X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=7ff4f8718c91fc5f7c6474cb910ee303849473d4;hp=6a134b79b2f6540ad177019129762f8252b66bbd;hb=35f1190c8c8036ed11180656769cf0c1cbf7c2b3;hpb=85336af25da0c613460bbeda4ff7553933e13064

diff --git a/src/bezier.h b/src/bezier.h
index 6a134b7..7ff4f87 100644
--- a/src/bezier.h
+++ b/src/bezier.h
@@ -11,49 +11,11 @@ namespace IPDF
 	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)
-	{
-		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);
-	}
+	extern std::vector<Real> SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min = 0, const Real & max = 1);
 
-	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...
-		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);
-			x /= maxi;
-			Real y = a*(x*x*x) + b*(x*x) + c*x + d;
-			if ( ((y < Real(0)) && (prevRes > Real(0))) || ((y > Real(0)) && (prevRes < Real(0))))
-			{
-				Debug("Found root of %fx^3 + %fx^2 + %fx + %f at %f (%f)", a, b, c, d, x, y);
-				roots.push_back(x);
-			}
-			prevRes = y;
-		}
-		return roots;
-			
-	}
+	extern std::vector<Real> SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d, const Real & min = 0, const Real & max = 1, const Real & delta = 1e-4);
 
 	/** A _cubic_ bezier. **/
 	struct Bezier
@@ -106,6 +68,11 @@ namespace IPDF
 
 		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);
@@ -230,32 +197,32 @@ namespace IPDF
 			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());
@@ -269,7 +236,7 @@ namespace IPDF
 			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;
@@ -282,10 +249,14 @@ namespace IPDF
 				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;
@@ -300,6 +271,30 @@ namespace IPDF
 			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];
 		}
+		std::vector<Vec2> Evaluate(const std::vector<Real> & u) const;
+		
+		std::vector<Real> SolveXParam(const Real & x) const;
+		std::vector<Real> SolveYParam(const Real & x) const;
+		
+		// Get points with same X
+		inline std::vector<Vec2> SolveX(const Real & x) const
+		{
+			return Evaluate(SolveXParam(x));
+		}
+		// Get points with same Y
+		inline std::vector<Vec2> SolveY(const Real & y) const
+		{
+			return Evaluate(SolveYParam(y));
+		}
+		
+		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);}
 
 	};