X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=a7124afd8f250a03460968ff355e70282a4d1961;hp=03e789cf64af4b17352254d6f62d1d75c6c6707a;hb=8b3424a48d2d2e20de1a0e60ff6e1d84b9b5e226;hpb=d272af0f7f981cea9d1024b6a730be73dd22276a diff --git a/src/bezier.h b/src/bezier.h index 03e789c..a7124af 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -13,64 +13,9 @@ namespace IPDF 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) - { - Real x0((-b + Sqrt(b*b - Real(4)*a*c))/(Real(2)*a)); - Real x1((-b - Sqrt(b*b - Real(4)*a*c))/(Real(2)*a)); - return std::pair(x0,x1); - } - - inline std::vector SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d) - { - // This is going to be a big one... - // See http://en.wikipedia.org/wiki/Cubic_function#General_formula_for_roots - - // delta = 18abcd - 4 b^3 d + b^2 c^2 - 4ac^3 - 27 a^2 d^2 - - 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; - - std::vector roots; - - 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); + extern std::vector SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min = 0, const Real & max = 1); - return roots; - - } - - ////HACK: We know any roots we care about will be between 0 and 1, so... - Real maxi(100); - Real prevRes(d); - 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)) && (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; - - } + 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); /** A _cubic_ bezier. **/ struct Bezier @@ -80,16 +25,72 @@ 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; + } + const 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 (d1 == d2 && d2 == d3 && d3 == 0) + { + 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 (delta1 == delta2 && delta2 == delta3 && delta3 == 0) + { + type = QUADRATIC; + + //Debug("QUADRATIC %s", Str().c_str()); + return type; + } + + Real discriminant = d1*d3*4 -d2*d2; + if (discriminant == 0) + { + 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()); + } + return type; + } + + std::string Str() const { std::stringstream s; @@ -101,7 +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), type(cpy.type) + 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) { x0 *= t.w; y0 *= t.h; @@ -326,6 +327,21 @@ 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]; } + std::vector Evaluate(const std::vector & u) const; + + std::vector SolveXParam(const Real & x) const; + std::vector SolveYParam(const Real & x) const; + + // Get points with same X + inline std::vector SolveX(const Real & x) const + { + return Evaluate(SolveXParam(x)); + } + // Get points with same Y + inline std::vector SolveY(const Real & y) const + { + return Evaluate(SolveYParam(y)); + } bool operator==(const Bezier & equ) const {