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#include "bltInt.h"
/*
* Quadratic spline parameters
*/
#define E1 param[0]
#define E2 param[1]
#define V1 param[2]
#define V2 param[3]
#define W1 param[4]
#define W2 param[5]
#define Z1 param[6]
#define Z2 param[7]
#define Y1 param[8]
#define Y2 param[9]
#ifdef __STDC__
static Tcl_CmdProc SplineCmd;
#endif
static INLINE double
Fabs(x)
double x;
{
return ((x < 0.0) ? -x : x);
}
/*
* -----------------------------------------------------------------------
*
* Search --
*
* Conducts a binary search for a value. This routine is called
* only if key is between x(0) and x(len - 1).
*
* Results:
* Returns the index of the largest value in xtab for which
* x[i] < key.
*
* -----------------------------------------------------------------------
*/
static int
Search(x, len, key, foundPtr)
double x[]; /* Contains the abscissas of the data
* points of interpolation. */
int len; /* Dimension of x. */
double key; /* Value whose relative position in
* x is to be located. */
int *foundPtr; /* (out) Returns 1 if s is found in
* x and 0 otherwise. */
{
int high, low, middle;
low = 0;
high = len - 1;
while (high >= low) {
middle = (high + low) / 2;
if (key > x[middle]) {
low = middle + 1;
} else if (key < x[middle]) {
high = middle - 1;
} else {
*foundPtr = 1;
return (middle);
}
}
*foundPtr = 0;
return (low);
}
/*
*-----------------------------------------------------------------------
*
* QuadChoose --
*
* Determines the case needed for the computation of the parame-
* ters of the quadratic spline.
*
* Results:
* Returns a case number (1-4) which controls how the parameters
* of the quadratic spline are evaluated.
*
*-----------------------------------------------------------------------
*/
static int
QuadChoose(x1, y1, m1, x2, y2, m2, epsilon)
double x1, y1; /* Coordinates of one of the points of
* interpolation */
double m1; /* Derivative condition at point x1, y1 */
double x2, y2; /* Coordinates of one of the points of
* interpolation */
double m2; /* Derivative condition at point x2, y2 */
double epsilon; /* Error tolerance used to distinguish
* cases when m1 or m2 is relatively
* close to the slope or twice the
* slope of the line segment joining
* the points x1, y1 and x2, y2. If
* epsilon is not 0.0, then epsilon
* should be greater than or equal to
* machine epsilon. */
{
double slope;
/* Calculate the slope of the line joining x1,y1 and x2,y2. */
slope = (y2 - y1) / (x2 - x1);
if (slope != 0.0) {
double relerr;
double mref, mref1, mref2, prod1, prod2;
prod1 = slope * m1;
prod2 = slope * m2;
/* Find the absolute values of the slopes slope, m1, and m2. */
mref = Fabs(slope);
mref1 = Fabs(m1);
mref2 = Fabs(m2);
/*
* If the relative deviation of m1 or m2 from slope is less than
* epsilon, then choose case 2 or case 3.
*/
relerr = epsilon * mref;
if ((Fabs(slope - m1) > relerr) && (Fabs(slope - m2) > relerr) &&
(prod1 >= 0.0) && (prod2 >= 0.0)) {
double prod;
prod = (mref - mref1) * (mref - mref2);
if (prod < 0.0) {
/*
* l1, the line through (x1,y1) with slope m1, and l2,
* the line through (x2,y2) with slope m2, intersect
* at a point whose abscissa is between x1 and x2.
* The abscissa becomes a knot of the spline.
*/
return 1;
}
if (mref1 > (mref * 2.0)) {
if (mref2 <= ((2.0 - epsilon) * mref)) {
return 3;
}
} else if (mref2 <= (mref * 2.0)) {
/*
* Both l1 and l2 cross the line through (x1+x2)/2.0,y1
* and (x1+x2)/2.0,y2, which is the midline of the
* rectangle formed by (x1,y1),(x2,y1), (x2,y2), and
* (x1,y2), or both m1 and m2 have signs different
* than the sign of slope, or one of m1 and m2 has
* opposite sign from slope and l1 and l2 intersect to
* the left of x1 or to the right of x2. The point
* (x1+x2)/2. is a knot of the spline.
