X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=206cbc8a17795d7d267fd02dd029cfeaccd963fc;hp=7ff4f8718c91fc5f7c6474cb910ee303849473d4;hb=36b4b285d3dbdab423511e7188c37bd1d0443edb;hpb=35f1190c8c8036ed11180656769cf0c1cbf7c2b3 diff --git a/src/bezier.h b/src/bezier.h index 7ff4f87..206cbc8 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -25,16 +25,73 @@ namespace IPDF Real x2; Real y2; Real x3; Real y3; - typedef enum {LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type; + typedef enum {UNKNOWN, LINE, QUADRATIC, CUSP, LOOP, SERPENTINE} Type; Type type; Bezier() = default; // Needed so we can fread/fwrite this struct... for now. - Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2, Real _x3, Real _y3) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3) + Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2, Real _x3, Real _y3) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3), type(UNKNOWN) { - //TODO: classify the curve - type = SERPENTINE; + + } + + Type GetType() + { + if (type != Bezier::UNKNOWN) + return type; + // From Loop-Blinn 2005, with w0 == w1 == w2 == w3 = 1 + // Transformed control points: (a0 = x0, b0 = y0) + Real a1 = (x1-x0)*3; + Real a2 = (x0- x1*2 +x2)*3; + Real a3 = (x3 - x0 + (x1 - x2)*3); + + Real b1 = (y1-y0)*3; + Real b2 = (y0- y1*2 +y2)*3; + Real b3 = (y3 - y0 + (y1 - y2)*3); + + // d vector (d0 = 0 since all w = 1) + Real d1 = a2*b3 - a3*b2; + Real d2 = a3*b1 - a1*b3; + Real d3 = a1*b2 - a2*b1; + + if (Abs(d1+d2+d3) < 1e-6) + { + type = LINE; + //Debug("LINE %s", Str().c_str()); + return type; + } + + Real delta1 = -(d1*d1); + Real delta2 = d1*d2; + Real delta3 = d1*d3 -(d2*d2); + if (Abs(delta1+delta2+delta3) < 1e-6) + { + type = QUADRATIC; + + //Debug("QUADRATIC %s", Str().c_str()); + return type; + } + + Real discriminant = d1*d3*4 -d2*d2; + if (Abs(discriminant) < 1e-6) + { + type = CUSP; + //Debug("CUSP %s", Str().c_str()); + } + else if (discriminant > 0) + { + type = SERPENTINE; + //Debug("SERPENTINE %s", Str().c_str()); + } + else + { + type = LOOP; + //Debug("LOOP %s", Str().c_str()); + } + //Debug("disc %.30f", discriminant); + return type; } + std::string Str() const { std::stringstream s; @@ -122,69 +179,69 @@ namespace IPDF } // Performs one round of De Casteljau subdivision and returns the [t,1] part. - Bezier DeCasteljauSubdivideRight(const Real& t) + 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 x01 = x1*t + x0*one_minus_t; + Real x12 = x2*t + x1*one_minus_t; + Real x23 = x3*t + x2*one_minus_t; - Real x012 = x01*t + x12*one_minus_t; - Real x123 = x12*t + x23*one_minus_t; + Real x012 = x12*t + x01*one_minus_t; + Real x123 = x23*t + x12*one_minus_t; - Real x0123 = x012*t + x123*one_minus_t; + Real x0123 = x123*t + x012*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 y01 = y1*t + y0*one_minus_t; + Real y12 = y2*t + y1*one_minus_t; + Real y23 = y3*t + y2*one_minus_t; - Real y012 = y01*t + y12*one_minus_t; - Real y123 = y12*t + y23*one_minus_t; + Real y012 = y12*t + y01*one_minus_t; + Real y123 = y23*t + y12*one_minus_t; - Real y0123 = y012*t + y123*one_minus_t; + Real y0123 = y123*t + y012*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) + // 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 x01 = x1*t + x0*one_minus_t; + Real x12 = x2*t + x1*one_minus_t; + Real x23 = x3*t + x2*one_minus_t; - Real x012 = x01*t + x12*one_minus_t; - Real x123 = x12*t + x23*one_minus_t; + Real x012 = x12*t + x01*one_minus_t; + Real x123 = x23*t + x12*one_minus_t; - Real x0123 = x012*t + x123*one_minus_t; + Real x0123 = x123*t + x012*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 y01 = y1*t + y0*one_minus_t; + Real y12 = y2*t + y1*one_minus_t; + Real y23 = y3*t + y2*one_minus_t; - Real y012 = y01*t + y12*one_minus_t; - Real y123 = y12*t + y23*one_minus_t; + Real y012 = y12*t + y01*one_minus_t; + Real y123 = y23*t + y12*one_minus_t; - Real y0123 = y012*t + y123*one_minus_t; + Real y0123 = y123*t + y012*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); + Debug("Reparametrise: %f -> %f",Double(t0),Double(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); + Debug("New t0 = %f", Double(new_t0)); new_bezier = new_bezier.DeCasteljauSubdivideRight(new_t0); Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str()); @@ -196,35 +253,19 @@ namespace IPDF // 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 x_intersection = SolveCubic(xa, xb, xc, xd); + std::vector x_intersection = SolveXParam(r.x); // And for the other side. - xd = x0 - r.x - r.w; - std::vector x_intersection_pt2 = SolveCubic(xa, xb, xc, xd); + std::vector x_intersection_pt2 = SolveXParam(r.x + r.w); 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 y_intersection = SolveCubic(ya, yb, yc, yd); - - // And for the other side. - yd = y0 - r.y - r.h; + std::vector y_intersection = SolveYParam(r.y); - std::vector y_intersection_pt2 = SolveCubic(ya, yb, yc, yd); + std::vector y_intersection_pt2 = SolveYParam(r.y+r.h); y_intersection.insert(y_intersection.end(), y_intersection_pt2.begin(), y_intersection_pt2.end()); // Merge and sort. @@ -234,6 +275,12 @@ namespace IPDF std::sort(x_intersection.begin(), x_intersection.end()); Debug("Found %d intersections.\n", x_intersection.size()); + for(auto t : x_intersection) + { + Real ptx, pty; + Evaluate(ptx, pty, t); + Debug("Root: t = %f, (%f,%f)", Double(t), Double(ptx), Double(pty)); + } std::vector all_beziers; if (x_intersection.size() <= 2) @@ -246,16 +293,17 @@ namespace IPDF { Real t1 = *it; if (t1 == t0) continue; - Debug(" -- t0: %f to t1: %f", t0, t1); + Debug(" -- t0: %f to t1: %f: %f", Double(t0), Double(t1), (t1 + t0)/Real(2)); Real ptx, pty; Evaluate(ptx, pty, ((t1 + t0) / Real(2))); - if (true || r.PointIn(ptx, pty)) + if (r.PointIn(ptx, pty)) { + Debug("Adding segment: (point at %f, %f)", Double(ptx), Double(pty)); all_beziers.push_back(this->ReParametrise(t0, t1)); } else { - Debug("Segment removed (point at %f, %f)", ptx, pty); + Debug("Segment removed (point at %f, %f)", Double(ptx), Double(pty)); } t0 = t1; }