X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.cpp;h=daa07360079ea818ca7050dc144b0adbbf87eb65;hp=b3129e4f7ee4f3b36c651cfe7dc408e2bcd89a89;hb=58a6719da2337b3e6e20b581885f170bbe5fc480;hpb=d9c0c3792133f87cd224dc22be428be8ddc016d8

diff --git a/src/bezier.cpp b/src/bezier.cpp
index b3129e4..daa0736 100644
--- a/src/bezier.cpp
+++ b/src/bezier.cpp
@@ -4,11 +4,107 @@
 #include <cmath>
 #include <algorithm>
 
+
+
 using namespace std;
 
 namespace IPDF
 {
 
+vector<Real> SolveQuadratic(const Real & a, const Real & b, const Real & c, const Real & min, const Real & max)
+{
+	vector<Real> roots; roots.reserve(2);
+	if (a == 0 && b != 0)
+	{
+		roots.push_back(-c/b);
+		return roots;
+	}
+	Real disc(b*b - Real(4)*a*c);
+	if (disc < 0)
+	{
+		return roots;
+	}
+	else if (disc == 0)
+	{
+		Real x(-b/Real(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));
+	if (x0 > x1)
+	{
+		Real 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<Real> & roots, const Real & a, const Real & b, const Real & c, const Real & d, Real & tl, Real & tu, const Real & 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;
+	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));
+		//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)
+	{
+		Real t(tu+tl);
+		t /= 2;
+		Real m = a*t*t*t + b*t*t + c*t + d;
+		if (m > 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<Real> SolveCubic(const Real & a, const Real & b, const Real & c, const Real & d, const Real & min, const Real & max, const Real & delta)
+{
+	vector<Real> roots; roots.reserve(3);
+	Real tu(max);
+	Real tl(min);
+	vector<Real> turns(SolveQuadratic(a*3, b*2, c));
+	//Debug("%u turning points", turns.size());
+	for (unsigned i = 1; i < turns.size(); ++i)
+	{
+		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
@@ -52,15 +148,15 @@ Real Bernstein(int k, int n, const Real & u)
  * In one coordinate direction
  */
 
-static pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3)
+pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, const Real & p2, const Real & p3)
 {
 	// straight line
 	if (p1 == p2 && p2 == p3)
 	{
 		return pair<Real,Real>(0, 1);
 	}
-	Real a = (3*(p1-p2) + p3 - p0);
-	Real b = 2*(p2 - 2*p1 + p0);
+	Real a = ((p1-p2)*3 + p3 - p0);
+	Real b = (p2 - p1*2 + p0)*2;
 	Real c = (p1-p0);
 	if (a == 0)
 	{
@@ -72,17 +168,19 @@ static pair<Real, Real> BezierTurningPoints(const Real & p0, const Real & p1, co
 		return pair<Real, Real>(t, t);
 	}
 	//Debug("a, b, c are %f, %f, %f", Float(a), Float(b), Float(c));
-	if (b*b - 4*a*c < 0)
+	if (b*b - a*c*4 < 0)
 	{
 		//Debug("No real roots");
 		return pair<Real, Real>(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<Real> tsols = SolveQuadratic(a, b, c);
+	if (tsols.size() == 1)
+		return pair<Real,Real>(tsols[0], tsols[0]);
+	else if (tsols.size() == 0)
+		return pair<Real, Real>(0,1);
+	
+	return pair<Real,Real>(tsols[0], tsols[1]);
+	
 }
 
 inline bool CompRealByPtr(const Real * a, const Real * b) 
@@ -90,6 +188,196 @@ inline bool CompRealByPtr(const Real * a, const Real * b)
 	return (*a) < (*b);
 }
 
+/**
+ * Get top most *point* on Bezier curve
+ */
+pair<Real,Real> Bezier::GetTop() const
+{
+	pair<Real, Real> tsols = BezierTurningPoints(y0,y1,y2,y3);
+	Real tx0; Real ty0;
+	Real tx1; Real ty1;
+	Evaluate(tx0, ty0, tsols.first);
+	Evaluate(tx1, ty1, tsols.second);
+	vector<const Real*> v(4);
+	v[0] = &y0;
+	v[1] = &y3;
+	v[2] = &ty0;
+	v[3] = &ty1;
+	sort(v.begin(), v.end(), CompRealByPtr);
+	pair<Real,Real> 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<Real,Real> Bezier::GetBottom() const
+{
+	pair<Real, Real> tsols = BezierTurningPoints(y0,y1,y2,y3);
+	Real tx0; Real ty0;
+	Real tx1; Real ty1;
+	Evaluate(tx0, ty0, tsols.first);
+	Evaluate(tx1, ty1, tsols.second);
+	vector<const Real*> v(4);
+	v[0] = &y0;
+	v[1] = &y3;
+	v[2] = &ty0;
+	v[3] = &ty1;
+	sort(v.begin(), v.end(), CompRealByPtr);
+	pair<Real,Real> 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<Real,Real> Bezier::GetLeft() const
+{
+	pair<Real, Real> tsols = BezierTurningPoints(x0,x1,x2,x3);
+	Real tx0; Real ty0;
+	Real tx1; Real ty1;
+	Evaluate(tx0, ty0, tsols.first);
+	Evaluate(tx1, ty1, tsols.second);
+	vector<const Real*> v(4);
+	v[0] = &x0;
+	v[1] = &x3;
+	v[2] = &tx0;
+	v[3] = &tx1;
+	sort(v.begin(), v.end(), CompRealByPtr);
+	pair<Real,Real> 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<Real,Real> Bezier::GetRight() const
+{
+	pair<Real, Real> tsols = BezierTurningPoints(x0,x1,x2,x3);
+	Real tx0; Real ty0;
+	Real tx1; Real ty1;
+	Evaluate(tx0, ty0, tsols.first);
+	Evaluate(tx1, ty1, tsols.second);
+	vector<const Real*> v(4);
+	v[0] = &x0;
+	v[1] = &x3;
+	v[2] = &tx0;
+	v[3] = &tx1;
+	sort(v.begin(), v.end(), CompRealByPtr);
+	pair<Real,Real> 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<Real> Bezier::SolveXParam(const Real & 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<Real> 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<Real> Bezier::SolveYParam(const Real & 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<Real> 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<Real> & 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
  */
@@ -138,3 +426,4 @@ Rect Bezier::SolveBounds() const
 }
 
 } // end namespace
+