X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=9dd38c0e7b7d8d7ec9993f63549d88146c6327d8;hp=9273ceecbddb78368deb10ba0898280ec3a638fb;hb=a69d8466e4ad4dd92488798582e680ae31029038;hpb=813591a7d8a7364003233939f52b0031f3a40d20 diff --git a/src/bezier.h b/src/bezier.h index 9273cee..9dd38c0 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -11,6 +11,7 @@ namespace IPDF extern int Factorial(int n); extern int BinomialCoeff(int n, int k); extern Real Bernstein(int k, int n, const Real & u); + extern std::pair BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3); inline std::pair SolveQuadratic(const Real & a, const Real & b, const Real & c) { @@ -24,27 +25,44 @@ namespace IPDF // This is going to be a big one... // See http://en.wikipedia.org/wiki/Cubic_function#General_formula_for_roots + std::vector roots; // delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2 - /* + +#if 0 Real discriminant = Real(18) * a * b * c * d - Real(4) * (b * b * b) * d + (b * b) * (c * c) - Real(4) * a * (c * c * c) - Real(27) * (a * a) * (d * d); - */ + + Debug("Trying to solve %fx^3 + %fx^2 + %fx + %f (Discriminant: %f)", a,b,c,d, discriminant); // discriminant > 0 => 3 distinct, real roots. // discriminant = 0 => a multiple root (1 or 2 real roots) // discriminant < 0 => 1 real root, 2 complex conjugate roots + Real delta0 = (b*b) - Real(3) * a * c; + Real delta1 = Real(2) * (b * b * b) - Real(9) * a * b * c + Real(27) * (a * a) * d; + + + Real C = pow((delta1 + Sqrt((delta1 * delta1) - 4 * (delta0 * delta0 * delta0)) ) / Real(2), 1/3); + + if (false && discriminant < 0) + { + Real real_root = (Real(-1) / (Real(3) * a)) * (b + C + delta0 / C); + + roots.push_back(real_root); + + return roots; + + } +#endif ////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 = -1; i <= 100; ++i) + for(int i = 0; i <= 100; ++i) { Real x(i); x /= maxi; Real y = a*(x*x*x) + b*(x*x) + c*x + d; - if ( ((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); @@ -62,14 +80,17 @@ namespace IPDF Real x1; Real y1; Real x2; Real y2; Real x3; Real y3; + + typedef enum {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) { - + //TODO: classify the curve + type = SERPENTINE; } - Bezier(Real _x0, Real _y0, Real _x1, Real _y1, Real _x2, Real _y2) : x0(_x0), y0(_y0), x1(_x1), y1(_y1), x2(_x2), y2(_y2), x3(_x2), y3(_y2) {} - std::string Str() const { std::stringstream s; @@ -81,7 +102,7 @@ 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) + 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; @@ -103,6 +124,11 @@ namespace IPDF Rect SolveBounds() const; + std::pair GetTop() const; + std::pair GetBottom() const; + std::pair GetLeft() const; + std::pair GetRight() const; + Bezier ToAbsolute(const Rect & bounds) const { return Bezier(*this, bounds); @@ -227,32 +253,32 @@ namespace IPDF 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; + 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); // And for the other side. - xd = x3 - r.x - r.w; + xd = x0 - 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; + 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 = y3 - r.y - r.h; + yd = y0 - 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()); @@ -266,7 +292,7 @@ namespace IPDF Debug("Found %d intersections.\n", x_intersection.size()); std::vector all_beziers; - if (x_intersection.empty()) + if (x_intersection.size() <= 2) { all_beziers.push_back(*this); return all_beziers; @@ -279,10 +305,14 @@ namespace IPDF Debug(" -- t0: %f to t1: %f", t0, t1); Real ptx, pty; Evaluate(ptx, pty, ((t1 + t0) / Real(2))); - if (r.PointIn(ptx, pty)) + if (true || r.PointIn(ptx, pty)) { all_beziers.push_back(this->ReParametrise(t0, t1)); } + else + { + Debug("Segment removed (point at %f, %f)", ptx, pty); + } t0 = t1; } return all_beziers; @@ -297,6 +327,15 @@ namespace IPDF x = x0*coeff[0] + x1*coeff[1] + x2*coeff[2] + x3*coeff[3]; y = y0*coeff[0] + y1*coeff[1] + y2*coeff[2] + y3*coeff[3]; } + + bool operator==(const Bezier & equ) const + { + return (x0 == equ.x0 && y0 == equ.y0 + && x1 == equ.x1 && y1 == equ.y1 + && x2 == equ.x2 && y2 == equ.y2 + && x3 == equ.x3 && y3 == equ.y3); + } + bool operator!=(const Bezier & equ) const {return !this->operator==(equ);} };