worked on 2D/3D raytracing

adjusted BVH
improved 2D/3D BVH
new bounding volumes
new test cases
renamed some test-cases for grouping reasons
made GPC header-only using slight adjustments

geo/BBox2.h

@@ -1,8 +1,9 @@
-#ifndef BBOX2_H
-#define BBOX2_H
+#ifndef GEO_BBOX2_H
+#define GEO_BBOX2_H
 
 #include "Point2.h"
 #include "Line2.h"
+#include <vector>
 
 class BBox2 {
 
@@ -105,6 +106,21 @@ public:
 		p2 += Point2(val, val);	// increase maximum
 	}
 
+	/** grow the bbox by the amount given for each dimension */
+	void growRel(const float val) {
+		const Point2 center = (p1+p2)/2;
+		p1 += (p1-center)*val;	// decrease minimum
+		p2 += (p2-center)*val;	// increase maximum
+	}
+
+
+	/** combine two bboxes */
+	static BBox2 join(const BBox2& bb1, const BBox2& bb2) {
+		const Point2 min( std::min(bb1.p1.x, bb2.p1.x), std::min(bb1.p1.y, bb2.p1.y) );
+		const Point2 max( std::max(bb1.p2.x, bb2.p2.x), std::max(bb1.p2.y, bb2.p2.y) );
+		return BBox2(min, max);
+	}
+
 };
 
-#endif // BBOX2_H
+#endif // GEO_BBOX2_H

geo/BBox3.h

@@ -103,6 +103,13 @@ public:
 		return true;
 	}
 
+	/** combine two bboxes */
+	static BBox3 join(const BBox3& bb1, const BBox3& bb2) {
+		const Point3 min( std::min(bb1.p1.x, bb2.p1.x), std::min(bb1.p1.y, bb2.p1.y), std::min(bb1.p1.z, bb2.p1.z) );
+		const Point3 max( std::max(bb1.p2.x, bb2.p2.x), std::max(bb1.p2.y, bb2.p2.y), std::max(bb1.p2.z, bb2.p2.z) );
+		return BBox3(min,max);
+	}
+
 };
 
