X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.cpp;h=19d89afcb8ab92a1790b74a472796bb065dc239d;hp=daa07360079ea818ca7050dc144b0adbbf87eb65;hb=326f04a375ce3120f7e8957e3d7cd5f296f513e3;hpb=ef0af5fd0129161a9e079bd3cd1298b53f1fe11a diff --git a/src/bezier.cpp b/src/bezier.cpp index daa0736..19d89af 100644 --- a/src/bezier.cpp +++ b/src/bezier.cpp @@ -11,32 +11,32 @@ using namespace std; namespace IPDF { -vector SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min, const Real & max) +vector SolveQuadratic(const BReal & a, const BReal & b, const BReal & c, const BReal & min, const BReal & max) { - vector roots; roots.reserve(2); + vector roots; roots.reserve(2); if (a == 0 && b != 0) { roots.push_back(-c/b); return roots; } - Real disc(b*b - Real(4)*a*c); + BReal disc(b*b - BReal(4)*a*c); if (disc < 0) { return roots; } else if (disc == 0) { - Real x(-b/Real(2)*a); + BReal x(-b/BReal(2)*a); if (x >= min && x <= max) roots.push_back(x); return roots; } - 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)); + BReal x0((-b - Sqrt(b*b - BReal(4)*a*c))/(BReal(2)*a)); + BReal x1((-b + Sqrt(b*b - BReal(4)*a*c))/(BReal(2)*a)); if (x0 > x1) { - Real tmp(x0); + BReal tmp(x0); x0 = x1; x1 = tmp; } @@ -51,10 +51,10 @@ vector SolveQuadratic(const Real & a, const Real & b, const Real & c, cons * Finds the root (if it exists) in a monotonicly in(de)creasing segment of a Cubic */ -static void CubicSolveSegment(vector & roots, const Real & a, const Real & b, const Real & c, const Real & d, Real & tl, Real & tu, const Real & delta) +static void CubicSolveSegment(vector & roots, const BReal & a, const BReal & b, const BReal & c, const BReal & d, BReal & tl, BReal & tu, const BReal & delta) { - Real l = a*tl*tl*tl + b*tl*tl + c*tl + d; - Real u = a*tu*tu*tu + b*tu*tu + c*tu + d; + BReal l = a*tl*tl*tl + b*tl*tl + c*tl + d; + BReal u = a*tu*tu*tu + b*tu*tu + c*tu + d; if ((l < 0 && u < 0) || (l > 0 && u > 0)) { //Debug("Discarding segment (no roots) l = %f (%f), u = %f (%f)", Double(tl), Double(l), Double(tu), Double(u)); @@ -65,9 +65,9 @@ static void CubicSolveSegment(vector & roots, const Real & a, const Real & //Debug("%ft^3 + %ft^2 + %ft + %f is negative (%f < %f) %d", Double(a),Double(b),Double(c),Double(d),Double(u),Double(l), negative); while (tu - tl > delta) { - Real t(tu+tl); + BReal t(tu+tl); t /= 2; - Real m = a*t*t*t + b*t*t + c*t + d; + BReal m = a*t*t*t + b*t*t + c*t + d; if (m > 0) { if (negative) @@ -87,12 +87,12 @@ static void CubicSolveSegment(vector & roots, const Real & a, const Real & } roots.push_back(tl); } -vector SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d, const Real & min, const Real & max, const Real & delta) +vector SolveCubic(const BReal & a, const BReal & b, const BReal & c, const BReal & d, const BReal & min, const BReal & max, const BReal & delta) { - vector roots; roots.reserve(3); - Real tu(max); - Real tl(min); - vector turns(SolveQuadratic(a*3, b*2, c)); + vector roots; roots.reserve(3); + BReal tu(max); + BReal tl(min); + vector turns(SolveQuadratic(a*3, b*2, c)); //Debug("%u turning points", turns.size()); for (unsigned i = 1; i < turns.size(); ++i) { @@ -137,9 +137,9 @@ int BinomialCoeff(int n, int k) /** * Bernstein Basis Polynomial */ -Real Bernstein(int k, int