#include <cmath>
#include <algorithm>
+
+
using namespace std;
namespace IPDF
{
+vector<BReal> SolveQuadratic(const BReal & a, const BReal & b, const BReal & c, const BReal & min, const BReal & max)
+{
+ vector<BReal> roots; roots.reserve(2);
+ if (a == BReal(0) && b != BReal(0))
+ {
+ roots.push_back(-c/b);
+ return roots;
+ }
+ BReal disc(b*b - BReal(4)*a*c);
+ if (disc < BReal(0))
+ {
+ return roots;
+ }
+ else if (disc == BReal(0))
+ {
+ BReal x(-b/BReal(2)*a);
+ if (x >= min && x <= max)
+ roots.push_back(x);
+ return roots;
+ }
+
+ 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)
+ {
+ BReal tmp(x0);
+ x0 = x1;
+ x1 = tmp;
+ }
+ if (x0 >= min && x0 <= max)
+ roots.push_back(x0);
+ if (x1 >= min && x1 <= max)
+ roots.push_back(x1);
+ return roots;
+}
+
+/**
+ * Finds the root (if it exists) in a monotonicly in(de)creasing segment of a Cubic
+ */
+
+static void CubicSolveSegment(vector<BReal> & roots, const BReal & a, const BReal & b, const BReal & c, const BReal & d, BReal & tl, BReal & tu, const BReal & delta)
+{
+ 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 < BReal(0) && u < BReal(0)) || (l > BReal(0) && u > BReal(0)))
+ {
+ //Debug("Discarding segment (no roots) l = %f (%f), u = %f (%f)", Double(tl), Double(l), Double(tu), Double(u));
+ //return;
+ }
+
+ bool negative = (u < l); // lower point > 0, upper point < 0
+ //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)
+ {
+ BReal t(tu+tl);
+ t /= 2;
+ BReal m = a*t*t*t + b*t*t + c*t + d;
+ if (m > BReal(0))
+ {
+ if (negative)
+ tl = t;
+ else
+ tu = t;
+ }
+ else if (negative)
+ {
+ tu = t;
+ }
+ else
+ {
+ tl = t;
+ }
+ //Debug("Delta is %f (%f - %f -> %f)", tu-tl, tu, tl, t);
+ }
+ roots.push_back(tl);
+}
+vector<BReal> SolveCubic(const BReal & a, const BReal & b, const BReal & c, const BReal & d, const BReal & min, const BReal & max, const BReal & delta)
+{
+ vector<BReal> roots; roots.reserve(3);
+ BReal tu(max);
+ BReal tl(min);
+ vector<BReal> turns(SolveQuadratic(a*BReal(3), b*BReal(2), c));
+ //Debug("%u turning points", turns.size());
+ for (unsigned i = 1; i < turns.size(); ++i)
+ {
+ //if (tl > max) break;
+ tu = turns[i];
+ CubicSolveSegment(roots, a, b, c, d, tl, tu,delta);
+ tl = turns[i];
+ }
+ tu = max;
+ CubicSolveSegment(roots, a, b, c, d, tl, tu,delta);
+ return roots;
+}
+
/**
* Factorial
* Use dynamic programming / recursion
/**
* 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);
}
* In one coordinate direction
*/
-static pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3)
+pair<BReal, BReal> BezierTurningPoints(const BReal & p0, const BReal & p1, const BReal & p2, const BReal & p3)
{
// straight line
if (p1 == p2 && p2 == p3)
{
- return pair<Real,Real>(0, 1);
+ return pair<BReal,BReal>(0, 1);
}
- Real a = (p1- p0 - 2*(p2-p1) + p3-p2);
- Real b = (p1-p0 - (p2-p1))*(p1-p0);
- Real c = (p1-p0);
- if (a == 0)
+ BReal a = ((p1-p2)*BReal(3) + p3 - p0);
+ BReal b = (p2 - p1*BReal(2) + p0)*BReal(2);
+ BReal c = (p1-p0);
+ if (a == BReal(0))
{
- if (b == 0)
- return pair<Real, Real>(0,1);
- Real t = -c/b;
- if (t > 1) t = 1;
- if (t < 0) t = 0;
- return pair<Real, Real>(t, t);
+ if (b == BReal(0))
+ return pair<BReal, BReal>(0,1);
+ BReal t = -c/b;
+ if (t > BReal(1)) t = 1;
+ if (t < BReal(0)) t = 0;
+ return pair<BReal, BReal>(t, t);
}
- Debug("a, b, c are %f, %f, %f", Float(a), Float(b), Float(c));
- if (b*b - 4*a*c < 0)
+ //Debug("a, b, c are %f, %f, %f", Float(a), Float(b), Float(c));
+ if (b*b - a*c*BReal(4) < BReal(0))
{
- return pair<Real, Real>(0,1);
+ //Debug("No real roots");
+ return pair<BReal, BReal>(0,1);
}
- pair<Real, Real> tsols = SolveQuadratic(a, b, c);
- if (tsols.first > 1) tsols.first = 1;
- if (tsols.first < 0) tsols.first = 0;
- if (tsols.second > 1) tsols.second = 1;
- if (tsols.second < 0) tsols.second = 0;
- return tsols;
+ vector<BReal> tsols = SolveQuadratic(a, b, c);
+ if (tsols.size() == 1)
+ return pair<BReal,BReal>(tsols[0], tsols[0]);
+ else if (tsols.size() == 0)
+ return pair<BReal, BReal>(0,1);
+
+ return pair<BReal,BReal>(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);
}
+/**
+ * Get top most *point* on Bezier curve
+ */
