X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=9ea730f78c0907a73ecfd5e4b727da5429636417;hp=449d7bde77271204aa2ff0e645fe7bef48f13443;hb=5456793e2aad4235c3db2ca75532c868aaa7c518;hpb=53579b1a949fa3e4e193f8dfba2064edbb123f57

diff --git a/src/bezier.h b/src/bezier.h
index 449d7bd..9ea730f 100644
--- a/src/bezier.h
+++ b/src/bezier.h
@@ -11,11 +11,45 @@ namespace IPDF
 	
 	inline std::pair<Real,Real> SolveQuadratic(const Real & a, const Real & b, const Real & c)
 	{
-		Real x0((b + Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
-		Real x1((b - Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
+		Real x0((-b + Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
+		Real x1((-b - Sqrt(b*b - Real(4)*a*c))/(Real(2)*a));
 		return std::pair<Real,Real>(x0,x1);
 	}
 
+	inline std::vector<Real> SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d)
+	{
+		// This is going to be a big one...
+		// 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);
+		*/
+		// 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
+
+		////HACK: We know any roots we care about will be between 0 and 1, so...
+		Real maxi(100);
+		Real prevRes(d);
+		std::vector<Real> roots;
+		for(int i = 0; i <= 100; ++i)
+		{
+			Real x(i);
+			x /= maxi;
+			Real y = a*(x*x*x) + b*(x*x) + c*x + d;
+			if (y == Real(0) || (y < Real(0) && prevRes > Real(0)) || (y > Real(0) && prevRes < Real(0)))
+			{
+				roots.push_back(x);
+			}
+		}
+		return roots;
+			
+	}
+		
+
 	/** A _cubic_ bezier. **/
 	struct Bezier
 	{
@@ -64,11 +98,16 @@ namespace IPDF
 
 		Rect SolveBounds() const;
 		
+		Bezier ToAbsolute(const Rect & bounds) const
+		{
+			return Bezier(*this, bounds);
+		}
+		
 		/** Convert absolute control points to control points relative to bounds
 		 * (This basically does the opposite of the Copy constructor)
 		 * ie: If this is absolute, the returned Bezier will be relative to the bounds rectangle
 		 */
-		Bezier CopyInverse(const Rect & bounds) const
+		Bezier ToRelative(const Rect & bounds) const
 		{
 			// x' <- (x - x0)/w etc
 			// special cases when w or h = 0