X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=9273ceecbddb78368deb10ba0898280ec3a638fb;hp=9ea730f78c0907a73ecfd5e4b727da5429636417;hb=813591a7d8a7364003233939f52b0031f3a40d20;hpb=398e6b2732decd57cdb57deb3f91d3ff08669e8b diff --git a/src/bezier.h b/src/bezier.h index 9ea730f..9273cee 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -1,6 +1,9 @@ #ifndef _BEZIER_H #define _BEZIER_H +#include +#include + #include "real.h" #include "rect.h" namespace IPDF @@ -32,23 +35,25 @@ 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 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 @@ -145,7 +150,143 @@ namespace IPDF } 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 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 x_intersection = SolveCubic(xa, xb, xc, xd); + + // And for the other side. + xd = x3 - r.x - r.w; + + std::vector 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 y_intersection = SolveCubic(ya, yb, yc, yd); + + // And for the other side. + yd = y3 - r.y - r.h; + + std::vector 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 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