*/
return 2;
} else if (mref1 <= ((2.0 - epsilon) * mref)) {
/*
* In cases 3 and 4, sign(m1)=sign(m2)=sign(slope).
* Either l1 or l2 crosses the midline, but not both.
* Choose case 4 if mref1 is greater than
* (2.-epsilon)*mref; otherwise, choose case 3.
*/
return 3;
}
/*
* If neither l1 nor l2 crosses the midline, the spline
* requires two knots between x1 and x2.
*/
return 4;
} else {
/*
* The sign of at least one of the slopes m1 or m2 does not
* agree with the sign of *slope*.
*/
if ((prod1 < 0.0) && (prod2 < 0.0)) {
return 2;
} else if (prod1 < 0.0) {
if (mref2 > ((epsilon + 1.0) * mref)) {
return 1;
} else {
return 2;
}
} else if (mref1 > ((epsilon + 1.0) * mref)) {
return 1;
} else {
return 2;
}
}
} else if ((m1 * m2) >= 0.0) {
return 2;
} else {
return 1;
}
}
/*
* -----------------------------------------------------------------------
*
* QuadCases --
*
* Computes the knots and other parameters of the spline on the
* interval (p1,q1).
*
*
* On input--
*
* (p1,y1) and (q1,q2) are the coordinates of the points of
* interpolation.
*
* m1 is the slope at (p1,p2).
*
* m2 is the slope at (q1,q2)
*
* ncase controls the number and location of the knots.
*
*
* On output--
*
* (v1,v2),(w1,w2),(z1,z2), and (e1,e2) are the coordinates of
* the knots and other parameters of the spline on (p1,q1).
* (e1,e2) and (y1,y2) are used only if ncase=4.
*
* -----------------------------------------------------------------------
*/
static void
QuadCases(p1, p2, m1, m2, q1, q2, param, which)
double p1, p2, m1, m2, q1, q2;
double param[];
int which;
{
if ((which == 3) || (which == 4)) { /* Parameters used in both 3 and 4 */
double mbar1, mbar2, mbar3, c1, d1, h1, j1, k1;
c1 = p1 + (q2 - p2) / m1;
d1 = q1 + (p2 - q2) / m2;
h1 = c1 * 2.0 - p1;
j1 = d1 * 2.0 - q1;
mbar1 = (q2 - p2) / (h1 - p1);
mbar2 = (p2 - q2) / (j1 - q1);
if (which == 4) { /* Case 4. */
Y1 = (p1 + c1) / 2.0;
V1 = (p1 + Y1) / 2.0;
V2 = m1 * (V1 - p1) + p2;
Z1 = (d1 + q1) / 2.0;
W1 = (q1 + Z1) / 2.0;
W2 = m2 * (W1 - q1) + q2;
mbar3 = (W2 - V2) / (W1 - V1);
Y2 = mbar3 * (Y1 - V1) + V2;
Z2 = mbar3 * (Z1 - V1) + V2;
E1 = (Y1 + Z1) / 2.0;
E2 = mbar3 * (E1 - V1) + V2;
} else { /* Case 3. */
k1 = (p2 - q2 + q1 * mbar2 - p1 * mbar1) / (mbar2 - mbar1);
if (Fabs(m1) > Fabs(m2)) {
Z1 = (k1 + p1) / 2.0;
} else {
Z1 = (k1 + q1) / 2.0;
}
V1 = (p1 + Z1) / 2.0;
V2 = p2 + m1 * (V1 - p1);
W1 = (q1 + Z1) / 2.0;
W2 = q2 + m2 * (W1 - q1);
Z2 = V2 + (W2 - V2) / (W1 - V1) * (Z1 - V1);
}
} else if (which == 2) { /* Case 2. */
Z1 = (p1 + q1) / 2.0;
V1 = (p1 + Z1) / 2.0;
V2 = p2 + m1 * (V1 - p1);
W1 = (Z1 + q1) / 2.0;
W2 = q2 + m2 * (W1 - q1);
Z2 = (V2 + W2) / 2.0;
} else { /* Case 1. */
double ztwo;
Z1 = (p2 - q2 + m2 * q1 - m1 * p1) / (m2 - m1);
ztwo = p2 + m1 * (Z1 - p1);
V1 = (p1 + Z1) / 2.0;
V2 = (p2 + ztwo) / 2.0;
W1 = (Z1 + q1) / 2.0;
W2 = (ztwo + q2) / 2.0;
Z2 = V2 + (W2 - V2) / (W1 - V1) * (Z1 - V1);
}
}
static int
QuadSelect(x1, y1, x2, y2, m1, m2, epsilon, param)
