X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=25b4796bd177c0403196734aa24f0721971fb899;hp=a7124afd8f250a03460968ff355e70282a4d1961;hb=fe80b0a479a44182b6e7e982fb6ff33b6e17303d;hpb=8b3424a48d2d2e20de1a0e60ff6e1d84b9b5e226 diff --git a/src/bezier.h b/src/bezier.h index a7124af..25b4796 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -15,7 +15,7 @@ namespace IPDF extern std::vector SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min = 0, const Real & max = 1); - extern std::vector SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d, const Real & min = 0, const Real & max = 1, const Real & delta = 1e-4); + extern std::vector SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d, const Real & min = 0, const Real & max = 1, const Real & delta = 1e-9); /** A _cubic_ bezier. **/ struct Bezier @@ -28,42 +28,42 @@ namespace IPDF 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), type(UNKNOWN) + //Bezier() = default; // Needed so we can fread/fwrite this struct... for now. + Bezier(Real _x0=0, Real _y0=0, Real _x1=0, Real _y1=0, Real _x2=0, Real _y2=0, Real _x3=0, Real _y3=0) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x3), y3(_y3), type(UNKNOWN) { } - const Type & GetType() + 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 a1 = (x1-x0)*Real(3); + Real a2 = (x0- x1*Real(2) +x2)*Real(3); + Real a3 = (x3 - x0 + (x1 - x2)*Real(3)); - Real b1 = (y1-y0)*3; - Real b2 = (y0- y1*2 +y2)*3; - Real b3 = (y3 - y0 + (y1 - y2)*3); + Real b1 = (y1-y0)*Real(3); + Real b2 = (y0- y1*Real(2) +y2)*Real(3); + Real b3 = (y3 - y0 + (y1 - y2)*Real(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 (d1 == d2 && d2 == d3 && d3 == 0) + if (Abs(d1+d2+d3) < Real(1e-6)) { type = LINE; //Debug("LINE %s", Str().c_str()); return type; } - Real delta1 = -d1*d1; + Real delta1 = -(d1*d1); Real delta2 = d1*d2; - Real delta3 = d1*d3 -d2*d2; - if (delta1 == delta2 && delta2 == delta3 && delta3 == 0) + Real delta3 = d1*d3 -(d2*d2); + if (Abs(delta1+delta2+delta3) < Real(1e-6)) { type = QUADRATIC; @@ -71,13 +71,13 @@ namespace IPDF return type; } - Real discriminant = d1*d3*4 -d2*d2; - if (discriminant == 0) + Real discriminant = d1*d3*Real(4) -d2*d2; + if (Abs(discriminant) < Real(1e-6)) { type = CUSP; //Debug("CUSP %s", Str().c_str()); } - else if (discriminant > 0) + else if (discriminant > Real(0)) { type = SERPENTINE; //Debug("SERPENTINE %s", Str().c_str()); @@ -87,6 +87,7 @@ namespace IPDF type = LOOP; //Debug("LOOP %s", Str().c_str()); } + //Debug("disc %.30f", discriminant); return type; } @@ -102,7 +103,7 @@ namespace IPDF * Construct absolute control points using relative control points to a bounding rectangle * ie: If cpy is relative to bounds rectangle, this will be absolute */ - Bezier(const Bezier & cpy, const Rect & t = Rect(0,0,1,1)) : x0(cpy.x0), y0(cpy.y0), x1(cpy.x1), y1(cpy.y1), x2(cpy.x2),y2(cpy.y2), x3(cpy.x3), y3(cpy.y3), type(UNKNOWN) + Bezier(const Bezier & cpy, const Rect & t = Rect(0,0,1,1)) : x0(cpy.x0), y0(cpy.y0), x1(cpy.x1), y1(cpy.y1), x2(cpy.x2),y2(cpy.y2), x3(cpy.x3), y3(cpy.y3), type(cpy.type) { x0 *= t.w; y0 *= t.h; @@ -145,7 +146,7 @@ namespace IPDF // (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) + if (bounds.w == Real(0)) { result.x0 = 0; result.x1 = 0; @@ -160,7 +161,7 @@ namespace IPDF result.x3 = (x3 - bounds.x)/bounds.w; } - if (bounds.h == 0) + if (bounds.h == Real(0)) { result.y0 = 0; result.y1 = 0; @@ -178,72 +179,72 @@ 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()); + //Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str()); return new_bezier; } @@ -252,36 +253,24 @@ 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); + //Debug("Found %d intersections on left edge", x_intersection.size()); // 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; + //Debug("Found %d intersections on right edge (total x: %d)", x_intersection_pt2.size(), x_intersection.size()); // 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); + //Debug("Found %d intersections on top edge", y_intersection.size()); - 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()); + //Debug("Found %d intersections on bottom edge (total y: %d)", y_intersection_pt2.size(), y_intersection.size()); // Merge and sort. x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end()); @@ -289,7 +278,13 @@ namespace IPDF x_intersection.push_back(Real(1)); std::sort(x_intersection.begin(), x_intersection.end()); - Debug("Found %d intersections.\n", x_intersection.size()); + //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) @@ -302,16 +297,17 @@ 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), Double((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; }