X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.h;h=77429cf9033ba06cb199d7ebb0d4fdaef042caa9;hp=0e9217f7a7d8690efe8074f54bc18e5b6f909680;hb=HEAD;hpb=d69b8de94411bee43edc9e16f33bfa0d5d1d6b3b diff --git a/src/bezier.h b/src/bezier.h index 0e9217f..77429cf 100644 --- a/src/bezier.h +++ b/src/bezier.h @@ -1,25 +1,101 @@ #ifndef _BEZIER_H #define _BEZIER_H -#include "real.h" +#include +#include #include "rect.h" +#include "real.h" + + + namespace IPDF { + typedef Real BReal; + typedef TRect BRect; + extern int Factorial(int n); extern int BinomialCoeff(int n, int k); - extern Real Bernstein(int k, int n, const Real & u); + extern BReal Bernstein(int k, int n, const BReal & u); + extern std::pair BezierTurningPoints(const BReal & p0, const BReal & p1, const BReal & p2, const BReal & p3); + + extern std::vector SolveQuadratic(const BReal & a, const BReal & b, const BReal & c, const BReal & min = 0, const BReal & max = 1); + + extern std::vector SolveCubic(const BReal & a, const BReal & b, const BReal & c, const BReal & d, const BReal & min = 0, const BReal & max = 1, const BReal & delta = 1e-9); /** A _cubic_ bezier. **/ struct Bezier { - Real x0; Real y0; - Real x1; Real y1; - Real x2; Real y2; - Real x3; Real y3; - 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) {} + BReal x0; BReal y0; + BReal x1; BReal y1; + BReal x2; BReal y2; + BReal x3; BReal 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(BReal _x0=0, BReal _y0=0, BReal _x1=0, BReal _y1=0, BReal _x2=0, BReal _y2=0, BReal _x3=0, BReal _y3=0) : 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) + BReal a1 = (x1-x0)*BReal(3); + BReal a2 = (x0- x1*BReal(2) +x2)*BReal(3); + BReal a3 = (x3 - x0 + (x1 - x2)*BReal(3)); + + BReal b1 = (y1-y0)*BReal(3); + BReal b2 = (y0- y1*BReal(2) +y2)*BReal(3); + BReal b3 = (y3 - y0 + (y1 - y2)*BReal(3)); + + // d vector (d0 = 0 since all w = 1) + BReal d1 = a2*b3 - a3*b2; + BReal d2 = a3*b1 - a1*b3; + BReal d3 = a1*b2 - a2*b1; + + if (Abs(d1+d2+d3) < BReal(1e-6)) + { + type = LINE; + //Debug("LINE %s", Str().c_str()); + return type; + } + + BReal delta1 = -(d1*d1); + BReal delta2 = d1*d2; + BReal delta3 = d1*d3 -(d2*d2); + if (Abs(delta1+delta2+delta3) < BReal(1e-6)) + { + type = QUADRATIC; + + //Debug("QUADRATIC %s", Str().c_str()); + return type; + } + + BReal discriminant = d1*d3*BReal(4) -d2*d2; + if (Abs(discriminant) < BReal(1e-6)) + { + type = CUSP; + //Debug("CUSP %s", Str().c_str()); + } + else if (discriminant > BReal(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 { @@ -27,7 +103,12 @@ namespace IPDF s << "Bezier{" << Float(x0) << "," << Float(y0) << " -> " << Float(x1) << "," << Float(y1) << " -> " << Float(x2) << "," << Float(y2) << " -> " << Float(x3) << "," << Float(y3) << "}"; return s.str(); } - 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) + + /** + * 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 BRect & t = BRect(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; @@ -47,17 +128,235 @@ namespace IPDF y3 += t.y; } - Rect ToRect() {return Rect(x0,y0,x3-x0,y3-y0);} + BRect SolveBounds() const; + + std::pair GetTop() const; + std::pair GetBottom() const; + std::pair GetLeft() const; + std::pair GetRight() const; + + Bezier ToAbsolute(const BRect & bounds) const + { + return Bezier(*this, bounds); + } + + /** Convert absolute control points to control points relative to bounds + * (This basically does the opposite of the Copy constructor) + * ie: If this is absolute, the returned Bezier will be relative to the bounds rectangle + */ + Bezier ToRelative(const BRect & bounds) const + { + // x' <- (x - x0)/w etc + // special cases when w or h = 0 + // (So can't just use the Copy constructor on the inverse of bounds) + // BRect inverse = {-bounds.x/bounds.w, -bounds.y/bounds.h, BReal(1)/bounds.w, BReal(1)/bounds.h}; + Bezier result; + if (bounds.w == BReal(0)) + { + result.x0 = 0; + result.x1 = 0; + result.x2 = 0; + result.x3 = 0; + } + else + { + result.x0 = (x0 - bounds.x)/bounds.w; + result.x1 = (x1 - bounds.x)/bounds.w; + result.x2 = (x2 - bounds.x)/bounds.w; + result.x3 = (x3 - bounds.x)/bounds.w; + } + + if (bounds.h == BReal(0)) + { + result.y0 = 0; + result.y1 = 0; + result.y2 = 0; + result.y3 = 0; + } + else + { + result.y0 = (y0 - bounds.y)/bounds.h; + result.y1 = (y1 - bounds.y)/bounds.h; + result.y2 = (y2 - bounds.y)/bounds.h; + result.y3 = (y3 - bounds.y)/bounds.h; + } + return result; + } + + // Performs one round of De Casteljau subdivision and returns the [t,1] part. + Bezier DeCasteljauSubdivideLeft(const BReal& t) + { + BReal one_minus_t = BReal(1) - t; + + // X Coordinates + BReal x01 = x1*t + x0*one_minus_t; + BReal x12 = x2*t + x1*one_minus_t; + BReal x23 = x3*t + x2*one_minus_t; + + BReal x012 = x12*t + x01*one_minus_t; + BReal x123 = x23*t + x12*one_minus_t; + + BReal x0123 = x123*t + x012*one_minus_t; + + // Y Coordinates + BReal y01 = y1*t + y0*one_minus_t; + BReal y12 = y2*t + y1*one_minus_t; + BReal y23 = y3*t + y2*one_minus_t; + + BReal y012 = y12*t + y01*one_minus_t; + BReal y123 = y23*t + y12*one_minus_t; + + BReal 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 BReal& t) + { + BReal one_minus_t = BReal(1) - t; + + // X Coordinates + BReal x01 = x1*t + x0*one_minus_t; + BReal x12 = x2*t + x1*one_minus_t; + BReal x23 = x3*t + x2*one_minus_t; + + BReal x012 = x12*t + x01*one_minus_t; + BReal x123 = x23*t + x12*one_minus_t; + + BReal x0123 = x123*t + x012*one_minus_t; + + // Y Coordinates + BReal y01 = y1*t + y0*one_minus_t; + BReal y12 = y2*t + y1*one_minus_t; + BReal y23 = y3*t + y2*one_minus_t; + + BReal y012 = y12*t + y01*one_minus_t; + BReal y123 = y23*t + y12*one_minus_t; + + BReal y0123 = y123*t + y012*one_minus_t; + + return Bezier(x0123, y0123, x123, y123, x23, y23, x3, y3); + } + + Bezier ReParametrise(const BReal& t0, const BReal& 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] + BReal new_t0 = t0 / t1; + //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()); + return new_bezier; + } + + std::vector ClipToRectangle(const BRect & r) + { + // Find points of intersection with the rectangle. + Debug("Clipping Bezier to BRect %s", r.Str().c_str()); + + bool isVerticalLine = false;//(x0 == x1 && x1 == x2 && x2 == x3); + bool isHorizontalLine = false;//(y0 == y1 && y1 == y2 && y2 == y3); + + // Find its roots. + + std::vector intersection; + + if (!isVerticalLine) + { + std::vector x_intersection = SolveXParam(r.x); + intersection.insert(intersection.end(), x_intersection.begin(), x_intersection.end()); + Debug("Number of top intersections: %d", x_intersection.size()); + + // And for the other side. + + std::vector x_intersection_pt2 = SolveXParam(r.x + r.w); + intersection.insert(intersection.end(), x_intersection_pt2.begin(), x_intersection_pt2.end()); + Debug("Number of bottom intersections: %d", x_intersection_pt2.size()); + } + + // Find its roots. + if (!isHorizontalLine) + { + std::vector y_intersection = SolveYParam(r.y); + intersection.insert(intersection.end(), y_intersection.begin(), y_intersection.end()); + Debug("Number of left intersections: %d", y_intersection.size()); + + std::vector y_intersection_pt2 = SolveYParam(r.y+r.h); + intersection.insert(intersection.end(), y_intersection_pt2.begin(), y_intersection_pt2.end()); + Debug("Number of right intersections: %d", y_intersection_pt2.size()); + } + + // Merge and sort. + intersection.push_back(BReal(0)); + intersection.push_back(BReal(1)); + std::sort(intersection.begin(), intersection.end()); + Debug("Number of intersections: %d", intersection.size()); + + std::vector all_beziers; + if (intersection.size() <= 2) + { + all_beziers.push_back(*this); + return all_beziers; + } + BReal t0 = *(intersection.begin()); + for (auto it = intersection.begin()+1; it != intersection.end(); ++it) + { + BReal t1 = *it; + if (t1 == t0) continue; + //Debug(" -- t0: %f to t1: %f: %f", Double(t0), Double(t1), Double((t1 + t0)/BReal(2))); + BReal ptx, pty; + Evaluate(ptx, pty, ((t1 + t0) / BReal(2))); + 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)", Double(ptx), Double(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) + void Evaluate(BReal & x, BReal & y, const BReal & u) const { - Real coeff[4]; + BReal coeff[4]; for (unsigned i = 0; i < 4; ++i) coeff[i] = Bernstein(i,3,u); 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 BReal & x) const; + std::vector SolveYParam(const BReal & x) const; + + // Get points with same X + inline std::vector SolveX(const BReal & x) const + { + return Evaluate(SolveXParam(x)); + } + // Get points with same Y + inline std::vector SolveY(const BReal & 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);} };