the X Consortium.
Copyright 1989, 1990, 1991 by Sun Microsystems, Inc.
All Rights Reserved
Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in
supporting documentation, and that the name of Sun Microsystems
not be used in advertising or publicity pertaining to distribution
of the software without specific, written prior permission.
SUN MICROSYSTEMS DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT
SHALL SUN MICROSYSTEMS BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL
DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
SOFTWARE.
*/
#include "X.h"
#include "misc.h"
#include "miscstruct.h"
#include "PEXErr.h"
#include "PEXproto.h"
#include "PEXprotost.h"
#include "ddpex.h"
#include "ddpex3.h"
#include "miRender.h"
#include "ddpex2.h"
#include "miNurbs.h"
/*
* mtx to convert polynomial coeffs ai, to fwd basis coeffs Aj is
* D j+1 k i
* Aj = Sum [Sum (-1) * (j!/k!(j-k)!)*(j-k) ] * ai where D=degree
* i=0 k=0
*/
#if MAXORD == 4
/* Debugging is often easier if MAXORD is made small. */
double mi_nu_ptofd[MAXORD][MAXORD] = {
{ 1.0, 0.0, 0.0, 0.0},
{ 0.0, 1.0, 1.0, 1.0},
{ 0.0, 0.0, 2.0, 6.0},
{ 0.0, 0.0, 0.0, 6.0}
};
#else
double mi_nu_ptofd[MAXORD][MAXORD] = {
{ 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0},
{ 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
{ 0.0, 0.0, 2.0, 6.0, 14.0, 30.0, 62.0, 126.0, 254.0, 510.0},
{ 0.0, 0.0, 0.0, 6.0, 36.0, 150.0, 540.0, 1806.0, 5796.0, 18150.0},
{ 0.0, 0.0, 0.0, 0.0, 24.0, 240.0, 1560.0, 8400.0, 40824.0, 186480.0},
{ 0.0, 0.0, 0.0, 0.0, 0.0, 120.0, 1800.0, 16800.0, 126000.0, 834120.0},
{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 720.0, 15120.0, 191520.0, 1905120.0},
{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 5040.0, 141120.0, 2328480.0},
{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 40320.0, 1451520.0},
{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 362880.0}
};
#endif
#define HUGE 10E30
/*++
|
| Function Name: mi_nu_preprocess_knots
|
| Function Description:
|
| Note(s):
|
--*/
void
mi_nu_preprocess_knots( order, nk, knots, rp )
ddUSHORT order;
int nk;
ddFLOAT *knots;
ddFLOAT rp[][MAXORD]; /* reciprocal of knots diff */
{
double x;
register int i, j;
for ( i = 0; i < nk; i++ )
rp[i][0] = 1.0 ;
for ( j = 1; j < order; j++ ) {
for ( i = 0; i <= nk - j; i++ ) {
if ( (x = knots[i+j] - knots[i]) == 0.0 ) {
rp[i][j] = HUGE;
} else {
rp[i][j] = 1.0 / x;
}
}
}
}
/*++
|
| Function Name: mi_nu_compute_nurb_basis_function
|
| Function Description:
|
| Recursive definition of polynomial coefficients for span (0<= s <=1).
