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CAGD_LIB
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CBZREVAL.C
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C/C++ Source or Header
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1991-05-18
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9KB
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236 lines
/******************************************************************************
* CBzrEval.c - Bezier curves handling routines - evaluation routines. *
*******************************************************************************
* Written by Gershon Elber, Mar. 90. *
******************************************************************************/
#ifdef __MSDOS__
#include <stdlib.h>
#endif /* __MSDOS__ */
#include <ctype.h>
#include <stdio.h>
#include <string.h>
#include "cagd_loc.h"
static int BezierCacheEnabled = FALSE;
static int CacheFineNess = 0, PowerCacheFineNess;
static CagdRType *BezierCache[CAGD_MAX_BEZIER_CACHE_ORDER + 1]
[CAGD_MAX_BEZIER_CACHE_ORDER + 1];
static int IChooseK[CAGD_MAX_BEZIER_CACHE_ORDER + 1]
[CAGD_MAX_BEZIER_CACHE_ORDER + 1] =
{
{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0 },
{ 1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0 },
{ 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 0 },
{ 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0 },
{ 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0 },
{ 1, 7, 21, 35, 35, 21, 7, 1, 0, 0, 0 },
{ 1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0 },
{ 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0 },
{ 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 }
};
static CagdRType BzrCrvEvalFuncAux(int i, int k, CagdRType t);
/******************************************************************************
* Sets the bezier sampling cache - if enabled, a bezier can be evaluated *
* directly from pre sampled basis function. *
******************************************************************************/
void BzrCrvSetCache(int FineNess, CagdBType EnableCache)
{
int i, j, k;
if (BezierCacheEnabled == EnableCache && FineNess == CacheFineNess)
return;
if (BezierCacheEnabled) {
/* Free old cache if was one. */
for (k = 2; k <= CAGD_MAX_BEZIER_CACHE_ORDER; k++)
for (i = 0; i < k; i++)
if (BezierCache[k][i] != NULL) {
CagdFree((VoidPtr) BezierCache[k][i]);
BezierCache[k][i] = NULL;
}
}
if ((BezierCacheEnabled = EnableCache) != FALSE) {
/* Allocate the new cache and initalize it: */
if (FineNess < 2) FineNess = 2;
if (FineNess > CAGD_MAX_BEZIER_CACHE_FINENESS)
FineNess = CAGD_MAX_BEZIER_CACHE_FINENESS;
CacheFineNess = FineNess;
PowerCacheFineNess = 1 << FineNess;
for (k = 2; k <= CAGD_MAX_BEZIER_CACHE_ORDER; k++)/* For all orders. */
for (i = 0; i < k; i++) { /* Allocate and set all basis func. */
BezierCache[k][i] = (CagdRType *)
CagdMalloc(sizeof(CagdRType) * PowerCacheFineNess);
for (j = 0; j < PowerCacheFineNess; j++)
BezierCache[k][i][j] = BzrCrvEvalFuncAux(i, k,
((CagdRType) j) / (PowerCacheFineNess - 1));
}
}
}
/******************************************************************************
* Assumes Vec holds control points for scalar bezier curve of order Order, *
* and evaluates and returns that curve value at parameter value t. *
* Vec is incremented by VecInc (usually by 1) after each iteration. *
******************************************************************************/
CagdRType BzrCrvEvalVecAtParam(CagdRType *Vec, int VecInc, int Order, CagdRType t)
{
int i;
CagdRType R = 0.0;
if (VecInc == 1)
for (i = 0; i < Order; i++)
R += BzrCrvEvalFuncAux(i, Order, t) * *Vec++;
else
for (i = 0; i < Order; i++) {
R += BzrCrvEvalFuncAux(i, Order, t) * *Vec;
Vec += VecInc;
}
return R;
}
/******************************************************************************
* Returns a pointer to a static data, holding the value of the curve at given *
* parametric location t. The curve is assumed to be Bezier. *
