Merge branch 'master' of git.ucc.asn.au:ipdf/code

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

diff --git a/src/bezier.h b/src/bezier.h
index 6a134b7..17bc5b6 100644 (file)
--- a/src/bezier.h
+++ b/src/bezier.h
@@ -25,20 +25,36 @@ namespace IPDF
                // 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);
@@ -230,32 +246,32 @@ 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());
@@ -286,6 +302,10 @@ namespace IPDF
                                {
                                        all_beziers.push_back(this->ReParametrise(t0, t1));
                                }
+                               else
+                               {
+                                       Debug("Segment removed (point at %f, %f)", ptx, pty);
+                               }
                                t0 = t1;
                        }
                        return all_beziers;