+ 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);
+ }
+
+ /** 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 ToRelative(const Rect & bounds) const
+ {
+ // x' <- (x - x0)/w etc
+ // special cases when w or h = 0
+ // (So can't just use the Copy constructor on the inverse of bounds)
+ // Rect inverse = {-bounds.x/bounds.w, -bounds.y/bounds.h, Real(1)/bounds.w, Real(1)/bounds.h};
+ Bezier result;
+ if (bounds.w == 0)
+ {
+ result.x0 = 0;
+ result.x1 = 0;
+ result.x2 = 0;
+ result.x3 = 0;
+ }
+ else
+ {
+ result.x0 = (x0 - bounds.x)/bounds.w;
+ result.x1 = (x1 - bounds.x)/bounds.w;
+ result.x2 = (x2 - bounds.x)/bounds.w;
+ result.x3 = (x3 - bounds.x)/bounds.w;
+ }
+
+ if (bounds.h == 0)
+ {
+ result.y0 = 0;
+ result.y1 = 0;
+ result.y2 = 0;
+ result.y3 = 0;
+ }
+ else
+ {
+ result.y0 = (y0 - bounds.y)/bounds.h;
+ result.y1 = (y1 - bounds.y)/bounds.h;
+ result.y2 = (y2 - bounds.y)/bounds.h;
+ result.y3 = (y3 - bounds.y)/bounds.h;
+ }
+ return result;
+ }
+
+ // Performs one round of De Casteljau subdivision and returns the [t,1] part.
+ Bezier DeCasteljauSubdivideRight(const Real& t)
+ {
+ Real one_minus_t = Real(1) - t;
+
+ // X Coordinates
+ Real x01 = x0*t + x1*one_minus_t;
+ Real x12 = x1*t + x2*one_minus_t;
+ Real x23 = x2*t + x3*one_minus_t;
+
+ Real x012 = x01*t + x12*one_minus_t;
+ Real x123 = x12*t + x23*one_minus_t;
+
+ Real x0123 = x012*t + x123*one_minus_t;
+
+ // Y Coordinates
+ Real y01 = y0*t + y1*one_minus_t;
+ Real y12 = y1*t + y2*one_minus_t;
+ Real y23 = y2*t + y3*one_minus_t;
+
+ Real y012 = y01*t + y12*one_minus_t;
+ Real y123 = y12*t + y23*one_minus_t;
+
+ Real y0123 = y012*t + y123*one_minus_t;
+
+ return Bezier(x0, y0, x01, y01, x012, y012, x0123, y0123);
+ }
+ // Performs one round of De Casteljau subdivision and returns the [0,t] part.
+ Bezier DeCasteljauSubdivideLeft(const Real& t)
+ {
+ Real one_minus_t = Real(1) - t;
+
+ // X Coordinates
+ Real x01 = x0*t + x1*one_minus_t;
+ Real x12 = x1*t + x2*one_minus_t;
+ Real x23 = x2*t + x3*one_minus_t;
+
+ Real x012 = x01*t + x12*one_minus_t;
+ Real x123 = x12*t + x23*one_minus_t;
+
+ Real x0123 = x012*t + x123*one_minus_t;
+
+ // Y Coordinates
+ Real y01 = y0*t + y1*one_minus_t;
+ Real y12 = y1*t + y2*one_minus_t;
+ Real y23 = y2*t + y3*one_minus_t;
+
+ Real y012 = y01*t + y12*one_minus_t;
+ Real y123 = y12*t + y23*one_minus_t;
+
+ Real y0123 = y012*t + y123*one_minus_t;
+
+ return Bezier(x0123, y0123, x123, y123, x23, y23, x3, y3);
+ }
+
+ Bezier ReParametrise(const Real& t0, const Real& t1)
+ {
+ Debug("Reparametrise: %f -> %f",t0,t1);
+ Bezier new_bezier;
+ // Subdivide to get from [0,t1]
+ new_bezier = DeCasteljauSubdivideLeft(t1);
+ // Convert t0 from [0,1] range to [0, t1]
+ Real new_t0 = t0 / t1;
+ Debug("New t0 = %f", new_t0);
+ new_bezier = new_bezier.DeCasteljauSubdivideRight(new_t0);
+
+ Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str());
+ 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 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 = 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 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 = 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());
+
+ // Merge and sort.
+ x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end());
+ x_intersection.push_back(Real(0));
+ x_intersection.push_back(Real(1));
+ std::sort(x_intersection.begin(), x_intersection.end());
+
+ Debug("Found %d intersections.\n", x_intersection.size());
+
+ std::vector<Bezier> all_beziers;
+ if (x_intersection.size() <= 2)
+ {
+ 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;
+ if (t1 == t0) continue;
+ Debug(" -- t0: %f to t1: %f", t0, t1);
+ Real ptx, pty;
+ Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
+ 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;
+ }