n, const Real & u) +BReal Bernstein(int k, int n, const BReal & u) { - return Real(BinomialCoeff(n, k)) * Power(u, k) * Power(Real(1.0) - u, n-k); + return BReal(BinomialCoeff(n, k)) * Power(u, k) * Power(BReal(1.0) - u, n-k); } @@ -148,42 +148,42 @@ Real Bernstein(int k, int n, const Real & u) * In one coordinate direction */ -pair BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3) +pair BezierTurningPoints(const BReal & p0, const BReal & p1, const BReal & p2, const BReal & p3) { // straight line if (p1 == p2 && p2 == p3) { - return pair(0, 1); + return pair(0, 1); } - Real a = ((p1-p2)*3 + p3 - p0); - Real b = (p2 - p1*2 + p0)*2; - Real c = (p1-p0); + BReal a = ((p1-p2)*3 + p3 - p0); + BReal b = (p2 - p1*2 + p0)*2; + BReal c = (p1-p0); if (a == 0) { if (b == 0) - return pair(0,1); - Real t = -c/b; + return pair(0,1); + BReal t = -c/b; if (t > 1) t = 1; if (t < 0) t = 0; - return pair(t, t); + return pair(t, t); } //Debug("a, b, c are %f, %f, %f", Float(a), Float(b), Float(c)); if (b*b - a*c*4 < 0) { //Debug("No real roots"); - return pair(0,1); + return pair(0,1); } - vector tsols = SolveQuadratic(a, b, c); + vector tsols = SolveQuadratic(a, b, c); if (tsols.size() == 1) - return pair(tsols[0], tsols[0]); + return pair(tsols[0], tsols[0]); else if (tsols.size() == 0) - return pair(0,1); + return pair(0,1); - return pair(tsols[0], tsols[1]); + return pair(tsols[0], tsols[1]); } -inline bool CompRealByPtr(const Real * a, const Real * b) +inline bool CompBRealByPtr(const BReal * a, const BReal * b) { return (*a) < (*b); } @@ -191,20 +191,20 @@ inline bool CompRealByPtr(const Real * a, const Real * b) /** * Get top most *point* on Bezier curve */ -pair Bezier::GetTop() const +pair Bezier::GetTop() const { - pair tsols = BezierTurningPoints(y0,y1,y2,y3); - Real tx0; Real ty0; - Real tx1; Real ty1; + pair tsols = BezierTurningPoints(y0,y1,y2,y3); + BReal tx0; BReal ty0; + BReal tx1; BReal ty1; Evaluate(tx0, ty0, tsols.first); Evaluate(tx1, ty1, tsols.second); - vector v(4); + vector v(4); v[0] = &y0; v[1] = &y3; v[2] = &ty0; v[3] = &ty1; - sort(v.begin(), v.end(), CompRealByPtr); - pair result; + sort(v.begin(), v.end(), CompBRealByPtr); + pair result; result.second = *v[0]; if (v[0] == &y0) { @@ -228,20 +228,20 @@ pair Bezier::GetTop() const /** * Get bottom most *point* on Bezier curve */ -pair Bezier::GetBottom() const +pair Bezier::GetBottom() const { - pair tsols = BezierTurningPoints(y0,y1,y2,y3); - Real tx0; Real ty0; - Real tx1; Real ty1; + pair tsols = BezierTurningPoints(y0,y1,y2,y3); + BReal tx0; BReal ty0; + BReal tx1; BReal ty1; Evaluate(tx0, ty0, tsols.first); Evaluate(tx1, ty1, tsols.second); - vector v(4); + vector v(4); v[0] = &y0; v[1] = &y3; v[2] = &ty0; v[3] = &ty1; - sort(v.begin(), v.end(), CompRealByPtr); - pair result; + sort(v.begin(), v.end(), CompBRealByPtr); + pair result; result.second = *v[3]; if (v[3] == &y0) { @@ -265,20 +265,20 @@ pair Bezier::GetBottom() const /** * Get left most *point* on Bezier curve */ -pair Bezier::GetLeft() const +pair Bezier::GetLeft() const { - pair tsols = BezierTurningPoints(x0,x1,x2,x3); - Real tx0; Real ty0; - Real tx1; Real ty1; + pair tsols = BezierTurningPoints(x0,x1,x2,x3); + BReal tx0; BReal ty0; + BReal tx1; BReal