Terrible hacky SolveCubic.

[ipdf/code.git] / src / bezier.cpp

diff --git a/src/bezier.cpp b/src/bezier.cpp
index c71d0a9..da65336 100644 (file)
--- a/src/bezier.cpp
+++ b/src/bezier.cpp
@@ -2,6 +2,7 @@
 
 #include <unordered_map>
 #include <cmath>
 
 #include <unordered_map>
 #include <cmath>

+#include <algorithm>

 
 using namespace std;
 
 
 using namespace std;
 


@@ -34,7 +35,7 @@ int Factorial(int n)
  */
 int BinomialCoeff(int n, int k)
 {
  */
 int BinomialCoeff(int n, int k)
 {

-       return Factorial(n) / Factorial(k) / Factorial(n-k);
+       return Factorial(n) / (Factorial(k) * Factorial(n-k));

 }
 
 /**
 }
 
 /**


@@ -45,4 +46,95 @@ Real Bernstein(int k, int n, const Real & u)
        return Real(BinomialCoeff(n, k)) * Power(u, k) * Power(Real(1.0) - u, 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