X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fcode.git;a=blobdiff_plain;f=src%2Fbezier.cpp;h=83db943692e39a2f0509425234f2c43e82c49cdd;hp=15a5069a6703c08ec33841b82621176a0e99693c;hb=HEAD;hpb=f59f24dff392428d7219ba2d6be5e1e81c344ee0

diff --git a/src/bezier.cpp b/src/bezier.cpp
index 15a5069..83db943 100644
--- a/src/bezier.cpp
+++ b/src/bezier.cpp
@@ -2,12 +2,110 @@
 
 #include <unordered_map>
 #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
@@ -34,15 +132,299 @@ int Factorial(int n)
  */
 int BinomialCoeff(int n, int k)
 {
-	return Factorial(n) / Factorial(k) / Factorial(n-k);
+	return Factorial(n) / (Factorial(k) * Factorial(n-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)) * pow(u, k) * pow(Real(1.0) - u, n-k);
+	return BReal(BinomialCoeff(n, k)) * Power(u, k) * Power(BReal(1.0) - u, n-k);
 }
 
+
+/**
+ * Returns the parametric parameter at the turning point(s)
+ * In one coordinate direction
+ */
+
+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<BReal,BReal>(0, 1);
+	}
+	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 == 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 - a*c*BReal(4) < BReal(0))
+	{
+		//Debug("No real roots");
+		return pair<BReal, BReal>(0,1);
+	}
+	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 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
+ */
+BRect Bezier::SolveBounds() const
+{
+	BRect result;
+	pair<BReal, BReal> tsols = BezierTurningPoints(x0, x1, x2, x3);
+	
+	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<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(), CompBRealByPtr);
+
+	result.x = *(v[0]);
+	result.w = *(v[3]) - result.x;
+
+	// Do the same thing for y component (wow this is a mess)
+	tsols = BezierTurningPoints(y0, y1, y2, y3);
+	Evaluate(o, tp0, tsols.first);
+	Evaluate(o, tp1, tsols.second);
+	
+	
+	//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(), 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());
+	return result;
+}
+
+} // end namespace
+