double x1, y1, x2, y2;
double m1, m2;
double epsilon;
double param[];
{
int ncase;
ncase = QuadChoose(x1, y1, m1, x2, y2, m2, epsilon);
QuadCases(x1, y1, m1, m2, x2, y2, param, ncase);
return (ncase);
}
/*
* -----------------------------------------------------------------------
*
* QuadGetImage --
*
* -----------------------------------------------------------------------
*/
INLINE static double
QuadGetImage(p1, p2, p3, x1, x2, x3)
double p1, p2, p3;
double x1, x2, x3;
{
double A, B, C;
double y;
A = x1 - x2;
B = x2 - x3;
C = x1 - x3;
y = (p1 * (A * A) + p2 * 2.0 * B * A + p3 * (B * B)) / (C * C);
return (y);
}
/*
* -----------------------------------------------------------------------
*
* QuadSpline --
*
* Finds the image of a point in x.
*
* On input
*
* x Contains the value at which the spline is evaluated.
* leftX, leftY
* Coordinates of the left-hand data point used in the
* evaluation of xvals.
* rightX, rightY
* Coordinates of the right-hand data point used in the
* evaluation of xvals.
* Z1, Z2, Y1, Y2, E2, W2, V2
* Parameters of the spline.
* ncase Controls the evaluation of the spline by indicating
* whether one or two knots were placed in the interval
* (xtabs,xtabs1).
*
* Results:
* The image of the spline at x.
*
* -----------------------------------------------------------------------
*/
static double
QuadSpline(x, leftX, leftY, rightX, rightY, param, ncase)
double x; /* Value at which spline is evaluated */
double leftX, leftY; /* Point to the left of the data point to
* be evaluated */
double rightX, rightY; /* Point to the right of the data point to
* be evaluated */
double param[]; /* Parameters of the spline */
int ncase; /* Controls the evaluation of the
* spline by indicating whether one or
* two knots were placed in the
* interval (leftX,rightX) */
{
if (ncase == 4) {
/*
* Case 4: More than one knot was placed in the interval.
*/
/*
* Determine the location of data point relative to the 1st knot.
*/
if (Y1 > x) {
return QuadGetImage(leftY, V2, Y2, Y1, x, leftX);
} else if (Y1 < x) {
/*
* Determine the location of the data point relative to
* the 2nd knot.
*/
if (Z1 > x) {
return QuadGetImage(Y2, E2, Z2, Z1, x, Y1);
} else if (Z1 < x) {
return QuadGetImage(Z2, W2, rightY, rightX, x, Z1);
} else {
return (Z2);
}
} else {
return (Y2);
}
} else {
/*
* Cases 1, 2, or 3:
*
* Determine the location of the data point relative to the
* knot.
*/
if (Z1 < x) {
return QuadGetImage(Z2, W2, rightY, rightX, x, Z1);
} else if (Z1 > x) {
return QuadGetImage(leftY, V2, Z2, Z1, x, leftX);
} else {
return (Z2);
}
}
}
/*
* -----------------------------------------------------------------------
*
* QuadSlopes --
*
* Calculates the derivative at each of the data points. The
* slopes computed will insure that an osculatory quadratic
* spline will have one additional knot between two adjacent
* points of interpolation. Convexity and monotonicity are
* preserved wherever these conditions are compatible with the
* data.
