static void CalcBSpline(
IntCoord cminus1x, IntCoord cminus1y, IntCoord cx, IntCoord cy,
IntCoord cplus1x, IntCoord cplus1y, IntCoord cplus2x, IntCoord cplus2y
) {
double p0x, p1x, p2x, p3x, tempx,
p0y, p1y, p2y, p3y, tempy;
ThirdPoint(
double(cx), double(cy), double(cplus1x), double(cplus1y), p1x, p1y
);
ThirdPoint(
double(cplus1x), double(cplus1y), double(cx), double(cy), p2x, p2y
);
ThirdPoint(
double(cx), double(cy), double(cminus1x), double(cminus1y),
tempx, tempy
);
Midpoint(tempx, tempy, p1x, p1y, p0x, p0y);
ThirdPoint(
double(cplus1x), double(cplus1y), double(cplus2x), double(cplus2y),
tempx, tempy
);
Midpoint(tempx, tempy, p2x, p2y, p3x, p3y);
AddBezierCurve(p0x, p0y, p1x, p1y, p2x, p2y, p3x, p3y);
}
void Painter::Curve(
Canvas* c, IntCoord x0, IntCoord y0, IntCoord x1, IntCoord y1,
IntCoord x2, IntCoord y2, IntCoord x3, IntCoord y3
) {
IntCoord tx0, ty0, tx1, ty1, tx2, ty2, tx3, ty3;
llcount = 0;
Map(c, x0, y0, tx0, ty0);
Map(c, x1, y1, tx1, ty1);
Map(c, x2, y2, tx2, ty2);
Map(c, x3, y3, tx3, ty3);
AddBezierCurve(tx0, ty0, tx1, ty1, tx2, ty2, tx3, ty3);
MultiLineNoMap(c, llx, lly, llcount);
}
static void AddBezierCurve(
double x0, double y0, double x1, double y1,
double x2, double y2, double x3, double y3
) {
double midx01, midx12, midx23, midlsegx, midrsegx, cx;
double midy01, midy12, midy23, midlsegy, midrsegy, cy;
Midpoint(x0, y0, x1, y1, midx01, midy01);
Midpoint(x1, y1, x2, y2, midx12, midy12);
Midpoint(x2, y2, x3, y3, midx23, midy23);
Midpoint(midx01, midy01, midx12, midy12, midlsegx, midlsegy);
Midpoint(midx12, midy12, midx23, midy23, midrsegx, midrsegy);
Midpoint(midlsegx, midlsegy, midrsegx, midrsegy, cx, cy);
if (CanApproxWithLine(x0, y0, midlsegx, midlsegy, cx, cy)) {
AddLine(x0, y0, cx, cy);
} else if (
(midx01 != x1) || (midy01 != y1) ||
(midlsegx != x2) || (midlsegy != y2) ||
(cx != x3) || (cy != y3)
) {
AddBezierCurve(
x0, y0, midx01, midy01, midlsegx, midlsegy, cx, cy
);
}
if (CanApproxWithLine(cx, cy, midx23, midy23, x3, y3)) {
AddLine(cx, cy, x3, y3);
} else if (
(cx != x0) || (cy != y0) ||
(midrsegx != x1) || (midrsegy != y1) ||
(midx23 != x2) || (midy23 != y2)
) {
AddBezierCurve(
cx, cy, midrsegx, midrsegy, midx23, midy23, x3, y3
);
}
}
/*
* FitCubic :
* Fit a Bezier curve to a (sub)set of digitized points
*/
void CBCStroke::FitCubic(
DISCURVE& d, /* Array of digitized points */
int first,int last,/* Indices of first and last pts in region */
Vector2 tHat1,Vector2 tHat2, /* Unit tangent vectors at endpoints */
double error) /* User-defined error squared */
{
BezierCurve bezCurve; /*Control points of fitted Bezier curve*/
double *u; /* Parameter values for point */
double *uPrime; /* Improved parameter values */
double maxError; /* Maximum fitting error */
int splitPoint; /* Point to split point set at */
int nPts; /* Number of points in subset */
double iterationError; /*Error below which you try iterating */
int maxIterations = 5; /* Max times to try iterating */
Vector2 tHatCenter; /* Unit tangent vector at splitPoint */
int i;
iterationError = error * error;
nPts = last - first + 1;
/* Use heuristic if region only has two points in it */
if (nPts == 2) {
double dist = V2DistanceBetween2Points(&d[last], &d[first]) / 3.0;
bezCurve = (Point2 *)malloc(4 * sizeof(Point2));
bezCurve[0] = d[first];
bezCurve[3] = d[last];
V2Add(&bezCurve[0], V2Scale(&tHat1, dist), &bezCurve[1]);
V2Add(&bezCurve[3], V2Scale(&tHat2, dist), &bezCurve[2]);
//DrawBezierCurve(, bezCurve);
double u[2];
u[0]=0;
u[1]=1;
PARAMERLIST paramList;
CopyParamList(first,last,u,paramList);
AddBezierCurve(3,bezCurve,paramList);
free((void *)bezCurve);
return;
}
/* Parameterize points, and attempt to fit curve */
u = ChordLengthParameterize(d, first, last);
bezCurve = GenerateBezier(d, first, last, u, tHat1, tHat2);
/* Find max deviation of points to fitted curve */
maxError = ComputeMaxError(d, first, last, bezCurve, u, &splitPoint);
if (maxError < error) {
//DrawBezierCurve(3, bezCurve);
PARAMERLIST paramList;
CopyParamList(first,last,u,paramList);
AddBezierCurve(3,bezCurve,paramList);
free((void *)u);
free((void *)bezCurve);
return;
}
/* If error not too large, try some reparameterization */
/* and iteration */
if (maxError < iterationError) {
for (i = 0; i < maxIterations; i++) {
uPrime = Reparameterize(d, first, last, u, bezCurve);
bezCurve = GenerateBezier(d, first, last, uPrime, tHat1, tHat2);
maxError = ComputeMaxError(d, first, last,
bezCurve, uPrime, &splitPoint);
if (maxError < error) {
//DrawBezierCurve(3, bezCurve);
PARAMERLIST paramList;
CopyParamList(first,last,u,paramList);
AddBezierCurve(3,bezCurve,paramList);
free((void *)u);
free((void *)bezCurve);
return;
}
free((void *)u);
u = uPrime;
}
}
/* Fitting failed -- split at max error point and fit recursively */
free((void *)u);
free((void *)bezCurve);
tHatCenter = ComputeCenterTangent(d, splitPoint);
FitCubic(d, first, splitPoint, tHat1, tHatCenter, error);
V2Negate(&tHatCenter);
FitCubic(d, splitPoint, last, tHatCenter, tHat2, error);
}