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BSPCOXDB.C
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1991-05-18
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/******************************************************************************
* BspCoxDB.c - Bspline evaluation using Cox - de Boor recursive algorithm. *
*******************************************************************************
* Written by Gershon Elber, Aug. 90. *
******************************************************************************/
#ifdef __MSDOS__
#include <stdlib.h>
#endif /* __MSDOS__ */
#include <ctype.h>
#include <stdio.h>
#include <string.h>
#include "cagd_loc.h"
/******************************************************************************
* Returns a pointer to a static data, holding the value of the curve at given *
* parametric location t. The curve is assumed to be non uniform spline. *
* Uses the recursive Cox de Boor algorithm, to evaluate the spline. *
******************************************************************************/
CagdRType *BspCrvEvalCoxDeBoor(CagdCrvStruct *Crv, CagdRType t)
{
static CagdRType Pt[CAGD_MAX_PT_COORD];
CagdBType
IsNotRational = !CAGD_IS_RATIONAL_CRV(Crv);
CagdRType *p, *BasisFunc;
int i, j, l, IndexFirst,
k = Crv -> Order,
MaxCoord = CAGD_NUM_OF_PT_COORD(Crv -> PType);
BasisFunc = BspCrvCoxDeBoorBasis(Crv -> KnotVector, k, Crv -> Length,
t, &IndexFirst);
/* And finally multiply the basis functions with the control polygon. */
for (i = IsNotRational; i <= MaxCoord; i++) {
Pt[i] = 0;
p = Crv -> Points[i];
for (j = IndexFirst, l = 0; l < k; )
Pt[i] += p[j++] * BasisFunc[l++];
}
return Pt;
}
/******************************************************************************
* Returns a pointer to a vector of size order, holding values of the non zero *
* basis functions of a given curve at given parametric location t. *
* This vector SHOULD NOT BE FREED. Although it is dynamically allocated, the *
* returned pointer does not point to the beginning of this memory and it will *
* be maintained by this routine (i.e. it will be freed next time this routine *
* is called). *
* IndexFirst returns the index of first non zero basis function for given t. *
* The curve is assumed to be non uniform bspline. *
* Uses the recursive Cox de Boor algorithm, to evaluate the spline. *
* Algorithm: *
* Use the following recursion relation with B(i,0) == 1. *
* *
* t - t(i) t(i+k) - t *
* B(i,k) = --------------- B(i,k-1) + --------------- B(i+1,k-1) *
* t(i+k-1) - t(i) t(i+k) - t(i+1) *
* *
* Starting with constant spline (k == 1) only one basis func. is non zero and *
* equal to one. This is the constant spline spanning interval t(i)..t(i+1) *
* such that t(i) <= t and t(i+1) > t. We then raise this constant spline *
* to the Crv order and finding in this process all the basis functions that *
* are non zero in t for order Order. Sound limple hah!? *
******************************************************************************/
CagdRType *BspCrvCoxDeBoorBasis(CagdRType *KnotVector, int Order, int Len,
CagdRType t, int *IndexFirst)
{
static CagdRType *B = NULL;
CagdRType s1, s2, *BasisFunc;
int i, l,
KVLen = Order + Len,
Index = BspKnotLastIndexLE(KnotVector, KVLen, t);
if (!BspKnotParamInDomain(KnotVector, Len, Order, t))
FATAL_ERROR(CAGD_ERR_T_NOT_IN_CRV);
/* Starting the recursion from constant splines - one spline is non */
/* zero and is equal to one. This is the spline that starts at Index. */
/* As We are going to reference index -1 we increment the buffer by one */
/* and save 0.0 at index -1. We then initialize the constant spline */
/* values - all are zero but the one from t(i) to t(i+1). */
if (B != NULL) CagdFree((VoidPtr) B);
BasisFunc = B = (CagdRType *) CagdMalloc(sizeof(CagdRType) * (1 + Order));
*BasisFunc++ = 0.0;
if (Index >= Len + Order - 1) {
/* We are at the end of the parametric domain and this is open */
/* end comdition - simply return last point. */
for (i = 0; i < Order; i++)
BasisFunc[i] = (CagdRType) (i == Order - 1);
*IndexFirst = Len - Order;
return BasisFunc;
}
else
for (i = 0; i < Order; i++) BasisFunc[i] = (CagdRType) (i == 0);
/* Here is the tricky part. we raise these constant splines to the */
/* required order of the curve Crv for the given parameter t. There are */
/* at most order non zero function at param. value t. These functions */
/* start at Index-order+1 up to Index (order functions overwhole). */
for (i = 2; i <= Order; i++) { /* Goes through all orders... */
for (l = i - 1; l >= 0; l--) { /* And all basis funcs. of order i. */
s1 = (KnotVector[Index + l] - KnotVector[Index + l - i + 1]);
s1 = APX_EQ(s1, 0.0) ? 0.0 : (t - KnotVector[Index + l - i + 1]) / s1;
s2 = (KnotVector[Index + l + 1] - KnotVector[Index + l - i + 2]);
s2 = APX_EQ(s2, 0.0) ? 0.0 : (KnotVector[Index + l + 1] - t) / s2;
BasisFunc[l] = s1 * BasisFunc[l - 1] + s2 * BasisFunc[l];
}
}
*IndexFirst = Index - Order + 1;
return BasisFunc;
}