******************************************************************************/
CagdRType *BzrCrvEvalAtParam(CagdCrvStruct *Crv, CagdRType t)
{
static CagdRType Pt[CAGD_MAX_PT_COORD];
CagdBType
IsNotRational = !CAGD_IS_RATIONAL_CRV(Crv);
int i, j,
k = Crv -> Order,
MaxCoord = CAGD_NUM_OF_PT_COORD(Crv -> PType);
CagdRType B;
for (j = IsNotRational; j <= MaxCoord; j++) Pt[j] = 0.0;
for (i = 0; i < k; i++) {
B = BzrCrvEvalFuncAux(i, k, t);
for (j = IsNotRational; j <= MaxCoord; j++)
Pt[j] += B * Crv -> Points[j][i];
}
return Pt;
}
/******************************************************************************
* Samples the curves at FineNess location equally spaced in the Bezier *
* parametric domain [0..1]. If Cache is enabled, and FineNess is power of *
* two, upto or equal to CacheFineNess, the cache is used, otherwise the *
* points are evaluated manually for each of the samples. *
* Data is saved at the Points array of vectors (according to Curve PType), *
* each vector is assumed to be allocated for FineNess CagdRType points. *
******************************************************************************/
void BzrCrvEvalToPolyline(CagdCrvStruct *Crv, int FineNess,
CagdRType *Points[])
{
CagdBType
UseCache = BezierCacheEnabled && FineNess == CacheFineNess,
IsNotRational = !CAGD_IS_RATIONAL_CRV(Crv);
int i, j, Count,
k = Crv -> Order,
MaxCoord = CAGD_NUM_OF_PT_COORD(Crv -> PType);
CagdRType B;
if (UseCache) {
for (Count = 0; Count < PowerCacheFineNess; Count++) {
for (j = IsNotRational; j <= MaxCoord; j++) Points[j][Count] = 0.0;
for (i = 0; i < k; i++) {
B = BezierCache[k][i][Count];
for (j = IsNotRational; j <= MaxCoord; j++)
Points[j][Count] += B * Crv -> Points[j][i];
}
}
}
else {
FineNess = 1 << FineNess;
for (Count = 0; Count < FineNess; Count++) {
for (j = IsNotRational; j <= MaxCoord; j++) Points[j][Count] = 0.0;
for (i = 0; i < k; i++) {
B = BzrCrvEvalFuncAux(i, k,
((CagdRType) Count) / (FineNess - 1));
for (j = IsNotRational; j <= MaxCoord; j++)
Points[j][Count] += Crv -> Points[j][i] * B;
}
}
}
}
/******************************************************************************
* Evaluate the i bezier function of order k, at parametric value t *
* (t in [0..1]). *
* This function is: i k - i - 1 i *
* Bi,k(t) = ( ) * t * (1 - t) *
* k *
******************************************************************************/
static CagdRType BzrCrvEvalFuncAux(int i, int k, CagdRType t)
{
if (APX_EQ(t, 0.0))
return (CagdRType) (i == 0);
else if (APX_EQ(t, 1.0))
return (CagdRType) (i == k - 1);
else
return (CagdRType) IChooseK[k - 1][i] *
pow(1.0 - t, k - i - 1.0) * pow(t, (CagdRType) i);
}
#ifdef K_CHOOSE_I_GEN
/******************************************************************************
* Evaluate the following: *
* k k! *
* ( ) = ------------- *
* i i! * (k - i)! *
******************************************************************************/
static int IChooseKGenOne(int i, int k)
{
int j;
long c = 1;
if ((k >> 1) > i) { /* i is less than half of k: */
for (j = k - i + 1; j <= k; j++) c *= j;
for (j = 2; j <= i; j++) c /= j;
}
else {
for (j = i + 1; j <= k; j++) c *= j;
for (j = 2; j <= k - i; j++) c /= j;
}
return (int) c;
}
/******************************************************************************
* Evaluate IChooseK for all possiblities and print them for the *
* IChooseK table defined in the beginning of this file. *
******************************************************************************/
void IChooseKGen(void)
{
int i, j;
for (i = 0; i <= MAX_BEZIER_CACHE_ORDER; i++) {
printf(" },\n {");
for (j = 0; j <= MAX_BEZIER_CACHE_ORDER; j++)
printf(" %4d,", j <= i ? IChooseKGenOne(j ,i) : 0);
}
}
/******************************************************************************
* main to create the table in the befinning of this file. *
******************************************************************************/
void main(void)
{
IChooseKGen();
}
#endif /* K_CHOOSE_I_GEN */