*
* Results:
* The output array "m" is filled with the derivates at each
* data point.
*
* -----------------------------------------------------------------------
*/
static void
QuadSlopes(x, y, m, len)
double x[]; /* Abscissas of the data points. */
double y[]; /* Ordinates of the data points. */
double m[]; /* (out) To be filled with the first
* derivative at each data point. */
int len; /* Number of data points (dimension of
* x, y, and m). */
{
double xbar, xmid, xhat, ydif1, ydif2;
double yxmid;
double m1, m2;
double m1s, m2s;
register int i, next, last;
m1s = m2s = m1 = m2 = 0;
for (i = 1, next = 2, last = 0; i < (len - 1); i++, next++, last++) {
/*
* Calculate the slopes of the two lines joining three
* consecutive data points.
*/
ydif1 = y[i] - y[last];
ydif2 = y[next] - y[i];
m1 = ydif1 / (x[i] - x[last]);
m2 = ydif2 / (x[next] - x[i]);
if (i == 1) {
m1s = m1, m2s = m2; /* Save slopes of starting point */
}
/*
* If one of the preceding slopes is zero or if they have opposite
* sign, assign the value zero to the derivative at the middle
* point.
*/
if ((m1 == 0.0) || (m2 == 0.0) || ((m1 * m2) <= 0.0)) {
m[i] = 0.0;
} else if (Fabs(m1) > Fabs(m2)) {
/*
* Calculate the slope by extending the line with slope m1.
*/
xbar = ydif2 / m1 + x[i];
xhat = (xbar + x[next]) / 2.0;
m[i] = ydif2 / (xhat - x[i]);
} else {
/*
* Calculate the slope by extending the line with slope m2.
*/
xbar = -ydif1 / m2 + x[i];
xhat = (x[last] + xbar) / 2.0;
m[i] = ydif1 / (x[i] - xhat);
}
}
/* Calculate the slope at the last point, x(n). */
i = len - 2;
next = len - 1;
if ((m1 * m2) < 0.0) {
m[next] = m2 * 2.0;
} else {
xmid = (x[i] + x[next]) / 2.0;
yxmid = m[i] * (xmid - x[i]) + y[i];
m[next] = (y[next] - yxmid) / (x[next] - xmid);
if ((m[next] * m2) < 0.0) {
m[next] = 0.0;
}
}
/* Calculate the slope at the first point, x(0). */
if ((m1s * m2s) < 0.0) {
m[0] = m1s * 2.0;
} else {
xmid = (x[0] + x[1]) / 2.0;
yxmid = m[1] * (xmid - x[1]) + y[1];
m[0] = (yxmid - y[0]) / (xmid - x[0]);
if ((m[0] * m1s) < 0.0) {
m[0] = 0.0;
}
}
}
/*
* -----------------------------------------------------------------------
*
* QuadEval --
*
* QuadEval controls the evaluation of an osculatory quadratic
* spline. The user may provide his own slopes at the points of
* interpolation or use the subroutine 'QuadSlopes' to calculate
* slopes which are consistent with the shape of the data.
*
* ON INPUT--
* splX must be a nondecreasing vector of points at which the
* spline will be evaluated.
* x contains the abscissas of the data points to be
* interpolated. xtab must be increasing.
* y contains the ordinates of the data points to be
* interpolated.
* m contains the slope of the spline at each point of
* interpolation.
* len number of data points (dimension of xtab and y).
* numEval is the number of points of evaluation (dimension of
* xval and yval).
* epsilon is a relative error tolerance used in subroutine
* 'QuadChoose' to distinguish the situation m(i) or
* m(i+1) is relatively close to the slope or twice
* the slope of the linear segment between xtab(i) and
* xtab(i+1). If this situation occurs, roundoff may
* cause a change in convexity or monotonicity of the
* resulting spline and a change in the case number
* provided by 'QuadChoose'. If epsilon is not equal to zero,
* then epsilon should be greater than or equal to machine
* epsilon.
* ON OUTPUT--
* splY contains the images of the points in xval.
