X-Git-Url: https://git.ucc.asn.au/?a=blobdiff_plain;f=src%2Fbezier.h;h=9a54d0cd76aec5b9ba2d8de07863dcb4936aa930;hb=c2885c9d467ec359bccd7bbe7369ff4c02439414;hp=9ea730f78c0907a73ecfd5e4b727da5429636417;hpb=5456793e2aad4235c3db2ca75532c868aaa7c518;p=ipdf%2Fcode.git diff --git a/src/bezier.h b/src/bezier.h index 9ea730f..9a54d0c 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 +150,105 @@ namespace IPDF } return result; } + + Bezier ReParametrise(const Real& t0, const Real& t1) + { + // 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; + Real tdiff_cubed = tdiff*tdiff_squared; + + Real t0_squared = t0*t0; + Real t0_cubed = t0*t0_squared; + + // X coordinates + Real Dx0 = x0 / tdiff_cubed; + Real Dx1 = x1 / (tdiff_squared - tdiff_cubed); + Real Dx2 = x2 / (tdiff - Real(2)*tdiff_squared + tdiff_cubed); + Real Dx3 = x3 / (Real(1) - Real(3)*tdiff + Real(3)*tdiff_squared - tdiff_cubed); + + new_bezier.x3 = Dx3*t0_cubed + Real(3)*Dx3*t0_squared + Real(3)*Dx3*t0 + Dx3 - Dx2*t0_cubed - Real(2)*Dx2*t0_squared - Dx2*t0 + Dx1*t0_cubed + Dx1*t0_squared - Dx0*t0_cubed; + new_bezier.x2 = Real(3)*Dx0*t0_squared - Real(2)*Dx1*t0 - Real(3)*Dx1*t0_squared + Dx2 + Real(4)*Dx2*t0 + Real(3)*Dx2*t0_squared - Real(3)*Dx3 - Real(6)*Dx3*t0 - Real(3)*Dx3*t0_squared + Real(3)*new_bezier.x3; + new_bezier.x1 = Real(-3)*Dx0*t0 + Real(3)*Dx1*t0 + Dx1 - Real(2)*Dx2 - Real(3)*Dx2*t0 + Real(3)*Dx3 + Real(3)*Dx3*t0 + Real(2)*new_bezier.x2 - Real(3)*new_bezier.x3; + new_bezier.x0 = Dx0 - Dx1 + Dx2 - Dx3 + new_bezier.x1 - new_bezier.x2 + new_bezier.x3; + + // Y coordinates + Real Dy0 = y0 / tdiff_cubed; + Real Dy1 = y1 / (tdiff_squared - tdiff_cubed); + Real Dy2 = y2 / (tdiff - Real(2)*tdiff_squared + tdiff_cubed); + Real Dy3 = y3 / (Real(1) - Real(3)*tdiff + Real(3)*tdiff_squared - tdiff_cubed); + + new_bezier.y3 = Dy3*t0_cubed + Real(3)*Dy3*t0_squared + Real(3)*Dy3*t0 + Dy3 - Dy2*t0_cubed - Real(2)*Dy2*t0_squared - Dy2*t0 + Dy1*t0_cubed + Dy1*t0_squared - Dy0*t0_cubed; + new_bezier.y2 = Real(3)*Dy0*t0_squared - Real(2)*Dy1*t0 - Real(3)*Dy1*t0_squared + Dy2 + Real(4)*Dy2*t0 + Real(3)*Dy2*t0_squared - Real(3)*Dy3 - Real(6)*Dy3*t0 - Real(3)*Dy3*t0_squared + Real(3)*new_bezier.y3; + new_bezier.y1 = Real(-3)*Dy0*t0 + Real(3)*Dy1*t0 + Dy1 - Real(2)*Dy2 - Real(3)*Dy2*t0 + Real(3)*Dy3 + Real(3)*Dy3*t0 + Real(2)*new_bezier.y2 - Real(3)*new_bezier.y3; + 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 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()); + 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; + 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