 #endif // BBOX3_H

geo/Circle2.h

@@ -0,0 +1,304 @@
+#ifndef CIRCLE2_H
+#define CIRCLE2_H
+
+#include <vector>
+
+#include "Point2.h"
+#include "Ray2.h"
+
+#include "../Assertions.h"
+
+//#include <KLib/misc/gnuplot/Gnuplot.h>
+//#include <KLib/misc/gnuplot/GnuplotPlot.h>
+//#include <KLib/misc/gnuplot/GnuplotPlotElementLines.h>
+//#include <KLib/misc/gnuplot/GnuplotPlotElementPoints.h>
+
+struct Circle2 {
+
+	Point2 center;
+
+	float radius;
+
+public:
+
+	/** empty ctor */
+	Circle2() : center(), radius(0) {;}
+
+	/** ctor */
+	Circle2(const Point2 center, const float radius) : center(center), radius(radius) {;}
+
+
+	/** does this circle contain the given point? */
+	bool contains(const Point2 p) const {
+		return center.getDistance(p) <= radius;
+	}
+
+	/** does this circle contain the given point? */
+	bool containsAll(const std::vector<Point2>& pts) const {
+		for (const Point2& p : pts) {
+			if (!contains(p)) {return false;}
+		}
+		return true;
+	}
+
+	/** get a point on the circle for the given radians */
+	Point2 getPointAt(const float rad) const {
+		return center + Point2(std::cos(rad), std::sin(rad)) * radius;
+	}
+
+
+	/** does this circle contain the given circle? */
+	bool contains(const Circle2 c) const {
+		return (center.getDistance(c.center)+c.radius) <= radius;
+	}
+
+	/** does this circle intersect with the given ray? */
+	bool intersects(const Ray2 ray) const {
+
+		// https://math.stackexchange.com/questions/311921/get-location-of-vector-circle-intersection
+		const float a = ray.dir.x*ray.dir.x + ray.dir.y*ray.dir.y;
+		const float b = 2 * ray.dir.x * (ray.start.x-center.x) + 2 * ray.dir.y * (ray.start.y - center.y);
+		const float c = (ray.start.x-center.x) * (ray.start.x-center.x) + (ray.start.y - center.y)*(ray.start.y - center.y) - radius*radius;
+		const float discr = b*b - 4*a*c;
+
+		return discr >= 0;
+
+	}
+
+
+	/** configure this sphere to contain the given point-set */
+	void adjustToPointSet(const std::vector<Point2>& lst) {
+
+		//adjustToPointSetAPX(lst);
+		adjustToPointSetExact(lst);
+
+		// validate
+		for (const Point2& p : lst) {
+			Assert::isTrue(this->contains(p), "calculated circle seems incorrect");
+		}
+
+	}
+
+	/** combine two circles into a new one containing both */
+	static Circle2 join(const Circle2& a, const Circle2& b) {
+
+		// if one already contains the other, just return it as-is
+		if (a.contains(b)) {return a;}
+		if (b.contains(a)) {return b;}
+
+		// create both maximum ends
+		const Point2 out1 = a.center + (a.center-b.center).normalized() * a.radius;
+		const Point2 out2 = b.center + (b.center-a.center).normalized() * b.radius;
+
+		// center is within both ends, so is the radius
+		Point2 newCen = (out1 + out2) / 2;
+		float newRad = out1.getDistance(out2) / 2 * 1.0001;	// slightly larger to prevent rounding issues
+		Circle2 res(newCen, newRad);
+
+		// check
+		Assert::isTrue(res.contains(a), "sphere joining error. base-spheres are not contained.");
+		Assert::isTrue(res.contains(b), "sphere joining error. base-spheres are not contained.");
+
+		return res;
+
+	}
+
+	float getArea() const  {
+		return M_PI * (radius*radius);
+	}
+
+private:
+
+	/*
+	void show(std::vector<Point2> pts, const Point2 P, const Point2 Q, const Point2 R = Point2(NAN, NAN)) {
+
+		static K::Gnuplot gp;
+
+		K::GnuplotPlot plot;
+		K::GnuplotPlotElementPoints gPoints; plot.add(&gPoints); gPoints.setColor(K::GnuplotColor::fromHexStr("#0000ff")); gPoints.setPointSize(1);
+		K::GnuplotPlotElementLines gLines; plot.add(&gLines);
+
+		for (const Point2 p : pts) {
+			K::GnuplotPoint2 p2(p.x, p.y);
+			gPoints.add(p2);
+		}
+
+		K::GnuplotPoint2 gP(P.x, P.y);
+		K::GnuplotPoint2 gQ(Q.x, Q.y);
+		gLines.addSegment(gP, gQ);
+
+		K::GnuplotPoint2 gR(R.x, R.y);
+		//gLines.addSegment(gP, gR);
+		gLines.addSegment(gQ, gR);
+
+		for (float f = 0; f < M_PI*2; f += 0.1) {
+			Point2 p = center + Point2(std::cos(f), std::sin(f)) * radius;
+			K::GnuplotPoint2 gp (p.x, p.y);
+			gLines.add(gp);
+		}
+
+		gp << "set size ratio -1\n";
+		gp.draw(plot);
+		gp.flush();
+
+		int i = 0; (void) i;
+
+	}
+	*/
+
+
+	// Graphic Gems 2 - Jon Rokne