* err is one of the following error codes:
* 0 - QuadEval ran normally.
* 1 - xval(i) is less than xtab(1) for at least one
* i or xval(i) is greater than xtab(num) for at
* least one i. QuadEval will extrapolate to provide
* function values for these abscissas.
* 2 - xval(i+1) < xval(i) for some i.
*
*
* QuadEval calls the following subroutines or functions:
* Search
* QuadCases
* QuadChoose
* QuadSpline
* -----------------------------------------------------------------------
*/
static int
QuadEval(splX, splY, x, y, m, len, splLen, epsilon)
double splX[]; /* Must be a nondecreasing vector of
* points at which the spline will be
* evaluated. */
double splY[]; /* (out) To be filled with the images
* of the points in splX. */
double x[]; /* Abscissas of the data points to
* be interpolated. X must be increasing. */
double y[]; /* Ordinates of the data points to be
* interpolated. */
double m[]; /* Slope of the spline at each point
* of interpolation. */
int len; /* Number of data points (dimension of
* X and y). */
int splLen; /* Number of points of evaluation
* (length of vectors of splX and splY). */
double epsilon; /* Relative error tolerance (see choose) */
{
int error;
register int i;
double param[10];
int ncase;
int splLast;
int start, last, prev;
/* Initialize indices and set error result */
start = 0;
splLast = splLen - 1;
error = 0;
last = len - 1;
prev = last - 1;
ncase = 1;
/*
* Determine if abscissas of new vector are non-decreasing.
*/
for (i = 1; i < splLen; i++) {
if (splX[i] < splX[i - 1]) {
return 2;
}
}
/*
* Determine if any of the points in splX are LESS than the
* abscissa of the first data point.
*/
for (i = 0; i < splLen; i++) {
if (splX[i] >= x[0]) {
break;
}
start = i + 1;
}
/*
* Determine if any of the points in splX are GREATER than the
* abscissa of the last data point.
*/
for (i = splLen - 1; i >= 0; i--) {
if (splX[i] <= x[last]) {
break;
}
splLast = i - 1;
}
if (start > 0) {
error = 1; /* Set error value to indicate that
* extrapolation has occurred. */
/*
* Calculate the images of points of evaluation whose abscissas
* are less than the abscissa of the first data point.
*/
ncase = QuadSelect(x[0], y[0], x[1], y[1], m[0], m[1], epsilon, param);
for (i = 0; i < (start - 1); i++) {
splY[i] = QuadSpline(splX[i], x[0], y[0], x[1], y[1], param, ncase);
}
if (splLen == 1) {
return (error);
}
}
if ((splLen > 1) || (splLast == (splLen - 1))) {
register int next, loc;
int found;
/*
* Search locates the interval in which the first in-range
* point of evaluation lies.
*/
loc = Search(x, len, splX[start], &found);
next = loc + 1;
/*
* If the first in-range point of evaluation is equal to one
* of the data points, assign the appropriate value from y.
* Continue until a point of evaluation is found which is not
* equal to a data point.
*/
if (found) {
do {
splY[start] = y[loc];
start++;
if (start >= splLen) {
return (error);
}
} while (splX[start - 1] == splX[start]);
for (;;) {
if (splX[start] < x[next]) {
break; /* Break out of for-loop */
}
if (splX[start] == x[next]) {
do {
splY[start] = y[next];
start++;
if (start >= splLen) {
return (error);
}
} while (splX[start] == splX[start - 1]);
}
loc++;
next++;
}
}
/*
* Calculate the images of all the points which lie within
* range of the data.
*/
if ((loc > 0) || (error != 1)) {
ncase = QuadSelect(x[loc], y[loc], x[next], y[next], m[loc],
m[next], epsilon, param);
}
for (i = start; i <= splLast; i++) {
/*
* If splX(i) - x(next) is negative, do not recalculate
* the parameters for this section of the spline since
* they are already known.