+pair<BReal,BReal> Bezier::GetTop() const
+{
+ pair<BReal, BReal> 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<const BReal*> v(4);
+ v[0] = &y0;
+ v[1] = &y3;
+ v[2] = &ty0;
+ v[3] = &ty1;
+ sort(v.begin(), v.end(), CompBRealByPtr);
+ pair<BReal,BReal> result;
+ result.second = *v[0];
+ if (v[0] == &y0)
+ {
+ result.first = x0;
+ }
+ else if (v[0] == &y3)
+ {
+ result.first = x3;
+ }
+ else if (v[0] == &ty0)
+ {
+ result.first = tx0;
+ }
+ else if (v[0] == &ty1)
+ {
+ result.first = tx1;
+ }
+ return result;
+}
+
+/**
+ * Get bottom most *point* on Bezier curve
+ */
+pair<BReal,BReal> Bezier::GetBottom() const
+{
+ pair<BReal, BReal> 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<const BReal*> v(4);
+ v[0] = &y0;
+ v[1] = &y3;
+ v[2] = &ty0;
+ v[3] = &ty1;
+ sort(v.begin(), v.end(), CompBRealByPtr);
+ pair<BReal,BReal> result;
+ result.second = *v[3];
+ if (v[3] == &y0)
+ {
+ result.first = x0;
+ }
+ else if (v[3] == &y3)
+ {
+ result.first = x3;
+ }
+ else if (v[3] == &ty0)
+ {
+ result.first = tx0;
+ }
+ else if (v[3] == &ty1)
+ {
+ result.first = tx1;
+ }
+ return result;
+}
+
+/**
+ * Get left most *point* on Bezier curve
+ */
+pair<BReal,BReal> Bezier::GetLeft() const
+{
+ pair<BReal, BReal> 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<const BReal*> v(4);
+ v[0] = &x0;
+ v[1] = &x3;
+ v[2] = &tx0;
+ v[3] = &tx1;
+ sort(v.begin(), v.end(), CompBRealByPtr);
+ pair<BReal,BReal> result;
+ result.first = *v[0];
+ if (v[0] == &x0)
+ {
+ result.second = y0;
+ }
+ else if (v[0] == &x3)
+ {
+ result.second = y3;
+ }
+ else if (v[0] == &tx0)
+ {
+ result.second = ty0;
+ }
+ else if (v[0] == &tx1)
+ {
+ result.second = ty1;
+ }
+ return result;
+}
+
+
+/**
+ * Get left most *point* on Bezier curve
+ */
+pair<BReal,BReal> Bezier::GetRight() const
+{
+ pair<BReal, BReal> 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<const BReal*> v(4);
+ v[0] = &x0;
+ v[1] = &x3;
+ v[2] = &tx0;
+ v[3] = &tx1;
+ sort(v.begin(), v.end(), CompBRealByPtr);
+ pair<BReal,BReal> result;
+ result.first = *v[3];
+ if (v[3] == &x0)
+ {
+ result.second = y0;
+ }
+ else if (v[3] == &x3)
+ {
+ result.second = y3;
+ }
+ else if (v[3] == &tx0)
+ {
+ result.second = ty0;
+ }
+ else if (v[3] == &tx1)
+ {
+ result.second = ty1;
+ }
+ return result;
+}
+
+vector<BReal> Bezier::SolveXParam(const BReal & x) const
+{
+ BReal d(x0 - x);
+ BReal c((x1 - x0)*BReal(3));
+ BReal b((x2 - x1)*BReal(3) - c);
+ BReal a(x3 -x0 - c - b);
+ vector<BReal> results(SolveCubic(a, b, c, d));
+ for (unsigned i = 0; i < results.size(); ++i)
+ {
+ Vec2 p;
+ Evaluate(p.x, p.y, results[i]);
+ }
+ return results;
+}
+
+
+vector<BReal> Bezier::SolveYParam(const BReal & y) const
+{
+ BReal d(y0 - y);
+ BReal c((y1 - y0)*BReal(3));
+ BReal b((y2 - y1)*BReal(3) - c);
+ BReal a(y3 -y0 - c - b);
+ vector<BReal> results(SolveCubic(a, b, c, d));
+ for (unsigned i = 0; i < results.size(); ++i)
+ {
+ Vec2 p;
+ Evaluate(p.x, p.y, results[i]);
+ }
+ return results;
+}
+
+vector<Vec2> Bezier::Evaluate(const vector<BReal> & u) const
+{
+ vector<Vec2> result(u.size());
+ for (unsigned i = 0; i < u.size(); ++i)
+ {
+ Evaluate(result[i].x, result[i].y, u[i]);
+ }
+ return result;
+}
+
/**
* Get Bounds Rectangle of Bezier
*/
-Rect Bezier::SolveBounds() const
+BRect Bezier::SolveBounds() const
{
- Rect result;
- pair<Real, Real> tsols = BezierTurningPoints(x0, x1, x2, x3);
+ BRect result;
+ pair<BReal, BReal> 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));
+ //Debug("x: tp0 is %f tp1 is %f", Float(tp0), Float(tp1));
- vector<const Real*> v(4);
+ vector<const BReal*> 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;
Evaluate(o, tp1, tsols.second);
- Debug("y: tp0 is %f tp1 is %f", Float(tp0), Float(tp1));
+ //Debug("y: tp0 is %f tp1 is %f", Float(tp0), Float(tp1));
v[0] = &y0;
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;
- Debug("Solved Bezier %s bounds as %s", Str().c_str(), result.Str().c_str());
+ //Debug("Solved Bezier %s bounds as %s", Str().c_str(), result.Str().c_str());
return result;
}
} // end namespace
+
git.ucc.asn.au / ipdf / code.git / blobdiff
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