+	void adjustToPointSetExact(const std::vector<Point2>& _lst) {
+
+		if (_lst.size() == 2) {
+			this->center = (_lst[0] + _lst[1]) / 2;
+			this->radius = _lst[0].getDistance(_lst[1]) / 2 * 1.0001f;
+			return;
+		}
+
+		std::vector<Point2> lst = _lst;
+
+		// find point P having min(p.y)
+		// NOTE: seems like the original work uses another coordinate system. so we search for max(p.y) instead!
+		auto compMinY = [] (const Point2 p1, const Point2 p2) {return p1.y < p2.y;};
+		auto it1 = std::max_element(lst.begin(), lst.end(), compMinY);
+		Point2 P = *it1;
+		lst.erase(it1);
+
+		// find a point Q such that the angle of the line segment
+		// PQ with the x axis is minimal
+		auto compMinAngleX = [&] (const Point2 p1, const Point2 p2) {
+
+			const Point2 PQ1 = p1 - P;
+			const Point2 PQ2 = p2 - P;
+
+			const float angle1 = dot(PQ1.normalized(), Point2(0,1));
+			const float angle2 = dot(PQ2.normalized(), Point2(0,1));
+
+			return std::acos(angle1) < std::acos(angle2);
+
+		};
+		auto it2 = std::min_element(lst.begin(), lst.end(), compMinAngleX);
+		Point2 Q = *it2;
+		lst.erase(it2);
+
+		// get the angle abc which is the angle at "b"
+		auto angle = [] (const Point2 a, const Point2 b, const Point2 c) {
+			const Point2 ba = a - b;
+			const Point2 bc = c - b;
+			return std::acos(dot(ba.normalized(), bc.normalized()));
+		};
+
+		// TODO: how many loops?
+		for (size_t xx = 0; xx < lst.size()*10; ++xx) {
+
+			auto compMinAnglePRQ = [P,Q,angle]  (const Point2 p1, const Point2 p2) {
+				return std::abs(angle(P,p1,Q)) < std::abs(angle(P,p2,Q));
+			};
+
+			auto it3 = std::min_element(lst.begin(), lst.end(), compMinAnglePRQ);
+
+			Point2 R = *it3;
+			lst.erase(it3);
+
+			const float anglePRQ = angle(P,R,Q);
+			const float angleRPQ = angle(R,P,Q);
+			const float anglePQR = angle(P,Q,R);
+
+			//check for case 1 (angle PRQ is obtuse), the circle is determined
+			//by two points, P and Q. radius = |(P-Q)/2|, center = (P+Q)/2
+			if (anglePRQ > M_PI/2) {
+
+				this->radius = P.getDistance(Q) / 2 * 1.001f;
+				this->center = (P+Q)/2;
+				//if (!containsAll(_lst)) {show(_lst, P, Q, R);}
+				return;
+
+			}
+
+			if (angleRPQ > M_PI/2) {
+				lst.push_back(P);
+				P = R;
+				continue;
+			}
+
+			if (anglePQR > M_PI/2) {
+				lst.push_back(Q);
+				Q = R;
+				continue;
+			}
+
+			const Point2 mPQ = (P+Q)/2;
+			const Point2 mQR = (Q+R)/2;
+
+			const float numer = -(-mPQ.y * R.y + mPQ.y * Q.y + mQR.y * R.y - mQR.y * Q.y - mPQ.x * R.x + mPQ.x * Q.x + mQR.x * R.x - mQR.x * Q.x);
+			const float denom =  (-Q.x * R.y + P.x * R.y - P.x * Q.y + Q.y * R.x - P.y * R.x + P.y * Q.x);
+			const float t = numer / denom;
+
+			const float cx  = -t * (Q.y - P.y) + mPQ.x;
+			const float cy  =  t * (Q.x - P.x) + mPQ.y;
+			this->center = Point2(cx, cy);
+			this->radius = this->center.getDistance(P) * 1.001f;
+
+			//if (!containsAll(_lst)) {show(_lst, P, Q, R);}
+
+			return;
+
+		}
+
+		throw Exception("should not happen");
+
+	}
+
+	/*
+	void adjustToPointSetRefine(const std::vector<Point2>& lst) {
+
+		float bestArea = 99999999;
+
+		for (size_t i = 0; i < lst.size(); ++i) {
+			for (size_t j = 0; j < lst.size(); ++j) {
+				if (i == j) {continue;}
+
+				const Point2 center = (lst[i] + lst[j]) / 3;
+				const float radius = lst[i].getDistance(lst[j]);
+				const Circle2 test(center, radius);
+
+				if (test.containsAll(lst)) {
+					if (test.getArea() < bestArea) {
+						bestArea = test.getArea();
+						this->radius = test.radius;
+						this->center = test.center;
+					}
+				}
+			}
+		}
+
+	}
+*/
+	void adjustToPointSetAPX(const std::vector<Point2>& lst) {
+
+		// NOT OPTIMAL but fast
+
+		// calculate the point set's center
+		Point2 sum(0,0);
+		for (const Point2 p : lst) {sum += p;}
+		const Point2 center = sum / lst.size();
+
+		// calculate the sphere's radius (maximum distance from center
+		float radius = 0;
+		for (const Point2 p : lst) {
+			const float dist = center.getDistance(p);
+			if (dist > radius) {radius = dist;}
+		}
+
+		this->radius = radius;
+		this->center = center;
+
+
+
+
+	}
+
+};
+
+#endif // CIRCLE2_H

