extern int Factorial(int n);
extern int BinomialCoeff(int n, int k);
extern Real Bernstein(int k, int n, const Real & u);
+ extern std::pair<Real,Real> BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3);
inline std::pair<Real,Real> SolveQuadratic(const Real & a, const Real & b, const Real & c)
{
// See http://en.wikipedia.org/wiki/Cubic_function#General_formula_for_roots
// delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2
- /*
+
Real discriminant = Real(18) * a * b * c * d - Real(4) * (b * b * b) * d
+ (b * b) * (c * c) - Real(4) * a * (c * c * c)
- Real(27) * (a * a) * (d * d);
- */
+
+ Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f (Discriminant: %f)", a,b,c,d, discriminant);
// discriminant > 0 => 3 distinct, real roots.
// discriminant = 0 => a multiple root (1 or 2 real roots)
// discriminant < 0 => 1 real root, 2 complex conjugate roots
+ Real delta0 = (b*b) - Real(3) * a * c;
+ Real delta1 = Real(2) * (b * b * b) - Real(9) * a * b * c + Real(27) * (a * a) * d;
+
+ std::vector<Real> roots;
+
+ Real C = pow((delta1 + Sqrt((delta1 * delta1) - 4 * (delta0 * delta0 * delta0)) ) / Real(2), 1/3);
+
+ if (false && discriminant < 0)
+ {
+ Real real_root = (Real(-1) / (Real(3) * a)) * (b + C + delta0 / C);
+
+ roots.push_back(real_root);
+
+ return roots;
+
+ }
+
////HACK: We know any roots we care about will be between 0 and 1, so...
- Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f", a,b,c,d);
Real maxi(100);
Real prevRes(d);
- std::vector<Real> roots;
for(int i = -1; i <= 100; ++i)
{
Real x(i);
Rect SolveBounds() const;
+ std::pair<Real,Real> GetTop() const;
+ std::pair<Real,Real> GetBottom() const;
+ std::pair<Real,Real> GetLeft() const;
+ std::pair<Real,Real> GetRight() const;
+
Bezier ToAbsolute(const Rect & bounds) const
{
return Bezier(*this, bounds);
Debug("Clipping Bezier to Rect %s", r.Str().c_str());
// Convert bezier coefficients -> cubic coefficients
- Real xa = x0-x1+x2-x3;
- Real xb = x1 - Real(2)*x2 + Real(3)*x3;
- Real xc = x2 - Real(3)*x3;
- Real xd = x3 - r.x;
+ Real xd = x0 - r.x;
+ Real xc = Real(3)*(x1 - x0);
+ Real xb = Real(3)*(x2 - x1) - xc;
+ Real xa = x3 - x0 - xc - xb;
// Find its roots.
std::vector<Real> x_intersection = SolveCubic(xa, xb, xc, xd);
// And for the other side.
- xd = x3 - r.x - r.w;
+ xd = x0 - r.x - r.w;
std::vector<Real> x_intersection_pt2 = SolveCubic(xa, xb, xc, xd);
x_intersection.insert(x_intersection.end(), x_intersection_pt2.begin(), x_intersection_pt2.end());
// Similarly for y-coordinates.
// Convert bezier coefficients -> cubic coefficients
- Real ya = y0-y1+y2-y3;
- Real yb = y1 - Real(2)*y2 + Real(3)*y3;
- Real yc = y2 - Real(3)*y3;
- Real yd = y3 - r.y;
+ Real yd = y0 - r.y;
+ Real yc = Real(3)*(y1 - y0);
+ Real yb = Real(3)*(y2 - y1) - yc;
+ Real ya = y3 - y0 - yc - yb;
// Find its roots.
std::vector<Real> y_intersection = SolveCubic(ya, yb, yc, yd);
// And for the other side.
- yd = y3 - r.y - r.h;
+ yd = y0 - r.y - r.h;
std::vector<Real> y_intersection_pt2 = SolveCubic(ya, yb, yc, yd);
y_intersection.insert(y_intersection.end(), y_intersection_pt2.begin(), y_intersection_pt2.end());
Debug("Found %d intersections.\n", x_intersection.size());
std::vector<Bezier> all_beziers;
- if (x_intersection.empty())
+ if (x_intersection.size() <= 2)
{
all_beziers.push_back(*this);
return all_beziers;
Debug(" -- t0: %f to t1: %f", t0, t1);
Real ptx, pty;
Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
- if (r.PointIn(ptx, pty))
+ if (true || r.PointIn(ptx, pty))
{
all_beziers.push_back(this->ReParametrise(t0, t1));
}
+ else
+ {
+ Debug("Segment removed (point at %f, %f)", ptx, pty);
+ }
t0 = t1;
}
return all_beziers;
x = x0*coeff[0] + x1*coeff[1] + x2*coeff[2] + x3*coeff[3];
y = y0*coeff[0] + y1*coeff[1] + y2*coeff[2] + y3*coeff[3];
}
+
+ bool operator==(const Bezier & equ) const
+ {
+ return (x0 == equ.x0 && y0 == equ.y0
+ && x1 == equ.x1 && y1 == equ.y1
+ && x2 == equ.x2 && y2 == equ.y2
+ && x3 == equ.x3 && y3 == equ.y3);
+ }
+ bool operator!=(const Bezier & equ) const {return !this->operator==(equ);}
};
git.ucc.asn.au / ipdf / code.git / blobdiff
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