ty1; Evaluate(tx0, ty0, tsols.first); Evaluate(tx1, ty1, tsols.second); - vector v(4); + vector v(4); v[0] = &x0; v[1] = &x3; v[2] = &tx0; v[3] = &tx1; - sort(v.begin(), v.end(), CompRealByPtr); - pair result; + sort(v.begin(), v.end(), CompBRealByPtr); + pair result; result.first = *v[0]; if (v[0] == &x0) { @@ -303,20 +303,20 @@ pair Bezier::GetLeft() const /** * Get left most *point* on Bezier curve */ -pair Bezier::GetRight() const +pair Bezier::GetRight() const { - pair tsols = BezierTurningPoints(x0,x1,x2,x3); - Real tx0; Real ty0; - Real tx1; Real ty1; + pair tsols = BezierTurningPoints(x0,x1,x2,x3); + BReal tx0; BReal ty0; + BReal tx1; BReal ty1; Evaluate(tx0, ty0, tsols.first); Evaluate(tx1, ty1, tsols.second); - vector v(4); + vector v(4); v[0] = &x0; v[1] = &x3; v[2] = &tx0; v[3] = &tx1; - sort(v.begin(), v.end(), CompRealByPtr); - pair result; + sort(v.begin(), v.end(), CompBRealByPtr); + pair result; result.first = *v[3]; if (v[3] == &x0) { @@ -337,13 +337,13 @@ pair Bezier::GetRight() const return result; } -vector Bezier::SolveXParam(const Real & x) const +vector Bezier::SolveXParam(const BReal & x) const { - Real d(x0 - x); - Real c((x1 - x0)*Real(3)); - Real b((x2 - x1)*Real(3) - c); - Real a(x3 -x0 - c - b); - vector results(SolveCubic(a, b, c, d)); + BReal d(x0 - x); + BReal c((x1 - x0)*BReal(3)); + BReal b((x2 - x1)*BReal(3) - c); + BReal a(x3 -x0 - c - b); + vector results(SolveCubic(a, b, c, d)); for (unsigned i = 0; i < results.size(); ++i) { Vec2 p; @@ -353,13 +353,13 @@ vector Bezier::SolveXParam(const Real & x) const } -vector Bezier::SolveYParam(const Real & y) const +vector Bezier::SolveYParam(const BReal & y) const { - Real d(y0 - y); - Real c((y1 - y0)*Real(3)); - Real b((y2 - y1)*Real(3) - c); - Real a(y3 -y0 - c - b); - vector results(SolveCubic(a, b, c, d)); + BReal d(y0 - y); + BReal c((y1 - y0)*BReal(3)); + BReal b((y2 - y1)*BReal(3) - c); + BReal a(y3 -y0 - c - b); + vector results(SolveCubic(a, b, c, d)); for (unsigned i = 0; i < results.size(); ++i) { Vec2 p; @@ -368,7 +368,7 @@ vector Bezier::SolveYParam(const Real & y) const return results; } -vector Bezier::Evaluate(const vector & u) const +vector Bezier::Evaluate(const vector & u) const { vector result(u.size()); for (unsigned i = 0; i < u.size(); ++i) @@ -381,25 +381,25 @@ vector Bezier::Evaluate(const vector & u) const /** * Get Bounds Rectangle of Bezier */ -Rect Bezier::SolveBounds() const +BRect Bezier::SolveBounds() const { - Rect result; - pair tsols = BezierTurningPoints(x0, x1, x2, x3); + BRect result; + pair tsols = BezierTurningPoints(x0, x1, x2, x3); - Real tp0; Real tp1; Real o; + BReal tp0; BReal tp1; BReal o; Evaluate(tp0, o, tsols.first); Evaluate(tp1, o, tsols.second); //Debug("x: tp0 is %f tp1 is %f", Float(tp0), Float(tp1)); - vector v(4); + vector v(4); v[0] = &x0; v[1] = &x3; v[2] = &tp0; v[3] = &tp1; // Not using a lambda to keep this compiling on cabellera - sort(v.begin(), v.end(), CompRealByPtr); + sort(v.begin(), v.end(), CompBRealByPtr); result.x = *(v[0]); result.w = *(v[3]) - result.x; @@ -416,7 +416,7 @@ Rect Bezier::SolveBounds() const v[1] = &y3; v[2] = &tp0; v[3] = &tp1; - sort(v.begin(), v.end(), CompRealByPtr); + sort(v.begin(), v.end(), CompBRealByPtr); result.y = *(v[0]); result.h = *(v[3]) - result.y;