| C(i,j,k) = a*C(i,j-1,k-1) + b*C(i,j,k-1) + c*C(i+1,j-1,k-1) + d*C(i+1,j,k-1)
| a = (s(l+1) - s(l))/(s(i+k-1) - s(i)), b = (s(l) - s(i))/(s(i+k-1) - s(i))
| c = -(s(l+1) - s(l))/(s(i+k) - s(i+1)), d = (s(i+k) - s(l))/(s(i+k) - s(i+1))
|
| Note(s):
|
--*/
void
mi_nu_compute_nurb_basis_function( order, span, knots, kr, C )
ddUSHORT order;
int span;
ddFLOAT *knots;
ddFLOAT kr[][MAXORD]; /* reciprocal of knots diff */
double C[MAXORD][MAXORD];
{
int i, j, k, m, im, degree = order - 1;
double t0, t1, t2, t3;
if ( order == 2 ) {
C[0][0] = 1.0;
C[0][1] = 0.0;
C[1][0] = -1.0;
C[1][1] = 1.0;
return;
}
/* Compute the coefficients of Nik in polynomial basis, for the span
* knots[i] to knots[i+1] where s goes from 0 to 1.0
*/
t1 = knots[span+1] - knots[span];
C[0][degree] = 1.0; /* Ni1 = 1.0 within span */
for ( k = 1; k < order; k++ ) { /* recurse on order for Cj,i,k */
t0 = t1 * kr[span-k+1][k];
im = degree - k;
C[0][im] = t0 * C[0][im+1]; /* top left coeff */
for ( j = k-1; j > 0; j-- )
C[j][im] = t0 * ( C[j][im+1] - C[j-1][im+1] ); /*middle*/
C[k][im] = -t0 * C[k-1][im+1]; /* top right coeff */
for (m=k-1; m>0; m--) { /* central section */
i = span - m; /* right edge first */
im = degree - m;
C[k][im] = t1 * (kr[i][k] * C[k-1][im] - kr[i+1][k] * C[k-1][im+1]);
t2 = knots[i+k+1] - knots[span];
t3 = knots[span] - knots[i];
for ( j = k-1; j > 0; j-- ) /* then j down to 1 */
C[j][im] =
kr[i][k] * (t1 * C[j-1][im]
+ t3 * C[j][im])
+ kr[i+1][k] * (t2 * C[j][im+1] - t1 * C[j-1][im+1]);
C[0][im] = kr[i][k] * t3 * C[0][im]
+ kr[i+1][k] * t2 * C[0][im+1]; /* left edge */
}
t0 = t1 * kr[span][k]; /* bottom rt,middle coeffs */
for ( j = k; j > 0; j-- )
C[j][degree] = t0 * C[j-1][degree];
C[0][degree] = 0.0; /* bottom left coeff */
}
}
/*++
|
| Function Name: mi_nu_insert_knots
|
| Function Description:
|
| Note(s):
|
--*/
int
mi_nu_insert_knots( order, pt_type,
numinknots, oknots, opoints,
numoutknots, nknots, npoints )
ddUSHORT order;
ddPointType pt_type;
ddUSHORT numinknots;
ddFLOAT *oknots; /* original knots */
ddFLOAT *opoints; /* original control points */
int *numoutknots;
ddFLOAT *nknots; /* new knots */
ddFLOAT *npoints; /* new control points */
{
/*
* Assumptions: - inserted knots are within range of original knots.
*/
int i, k, iok, ink, mult, num_pts;
int numtmpknots;
ddFLOAT *tmpknots;
ddFLOAT alpha, alph1;
ddCoord2D *npts2;
ddCoord3D *npts3;
ddCoord4D *npts4;
/* Check to see if new knots needed. Copy and return if not. */
if ( *numoutknots <= 0 ) {
*numoutknots = numinknots;
memcpy( (char *)nknots, (char *)oknots, (int)numinknots * sizeof(ddFLOAT) );
return 1;
}
/* Copy old control points into new space. */
num_pts = numinknots - order;
if ( DD_IsVert2D(pt_type) ) {
memcpy( (char *)npoints, (char *)opoints, num_pts * sizeof(ddCoord2D));
npts2 = (ddCoord2D *)npoints;
} else if ( DD_IsVert3D(pt_type) ) {
memcpy( (char *)npoints, (char *)opoints, num_pts * sizeof(ddCoord3D));
npts3 = (ddCoord3D *)npoints;
} else if ( DD_IsVert4D(pt_type) ) {
memcpy( (char *)npoints, (char *)opoints, num_pts * sizeof(ddCoord4D));
npts4 = (ddCoord4D *)npoints;
} else return (1);
if ( !(tmpknots = (ddFLOAT *)
Xalloc( (numinknots + *numoutknots) * sizeof(float))) )
return 0;
/* Insert new knots and control points, starting from the end of the
* original lists.
*/
memcpy( (char *)tmpknots, (char *)oknots, (int)numinknots * sizeof(ddFLOAT) );
numtmpknots = numinknots;
ink = *numoutknots;
iok = numinknots - 1;
while ( ink > 0 ) {
mult = 1;
--ink;
/* Count mutiplicity of the new knot to be inserted. */
while ( ink > 0 && nknots[ink] == nknots[ink-1] ) {
++mult;
--ink;
}
/* Find position of knot(s) to insert. */
while ( iok >= 0 && tmpknots[iok] >= nknots[ink] )
--iok;
/* Move control points down to make space for inserted ones.