*/
if (splX[i] == x[next]) {
splY[i] = y[next];
continue;
} else if (splX[i] > x[next]) {
double delta;
/* Determine that the routine is in the correct part of
the spline. */
do {
loc++, next++;
delta = splX[i] - x[next];
} while (delta > 0.0);
if (delta < 0.0) {
ncase = QuadSelect(x[loc], y[loc], x[next], y[next], m[loc],
m[next], epsilon, param);
} else if (delta == 0.0) {
splY[i] = y[next];
continue;
}
}
splY[i] = QuadSpline(splX[i], x[loc], y[loc], x[next], y[next],
param, ncase);
}
if (splLast == (splLen - 1)) {
return (error);
}
if ((next == last) && (splX[splLast] != x[last])) {
goto noExtrapolation;
}
}
error = 1; /* Set error value to indicate that
* extrapolation has occurred. */
ncase = QuadSelect(x[prev], y[prev], x[last], y[last], m[prev], m[last],
epsilon, param);
noExtrapolation:
/*
* Calculate the images of the points of evaluation whose
* abscissas are greater than the abscissa of the last data point.
*/
for (i = (splLast + 1); i < splLen; i++) {
splY[i] = QuadSpline(splX[i], x[prev], y[prev], x[last], y[last],
param, ncase);
}
return (error);
}
/*
* -----------------------------------------------------------------------
*
* Shape preserving quadratic splines
* by D.F.Mcallister & J.A.Roulier
* Coded by S.L.Dodd & M.Roulier
* N.C.State University
*
* -----------------------------------------------------------------------
*/
/*
* Driver routine for quadratic spline package
* On input--
* X,Y Contain n-long arrays of data (x is increasing)
* XM Contains m-long array of x values (increasing)
* eps Relative error tolerance
* n Number of input data points
* m Number of output data points
* On output--
* work Contains the value of the first derivative at each data point
* ym Contains the interpolated spline value at each data point
*/
static int
QuadraticSpline(x, y, len, splX, splY, splLen, work, epsilon)
double x[], y[];
int len;
double splX[], splY[];
int splLen;
double work[];
double epsilon;
{
QuadSlopes(x, y, work, len);
return QuadEval(splX, splY, x, y, work, len, splLen, epsilon);
}
/*
* ------------------------------------------------------------------------
*
* Reference:
* Numerical Analysis, R. Burden, J. Faires and A. Reynolds.
* Prindle, Weber & Schmidt 1981 pp 112
*
* Parameters:
* x - vector of points, assumed to be sorted.
* y - vector of corresponding function values.
* splX - vector of new points.
* splY - vector of new function values.
*
* ------------------------------------------------------------------------
*/
static int
NaturalSpline(x, y, len, splX, splY, splLen, work)
double x[]; /* Vector of points in ascending order */
double y[]; /* Vector of function values f(x) */
int len;
double splX[]; /* New mapping of points */
double splY[]; /* (out) Function values f(nx) */
int splLen;
double work[]; /* Working storage */
{
int end;
int loc, found;
register int i, j, n;
double *h; /* vector of deltas in x */
double *alpha;
double *l, *mu, *z, *a, *b, *c, *d, v;
end = len - 1;
a = work;
b = a + len;
c = b + len;
d = c + len;
h = d + len;
l = h + len;
z = l + len;
mu = z + len;
alpha = mu + len;
for (i = 0; i < len; i++) {
a[i] = y[i];
}
/* Calculate vector of differences */
for (i = 0; i < end; i++) {
