X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=52a5264527ce408b71c09cc0bd6dbd7cbd25deee;hp=722ed572810a95c41713899695b7b585aa77758c;hb=0361b11485ec41d2c2ddeb279abf846f777f5363;hpb=e88c1ef58e2446cf57d5f7b0d5d4e5bfff0b8c37 diff --git a/src/bezier.h b/src/bezier.h index 722ed57..52a5264 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 @@ -8,13 +11,11 @@ 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) - { - 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); - } + 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-9); /** A _cubic_ bezier. **/ struct Bezier @@ -23,13 +24,73 @@ namespace IPDF Real x1; Real y1; Real x2; Real y2; Real x3; Real y3; + + 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) { + + } + + 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 (fabs(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 (fabs(delta1+delta2+delta3) < 1e-6) + { + type = QUADRATIC; + + //Debug("QUADRATIC %s", Str().c_str()); + return type; + } + + Real discriminant = d1*d3*4 -d2*d2; + if (fabs(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; } - 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 { @@ -42,7 +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) + 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; @@ -64,6 +125,11 @@ 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); @@ -111,7 +177,137 @@ namespace IPDF } return result; } + + // Performs one round of De Casteljau subdivision and returns the [t,1] part. + Bezier DeCasteljauSubdivideLeft(const Real& t) + { + Real one_minus_t = Real(1) - t; + + // X Coordinates + 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 = x12*t + x01*one_minus_t; + Real x123 = x23*t + x12*one_minus_t; + + Real x0123 = x123*t + x012*one_minus_t; + + // Y Coordinates + 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 = y12*t + y01*one_minus_t; + Real y123 = y23*t + y12*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 [t,1] part. + Bezier DeCasteljauSubdivideRight(const Real& t) + { + Real one_minus_t = Real(1) - t; + + // X Coordinates + 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 = x12*t + x01*one_minus_t; + Real x123 = x23*t + x12*one_minus_t; + + Real x0123 = x123*t + x012*one_minus_t; + + // Y Coordinates + 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 = y12*t + y01*one_minus_t; + Real y123 = y23*t + y12*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); + 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); + new_bezier = new_bezier.DeCasteljauSubdivideRight(new_t0); + + Debug("%s becomes %s", this->Str().c_str(), new_bezier.Str().c_str()); + 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()); + + + // Find its roots. + std::vector x_intersection = SolveXParam(r.x); + + // And for the other side. + + std::vector x_intersection_pt2 = SolveXParam(r.x + r.w); + x_intersection.insert(x_intersection.end(), x_intersection_pt2.begin(), x_intersection_pt2.end()); + + // Find its roots. + std::vector y_intersection = SolveYParam(r.y); + + 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. + x_intersection.insert(x_intersection.end(), y_intersection.begin(), y_intersection.end()); + x_intersection.push_back(Real(0)); + x_intersection.push_back(Real(1)); + 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)", t, ptx, pty); + } + + std::vector all_beziers; + if (x_intersection.size() <= 2) + { + 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; + if (t1 == t0) continue; + Debug(" -- t0: %f to t1: %f", t0, t1); + Real ptx, pty; + Evaluate(ptx, pty, ((t1 + t0) / Real(2))); + if (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; + } /** Evaluate the Bezier at parametric parameter u, puts resultant point in (x,y) **/ void Evaluate(Real & x, Real & y, const Real & u) const @@ -122,6 +318,30 @@ 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 + { + 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);} };