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CBSP_AUX.C
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1991-06-02
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/******************************************************************************
* CBsp-Aux.c - Bspline curve auxilary routines. *
*******************************************************************************
* 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"
/******************************************************************************
* Given a bspline curve - subdivide it into two at the given parametric value.*
* Returns pointer to first curve in a list of two curves (subdivided ones). *
* The subdivision is achieved by inserting (order-1) knot at the given param. *
* value t and spliting the control polygon and knot vector at that point. *
******************************************************************************/
CagdCrvStruct *BspCrvSubdivAtParam(CagdCrvStruct *Crv, CagdRType t)
{
CagdBType
IsNotRational = !CAGD_IS_RATIONAL_CRV(Crv);
int j,
k = Crv -> Order,
Len = Crv -> Length,
KVLen = k + Len,
Index1 = BspKnotLastIndexL(Crv -> KnotVector, KVLen, t),
Index2 = BspKnotFirstIndexG(Crv -> KnotVector, KVLen, t),
MaxCoord = CAGD_NUM_OF_PT_COORD(Crv -> PType);
CagdCrvStruct
*RefinedCrv = BspCrvKnotInsertNSame(Crv, t, k - 1),
*LCrv = BspCrvNew(Index1 + 1, k, Crv -> PType),
*RCrv = BspCrvNew(Len - Index2 + k, k, Crv -> PType);
/* Copy Curve into LCrv. */
for (j = IsNotRational; j <= MaxCoord; j++)
GEN_COPY(LCrv -> Points[j],
RefinedCrv -> Points[j],
sizeof(CagdRType) * (Index1 + 1));
GEN_COPY(LCrv -> KnotVector,
RefinedCrv -> KnotVector,
sizeof(CagdRType) * (Index1 + k));
/* Close the knot vector with multiplicity Order: */
LCrv -> KnotVector[Index1 + k] = LCrv -> KnotVector[Index1 + k - 1];
/* Copy Curve into RCrv. */
for (j = IsNotRational; j <= MaxCoord; j++)
GEN_COPY(RCrv -> Points[j],
&RefinedCrv -> Points[j][Index1],
sizeof(CagdRType) * (Len - Index2 + k));
GEN_COPY(&RCrv -> KnotVector[1],
&RefinedCrv -> KnotVector[Index1 + 1],
sizeof(CagdRType) * (Len - Index2 + k + k - 1));
/* Make sure knot vector starts with multiplicity Order: */
RCrv -> KnotVector[0] = RCrv -> KnotVector[1];
LCrv -> Pnext = RCrv;
CagdCrvFree(RefinedCrv);
return LCrv;
}
/******************************************************************************
* Return a new curve, identical to the original but with one degree higher *
******************************************************************************/
CagdCrvStruct *BspCrvDegreeRaise(CagdCrvStruct *Crv)
{
CagdBType
IsNotRational = !CAGD_IS_RATIONAL_CRV(Crv);
int i, i2, j, RaisedLen,
Order = Crv -> Order,
Length = Crv -> Length,
MaxCoord = CAGD_NUM_OF_PT_COORD(Crv -> PType);
CagdCrvStruct *RaisedCrv;
if (Order > 2) {
FATAL_ERROR(CAGD_ERR_NOT_IMPLEMENTED);
return NULL;
}
/* If curve is linear, degree raising means basically to increase the */
/* knot multiplicity of each segment by one and add a middle point for */
/* each such segment. */
RaisedLen = Length * 2 - 1;
RaisedCrv = BspCrvNew(RaisedLen, Order + 1, Crv -> PType);
/* Update the control polygon; */
for (j = IsNotRational; j <= MaxCoord; j++) /* First point. */
RaisedCrv -> Points[j][0] = Crv -> Points[j][0];
for (i = 1, i2 = 1; i < Length; i++, i2 += 2)
for (j = IsNotRational; j <= MaxCoord; j++) {
RaisedCrv -> Points[j][i2] =
Crv -> Points[j][i-1] * 0.5 + Crv -> Points[j][i] * 0.5;
RaisedCrv -> Points[j][i2 + 1] = Crv -> Points[j][i];
}
/* Update the knot vector. */
for (i = 0; i < 3; i++)
RaisedCrv -> KnotVector[i] = Crv -> KnotVector[0];
for (i = 2, j = 3; i < Length; i++, j += 2)
RaisedCrv -> KnotVector[j] = RaisedCrv -> KnotVector[j + 1] =
Crv -> KnotVector[i];
for (i = j; i < j + 3; i++)
RaisedCrv -> KnotVector[i] = Crv -> KnotVector[Length];
return RaisedCrv;
}
/******************************************************************************
* Return a normalized vector, equal to the tangent to Crv at parameter t. *
* Algorithm: insert (order - 1) knots and return control polygon tangent. *
******************************************************************************/
CagdVecStruct *BspCrvTangent(CagdCrvStruct *Crv, CagdRType t)
{
static CagdVecStruct P2;
CagdVecStruct P1;
CagdRType TMin, TMax;
int k = Crv -> Order,
Len = Crv -> Length,
Index = BspKnotLastIndexL(Crv -> KnotVector, k + Len, t);
CagdPointType