h[i] = x[i + 1] - x[i];
if (h[i] < 0.0) {
return -1;
}
}
/* Calculate alpha vector */
for (n = 0, i = 1; i < end; i++, n++) {
/* n = i - 1 */
alpha[i] = 3.0 * ((a[i + 1] / h[i]) - (a[i] / h[n]) - (a[i] / h[i]) +
(a[n] / h[n]));
}
/* Vectors to solve the tridiagonal matrix */
l[0] = l[end] = 1.0;
mu[0] = mu[end] = 0.0;
z[0] = z[end] = 0.0;
c[0] = c[end] = 0.0;
/* Calculate the intermediate results */
for (n = 0, i = 1; i < end; i++, n++) {
/* n = i - 1 */
l[i] = 2 * (h[i] + h[n]) - h[n] * mu[n];
mu[i] = h[i] / l[i];
z[i] = (alpha[i] - h[n] * z[n]) / l[i];
}
for (n = end, j = end - 1; j >= 0; j--, n--) {
/* n = j + 1 */
c[j] = z[j] - mu[j] * c[n];
b[j] = (a[n] - a[j]) / h[j] - h[j] * (c[n] + 2.0 * c[j]) / 3.0;
d[j] = (c[n] - c[j]) / (3.0 * h[j]);
}
/* Now calculate the new values */
for (j = 0; j < splLen; j++) {
v = splX[j];
splY[j] = 0.0;
/* Is it outside the interval? */
if ((v < x[0]) || (v > x[end])) {
continue;
}
/* Search for the interval containing v in the x vector */
loc = Search(x, len, v, &found);
if (found) {
splY[j] = y[loc];
} else {
loc--;
v -= x[loc];
splY[j] = a[loc] + v * (b[loc] + v * (c[loc] + v * d[loc]));
}
}
return 0;
}
int
Blt_NaturalSpline(x, y, length, splX, splY, splLen)
double x[], y[];
int length;
double splX[], splY[];
int splLen;
{
double *work;
int result;
work = (double *)malloc(sizeof(double) * length * 9);
assert(work);
result = NaturalSpline(x, y, length, splX, splY, splLen, work);
free((char *)work);
return (result);
}
int
Blt_QuadraticSpline(x, y, length, splX, splY, splLen, epsilon)
double x[], y[];
int length;
double splX[], splY[];
int splLen;
double epsilon;
{
double *work;
int result;
/* allocate space for vectors used in calculation */
work = (double *)malloc(length * sizeof(double));
assert(work);
result = QuadraticSpline(x, y, length, splX, splY, splLen, work, epsilon);
free((char *)work);
return (result);
}
/*ARGSUSED*/
static int
NaturalOp(tkwin, interp, x, y, splX, splY, argc, argv)
Tk_Window tkwin; /* Main window of the interpreter. Used to
* process options using Tk_ConfigureWidget */
Tcl_Interp *interp;
Blt_Vector *x, *y, *splX, *splY;
int argc; /* Not used */
char **argv; /* Not used */
{
if (Blt_NaturalSpline(Blt_VecData(x), Blt_VecData(y), Blt_VecLength(x),
Blt_VecData(splX), Blt_VecData(splY), Blt_VecLength(splX)) != 0) {
Tcl_AppendResult(interp, "x vector \"", argv[2],
"\" must be sorted in ascending order", (char *)NULL);
return TCL_ERROR;
}
return TCL_OK;
}
typedef struct {
double epsilon; /* Error setting for calculating the spline */
} QuadInfo;
#define DEF_QUAD_ERROR "0.0"
static Tk_ConfigSpec quadConfigSpecs[] =
{
{TK_CONFIG_DOUBLE, "-error", (char *)NULL, (char *)NULL,
DEF_QUAD_ERROR, Tk_Offset(QuadInfo, epsilon),
TK_CONFIG_DONT_SET_DEFAULT},
{TK_CONFIG_END, (char *)NULL, (char *)NULL, (char *)NULL,
(char *)NULL, 0, 0}
};
/* ARGSUSED */
static int
QuadraticOp(tkwin, interp, x, y, splX, splY, argc, argv)
Tk_Window tkwin; /* Main window of the interpreter. Used to
* process options using Tk_ConfigureWidget */
Tcl_Interp *interp;
Blt_Vector *x, *y, *splX, *splY;
int argc; /* Not used */
char **argv;
{
double epsilon;
int result;
epsilon = 0.0; /* TBA: adjust error via command-line option */
