More broken quadtree monstrosity.

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

diff --git a/src/bezier.h b/src/bezier.h
index 8e7cedc..9a54d0c 100644 (file)
--- a/src/bezier.h
+++ b/src/bezier.h
@@ -1,6 +1,9 @@
 #ifndef _BEZIER_H
 #define _BEZIER_H
 
+#include <vector>
+#include <algorithm>
+
 #include "real.h"
 #include "rect.h"
 namespace IPDF
@@ -32,18 +35,21 @@ namespace IPDF
                // 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 = 0; i <= 100; ++i)
+               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) || (y < Real(0) && prevRes > Real(0)) || (y > Real(0) && prevRes < Real(0)))
+                       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;
                        
@@ -149,6 +155,7 @@ namespace IPDF
                {
                        // This function is very, very ugly, but with luck my derivation is correct (even if it isn't optimal, performance wise)
                        // (Very) rough working for the derivation is at: http://davidgow.net/stuff/cubic_bezier_reparam.pdf
+                       Debug("Reparametrise: %f -> %f",t0,t1);
                        Bezier new_bezier;
                        Real tdiff = t1 - t0;
                        Real tdiff_squared = tdiff*tdiff;
@@ -180,9 +187,68 @@ namespace IPDF
                        new_bezier.y0 = Dy0 - Dy1 + Dy2 - Dy3 + new_bezier.y1 - new_bezier.y2 + new_bezier.y3;
 
 
+                       Debug("(%f,%f),(%f,%f),(%f,%f),(%f,%f) -> (%f,%f),(%f,%f),(%f,%f),(%f,%f)", x0, y0, x1, y1, x2, y2, x3, y3, new_bezier.x0, new_bezier.y0, new_bezier.x1, new_bezier.y1, new_bezier.x2, new_bezier.y2, new_bezier.x3, new_bezier.y3);
                        return new_bezier;
                }
                
+               std::vector<Bezier> ClipToRectangle(const Rect& r)
+               {
+                       // Find points of intersection with the rectangle.
+                       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;
+
+                       // Find its roots.
+                       std::vector<Real> x_intersection = SolveCubic(xa, xb, xc, xd);
+
+                       // And for the other side.
+                       xd = x3 - 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;
+
+                       // Find its roots.
+                       std::vector<Real> y_intersection = SolveCubic(ya, yb, yc, yd);
+
+                       // And for the other side.
+                       yd = y3 - 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());
+
+                       // Merge and sort.
+                       x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end());
+                       std::sort(x_intersection.begin(), x_intersection.end());
+
+                       Debug("Found %d intersections.\n", x_intersection.size());
+                       
+                       std::vector<Bezier> all_beziers;
+                       if (x_intersection.empty())
+                       {
+                               all_beziers.push_back(*this);
+                               return all_beziers;
+                       }
+                       Real t0 = *(x_intersection.begin());
+                       for (auto it = x_intersection.begin()+1; it != x_intersection.end(); ++it)
+                       {
+                               Real t1 = *it;
+                               Debug(" -- t0: %f to t1: %f", t0, t1);
+                               all_beziers.push_back(this->ReParametrise(t0, t1));
+                               t0 = t1;
+                       }
+                       return all_beziers;
+               }
 
                /** Evaluate the Bezier at parametric parameter u, puts resultant point in (x,y) **/
                void Evaluate(Real & x, Real & y, const Real & u) const