* Use memove so that the overlap is handled.
*/
/* note that the funky &blah[...] notation is equivalent
to blah+... since blah is a pointer. JSH 4-10-91
*/
if ( DD_IsVert2D(pt_type) )
memmove((char *)(&npts2[iok + 1 + mult]),(char *)(&npts2[iok + 1]),
((num_pts - iok) - 1) * sizeof(ddCoord2D) );
else if ( DD_IsVert3D(pt_type) )
memmove((char *)(&npts3[iok + 1 + mult]),(char *)(&npts3[iok + 1]),
((num_pts - iok) - 1) * sizeof(ddCoord3D) );
else
memmove((char *)(&npts4[iok + 1 + mult]),(char *)(&npts4[iok + 1]),
((num_pts - iok) - 1) * sizeof(ddCoord4D) );
/* Do de Boor to insert new knot with multiplicity `mult'. */
if ( DD_IsVert2D(pt_type) ) {
for ( k = 1; k <= mult; k++ ) {
/* Move pts down recursively. */
for ( i = iok + k; i > iok; i-- ) {
npts2[i].x = npts2[i-1].x;
npts2[i].y = npts2[i-1].y;
/********************************************************
if ( rat == PRATIONAL )
npts2[i].z = npts2[i-1].z;
********************************************************/
}
for ( i = iok; i > iok - order + k; i-- ) {
alpha = (nknots[ink] - tmpknots[i])
/ (tmpknots[i + order - k] - tmpknots[i]);
alph1 = 1.0 - alpha;
npts2[i].x = alpha * npts2[i].x + alph1 * npts2[i-1].x;
npts2[i].y = alpha * npts2[i].y + alph1 * npts2[i-1].y;
/********************************************************
if ( rat == PRATIONAL )
npts2[i].z = alpha * npts2[i].z + alph1 * npts2[i-1].z;
********************************************************/
}
}
} else if ( DD_IsVert3D(pt_type) ) { /* dim is 3 */
for ( k = 1; k <= mult; k++ ) {
for ( i = iok + k; i > iok; i-- ) {
npts3[i].x = npts3[i-1].x;
npts3[i].y = npts3[i-1].y;
npts3[i].z = npts3[i-1].z;
}
for ( i = iok; i > iok - order + k; i-- ) {
alpha = (nknots[ink] - tmpknots[i])
/ (tmpknots[i + order - k] - tmpknots[i]);
alph1 = 1.0 - alpha;
npts3[i].x = alpha * npts3[i].x + alph1 * npts3[i-1].x;
npts3[i].y = alpha * npts3[i].y + alph1 * npts3[i-1].y;
npts3[i].z = alpha * npts3[i].z + alph1 * npts3[i-1].z;
}
}
} else /* if ( DD_IsVert4D(pt_type) ) */ { /* dim is 4 */
for ( k = 1; k <= mult; k++ ) {
for ( i = iok + k; i > iok; i-- ) {
npts4[i].x = npts4[i-1].x;
npts4[i].y = npts4[i-1].y;
npts4[i].z = npts4[i-1].z;
npts4[i].w = npts4[i-1].w;
}
for ( i = iok; i > iok - order + k; i-- ) {
alpha = (nknots[ink] - tmpknots[i])
/ (tmpknots[i + order - k] - tmpknots[i]);
alph1 = 1.0 - alpha;
npts4[i].x = alpha * npts4[i].x + alph1 * npts4[i-1].x;
npts4[i].y = alpha * npts4[i].y + alph1 * npts4[i-1].y;
npts4[i].z = alpha * npts4[i].z + alph1 * npts4[i-1].z;
npts4[i].w = alpha * npts4[i].w + alph1 * npts4[i-1].w;
}
}
}
/* Total number of points and knots increased by `mult'. */
for ( k = numtmpknots - 1; k > iok; k-- )
tmpknots[k + mult] = tmpknots[k];
for ( k = 1; k <= mult; k++ )
tmpknots[iok + k] = nknots[ink];
numtmpknots += mult;
num_pts +=mult;
}
/* copy results into output buffers */
*numoutknots = numtmpknots; /* resulting total knots */
memcpy( (char *)nknots, (char *)tmpknots, numtmpknots * sizeof(ddFLOAT) );
free( (char *)tmpknots );
return 1;
}
|