PType = Crv -> PType;
CagdCrvStruct *RefinedCrv;
if (!BspKnotParamInDomain(Crv -> KnotVector, Len, k, t))
FATAL_ERROR(CAGD_ERR_T_NOT_IN_CRV);
BspCrvDomain(Crv, &TMin, &TMax);
if (APX_EQ(t, TMin)) {
/* Use Crv starting tangent direction. */
CagdCoerceToE3(P1.Vec, Crv -> Points, 0, PType);
CagdCoerceToE3(P2.Vec, Crv -> Points, 1, PType);
}
else if (APX_EQ(t, TMax)) {
/* Use Crv ending tangent direction. */
CagdCoerceToE3(P1.Vec, Crv -> Points, Len - 2, PType);
CagdCoerceToE3(P2.Vec, Crv -> Points, Len - 1, PType);
}
else {
RefinedCrv = BspCrvKnotInsertNSame(Crv, t, k - 1);
CagdCoerceToE3(P1.Vec, RefinedCrv -> Points, Index, PType);
CagdCoerceToE3(P2.Vec, RefinedCrv -> Points, Index + 1, PType);
CagdCrvFree(RefinedCrv);
}
CAGD_SUB_VECTOR(P2, P1);
CAGD_NORMALIZE_VECTOR(P2); /* Normalize the vector. */
return &P2;
}
/******************************************************************************
* Return a normalized vector, equal to the binormal to Crv at parameter t. *
* Algorithm: insert (order - 1) knots and using 3 consecutive control points *
* at the refined location (p1, p2, p3), compute to binormal to be the cross *
* product of the two vectors (p1 - p2) and (p2 - p3). *
******************************************************************************/
CagdVecStruct *BspCrvBiNormal(CagdCrvStruct *Crv, CagdRType t)
{
static CagdVecStruct P3;
CagdVecStruct P1, P2;
CagdRType TMin, TMax;
int k = Crv -> Order,
Len = Crv -> Length,
Index = BspKnotLastIndexL(Crv -> KnotVector, k + Len, t);
CagdPointType
PType = Crv -> PType;
CagdCrvStruct *RefinedCrv;
if (!BspKnotParamInDomain(Crv -> KnotVector, Len, k, t))
FATAL_ERROR(CAGD_ERR_T_NOT_IN_CRV);
/* Can not compute for linear curves. */
if (k <= 2) return NULL;
BspCrvDomain(Crv, &TMin, &TMax);
if (APX_EQ(t, TMin)) {
/* Use Crv starting tangent direction. */
CagdCoerceToE3(P1.Vec, Crv -> Points, 0, PType);
CagdCoerceToE3(P2.Vec, Crv -> Points, 1, PType);
CagdCoerceToE3(P3.Vec, Crv -> Points, 2, PType);
}
else if (APX_EQ(t, TMax)) {
/* Use Crv ending tangent direction. */
CagdCoerceToE3(P1.Vec, Crv -> Points, Len - 3, PType);
CagdCoerceToE3(P2.Vec, Crv -> Points, Len - 2, PType);
CagdCoerceToE3(P3.Vec, Crv -> Points, Len - 1, PType);
}
else {
RefinedCrv = BspCrvKnotInsertNSame(Crv, t, k - 1);
CagdCoerceToE3(P1.Vec, RefinedCrv -> Points, Index, PType);
CagdCoerceToE3(P2.Vec, RefinedCrv -> Points, Index + 1, PType);
CagdCoerceToE3(P3.Vec, RefinedCrv -> Points, Index + 2, PType);
CagdCrvFree(RefinedCrv);
}
CAGD_SUB_VECTOR(P1, P2);
CAGD_SUB_VECTOR(P2, P3);
CROSS_PROD(P3.Vec, P1.Vec, P2.Vec);
if ((t = CAGD_LEN_VECTOR(P3)) < EPSILON)
return NULL;
else
CAGD_DIV_VECTOR(P3, t); /* Normalize the vector. */
return &P3;
}
/******************************************************************************
* Return a normalized vector, equal to the normal to Crv at parameter t. *
* Algorithm: returns the cross product of the curve tangent and binormal. *
******************************************************************************/
CagdVecStruct *BspCrvNormal(CagdCrvStruct *Crv, CagdRType t)
{
static CagdVecStruct N, *T, *B;
T = BspCrvTangent(Crv, t);
B = BspCrvBiNormal(Crv, t);
if (T == NULL || B == NULL) return NULL;
CROSS_PROD(N.Vec, T -> Vec, B -> Vec);
CAGD_NORMALIZE_VECTOR(N); /* Normalize the vector. */
return &N;
}
/******************************************************************************
* Return a new curve, equal to the derived curve. If the original curve is *
* rational, NULL is return (curve must be non-rational for this one). *
* Let old control polygon be P(i), i = 0 to k-1, and Q(i) be new one then: *
* Q(i) = (k - 1) * P(i+1) - P(i), i = 0 to k-2. *
******************************************************************************/
CagdCrvStruct *BspCrvDerive(CagdCrvStruct *Crv)
{
CagdBType
IsNotRational = !CAGD_IS_RATIONAL_CRV(Crv);
int i, j,
k = Crv -> Order,
Len = Crv -> Length,
MaxCoord = CAGD_NUM_OF_PT_COORD(Crv -> PType);
CagdCrvStruct *DerivedCrv;
if (!IsNotRational || k < 3)
FATAL_ERROR(CAGD_ERR_RAT_LIN_NO_SUPPORT);
DerivedCrv = BspCrvNew(Len - 1, k - 1, Crv -> PType);
for (i = 0; i < Len - 1; i++)
for (j = IsNotRational; j <= MaxCoord; j++)
DerivedCrv -> Points[j][i] =
(k - 1) * (Crv -> Points[j][i+1] - Crv -> Points[j][i]);
GEN_COPY(DerivedCrv -> KnotVector,
&Crv -> KnotVector[1],
sizeof(CagdRType) * (k + Len - 2));
return DerivedCrv;
}