#include <unordered_map>
#include <cmath>
+#include <algorithm>
using namespace std;
*/
int BinomialCoeff(int n, int k)
{
- return Factorial(n) / Factorial(k) / Factorial(n-k);
+ return Factorial(n) / (Factorial(k) * Factorial(n-k));
}
/**
return Real(BinomialCoeff(n, k)) * Power(u, k) * Power(Real(1.0) - u, n-k);
}
+
+/**
+ * Returns the parametric parameter at the turning point(s)
+ * In one coordinate direction
+ */
+
+static pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3)
+{
+ // straight line
+ if (p1 == p2 && p2 == p3)
+ {
+ return pair<Real,Real>(0, 1);
+ }
+ Real a = (3*(p1-p2) + p3 - p0);
+ Real b = 2*(p2 - 2*p1 + p0);
+ Real c = (p1-p0);
+ if (a == 0)
+ {
+ if (b == 0)
+ return pair<Real, Real>(0,1);
+ Real t = -c/b;
+ if (t > 1) t = 1;
+ if (t < 0) t = 0;
+ return pair<Real, Real>(t, t);
+ }
+ //Debug("a, b, c are %f, %f, %f", Float(a), Float(b), Float(c));
+ if (b*b - 4*a*c < 0)
+ {
+ //Debug("No real roots");
+ return pair<Real, Real>(0,1);
+ }
+ pair<Real, Real> tsols = SolveQuadratic(a, b, c);
+ if (tsols.first > 1) tsols.first = 1;
+ if (tsols.first < 0) tsols.first = 0;
+ if (tsols.second > 1) tsols.second = 1;
+ if (tsols.second < 0) tsols.second = 0;
+ return tsols;
}
+
+inline bool CompRealByPtr(const Real * a, const Real * b)
+{
+ return (*a) < (*b);
+}
+
+/**
+ * Get Bounds Rectangle of Bezier
+ */
+Rect Bezier::SolveBounds() const
+{
+ Rect result;
+ pair<Real, Real> tsols = BezierTurningPoints(x0, x1, x2, x3);
+
+ Real tp0; Real tp1; Real o;
+ Evaluate(tp0, o, tsols.first);
+ Evaluate(tp1, o, tsols.second);
+
+ //Debug("x: tp0 is %f tp1 is %f", Float(tp0), Float(tp1));
+
+ vector<const Real*> v(4);
+ v[0] = &x0;
+ v[1] = &x3;
+ v[2] = &tp0;
+ v[3] = &tp1;
+
+ // Not using a lambda to keep this compiling on cabellera
+ sort(v.begin(), v.end(), CompRealByPtr);
+
+ result.x = *(v[0]);
+ result.w = *(v[3]) - result.x;
+
+ // Do the same thing for y component (wow this is a mess)
+ tsols = BezierTurningPoints(y0, y1, y2, y3);
+ Evaluate(o, tp0, tsols.first);
+ Evaluate(o, tp1, tsols.second);
+
+
+ //Debug("y: tp0 is %f tp1 is %f", Float(tp0), Float(tp1));
+
+ v[0] = &y0;
+ v[1] = &y3;
+ v[2] = &tp0;
+ v[3] = &tp1;
+ sort(v.begin(), v.end(), CompRealByPtr);
+
+ result.y = *(v[0]);
+ result.h = *(v[3]) - result.y;
+
+ //Debug("Solved Bezier %s bounds as %s", Str().c_str(), result.Str().c_str());
+ return result;
+}
+
+} // end namespace