if (argc > 6) {
QuadInfo info;
info.epsilon = 0.0;
if (Tk_ConfigureWidget(interp, tkwin, quadConfigSpecs, argc - 6,
argv + 6, (char *)&info, 0) != TCL_OK) {
return TCL_ERROR;
}
#ifdef notdef
if (info.epsilon < 0.0) {
info.epsilon = 0.0;
}
#endif
epsilon = info.epsilon;
}
result = Blt_QuadraticSpline(Blt_VecData(x), Blt_VecData(y),
Blt_VecLength(x), Blt_VecData(splX), Blt_VecData(splY),
Blt_VecLength(splX), epsilon);
if (result != 0) {
Tcl_AppendResult(interp, "error generating spline for \"", argv[2],
"\"", (char *)NULL);
return TCL_ERROR;
}
return TCL_OK;
}
static Blt_OpSpec operSpecs[] =
{
{"natural", 1, (Blt_Operation)NaturalOp, 6, 0,
"x y splx sply ?option value?...",},
{"quadratic", 1, (Blt_Operation)QuadraticOp, 6, 0,
"x y splx sply ?option value?...",},
};
static int numSpecs = sizeof(operSpecs) / sizeof(Blt_OpSpec);
static int
SplineCmd(clientData, interp, argc, argv)
ClientData clientData;
Tcl_Interp *interp;
int argc;
char **argv;
{
Tk_Window tkwin = (Tk_Window)clientData;
Blt_Operation proc;
Blt_Vector *x, *y, *splX, *splY;
register int i;
int result;
proc = Blt_GetOperation(interp, numSpecs, operSpecs, BLT_OPER_ARG1,
argc, argv);
if (proc == NULL) {
return TCL_ERROR;
}
if ((Blt_GetVector(interp, argv[2], &x) != TCL_OK) ||
(Blt_GetVector(interp, argv[3], &y) != TCL_OK) ||
(Blt_GetVector(interp, argv[4], &splX) != TCL_OK)) {
return TCL_ERROR;
}
if (Blt_VecLength(x) < 3) {
Tcl_AppendResult(interp, "length of vector \"", argv[2], "\" is < 3",
(char *)NULL);
return TCL_ERROR;
}
for (i = 1; i < Blt_VecLength(x); i++) {
if (Blt_VecData(x)[i] <= Blt_VecData(x)[i - 1]) {
Tcl_AppendResult(interp, "x vector \"", argv[2],
"\" must be monotonically increasing", (char *)NULL);
return TCL_ERROR;
}
}
if (Blt_VecLength(x) != Blt_VecLength(y)) {
Tcl_AppendResult(interp, "vectors \"", argv[2], "\" and \"", argv[3],
" have different lengths", (char *)NULL);
return TCL_ERROR;
}
if (Blt_GetVector(interp, argv[5], &splY) != TCL_OK) {
/*
* If the named vector to hold the ordinates of the spline
* doesn't exist, create one the same size as the vector
* containing the abscissas.
*/
if (Blt_CreateVector(interp, argv[5], Blt_VecLength(splX),
&splY) != TCL_OK) {
return TCL_ERROR;
}
} else if (Blt_VecLength(splX) != Blt_VecLength(splY)) {
/*
* The x and y vectors differ in size. Make the number of ordinates
* the same as the number of abscissas.
*/
if (Blt_ResizeVector(splY, Blt_VecLength(splX)) != TCL_OK) {
return TCL_ERROR;
}
}
result = (*proc) (tkwin, interp, x, y, splX, splY, argc, argv);
if (result != TCL_OK) {
return TCL_ERROR;
}
/*
* Update the vector. In this case, we're merely notifying the
* vector management routines that the values have changed (the
* memory is still the same). The vector does not need to be
* reallocated (TCL_STATIC is ignored).
*/
if (Blt_ResetVector(splY, Blt_VecData(splY), Blt_VecLength(splY),
Blt_VecSize(splY), TCL_STATIC) != TCL_OK) {
return TCL_ERROR;
}
return TCL_OK;
}
int
Blt_SplineInit(interp)
Tcl_Interp *interp;
{
static Blt_CmdSpec cmdSpec =
{"spline", SplineCmd,};
if (Blt_InitCmd(interp, "blt", &cmdSpec) == NULL) {
return TCL_ERROR;
}
return TCL_OK;
}
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