#ifndef _BEZIER_H
#define _BEZIER_H
+#include <vector>
+#include <algorithm>
+
#include "real.h"
#include "rect.h"
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;
}
-
/** A _cubic_ bezier. **/
struct Bezier
}
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 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());
+ 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.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;
+ if (t1 == t0) continue;
+ Debug(" -- t0: %f to t1: %f", t0, t1);
+ Real ptx, pty;
+ Evaluate(ptx, pty, ((t1 + t0) / Real(2)));
+ if (r.PointIn(ptx, pty))
+ {
+ 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
git.ucc.asn.au / ipdf / code.git / blobdiff
UCC git Repository :: git.ucc.asn.au