geo/Point2.h

@@ -68,6 +68,11 @@ struct Point2 {
 
 };
 
+inline float dot(const Point2 p1, const Point2 p2) {
+	return (p1.x*p2.x) + (p1.y*p2.y);
+}
+
+
 inline void swap(Point2& p1, Point2& p2) {
 	std::swap(p1.x, p2.x);
 	std::swap(p1.y, p2.y);

geo/Point3.h

@@ -1,5 +1,5 @@
-#ifndef POINT3_H
-#define POINT3_H
+#ifndef GEO_POINT3_H
+#define GEO_POINT3_H
 
 #include "../Assertions.h"
 #include <cmath>
@@ -128,4 +128,4 @@ inline Point3 cross(const Point3 a, const Point3 b) {
 	);
 }
 
-#endif // POINT3_H
+#endif // GEO_POINT3_H

geo/Ray2.h

@@ -0,0 +1,29 @@
+#ifndef GEO_RAY2_H
+#define GEO_RAY2_H
+
+
+#include "Point2.h"
+
+struct Ray2 {
+
+	/** starting point */
+	Point2 start;
+
+	/** ray's direction */
+	Point2 dir;
+
+public:
+
+	/** empty */
+	Ray2() : start(), dir() {
+		;
+	}
+
+	/** ctor */
+	Ray2(Point2 start, Point2 dir) : start(start), dir(dir) {
+		;
+	}
+
+};
+
+#endif // GEO_RAY2_H

geo/Ray3.h

@@ -1,5 +1,5 @@
-#ifndef RAY3_H
-#define RAY3_H
+#ifndef GEO_RAY3_H
+#define GEO_RAY3_H
 
 #include "Point3.h"
 
@@ -25,4 +25,4 @@ public:
 
 };
 
-#endif // RAY3_H
+#endif // GEO_RAY3_H

geo/Sphere3.h

@@ -1,5 +1,5 @@
-#ifndef SPHERE3_H
-#define SPHERE3_H
+#ifndef GEO_SPHERE3_H
+#define GEO_SPHERE3_H
 
 #include "Point3.h"
 #include "Ray3.h"
@@ -172,7 +172,7 @@ public:
 
 		// center is within both ends, so is the radius
 		Point3 newCen = (out1 + out2) / 2;
-		float newRad = out1.getDistance(out2) / 2 * 1.001;	// slightly larger to prevent rounding issues
+		float newRad = out1.getDistance(out2) / 2 * 1.0001;	// slightly larger to prevent rounding issues
 		Sphere3 res(newCen, newRad);
 
 		// check
@@ -185,4 +185,4 @@ public:
 
 };
 
-#endif // SPHERE3_H
+#endif // GEO_SPHERE3_H

geo/volume/BVH.h

@@ -4,29 +4,36 @@
 #include <vector>
 #include <functional>
 
+#include "../Ray2.h"
+#include "../Ray3.h"
+
 #include "BoundingVolume.h"
-#include "BoundingVolumeAABB.h"
-#include "BoundingVolumeSphere.h"
+
+#include "BoundingVolumeAABB2.h"
+#include "BoundingVolumeCircle2.h"
+
+#include "BoundingVolumeAABB3.h"
+#include "BoundingVolumeSphere3.h"
 
 
 
-
-template <typename Element, typename Volume, typename Wrapper> class BVH {
+template <typename Element, typename Ray, typename Point, typename Volume, typename Wrapper> class BVH {
 
 protected:
 
 	/** one node within the tree */
 	struct BVHNode {
-		bool isLeaf = true;
+		bool isLeaf;
+		bool check;
 		Volume boundingVolume;
 		std::vector<BVHNode*> childNodes;
-		BVHNode(bool isLeaf = false) : isLeaf(isLeaf) {;}
+		BVHNode(bool isLeaf = false, bool check = true) : isLeaf(isLeaf), check(check) {;}
 	};
 
 	/** one leaf within the tree */
 	struct BVHLeaf : public BVHNode {
 		Element element;
-		BVHLeaf(const Element& e) : BVHNode(true), element(e) {;}
+		BVHLeaf(const Element& e, const bool check) : BVHNode(true, check), element(e) {;}
 	};
 
 	/** the tree's root */
@@ -40,10 +47,10 @@ public:
 	}
 
 	/** add a new volume to the tree */
-	void add(const Element& element) {
+	void add(const Element& element, const bool leafCheck = true) {
 
 		// create a new leaf for this element
-		BVHLeaf* leaf = new BVHLeaf(element);
+		BVHLeaf* leaf = new BVHLeaf(element, leafCheck);
 
 		// get the element's boundin volume
 		leaf->boundingVolume = getBoundingVolume(element);
@@ -63,17 +70,17 @@ public:
 		return max;
 	}
 
-	void getHits(const Ray3 ray, std::function<void(const Element&)> func) const {
-		//int tests = 0; int leafs = 0;
+
+	void getHits(const Ray& ray, const std::function<void(const Element&)>& func) const {
 		getHits(ray, &root, func);
-		//std::cout << tests << " " << leafs << std::endl;
 	}
 
-	void getHits(const Ray3 ray, const BVHNode* node, std::function<void(const Element&)> func) const {
+	// this one has to be as fast as possible!
+	static void getHits(const Ray& ray, const BVHNode* node, const std::function<void(const Element&)>& func) {
 		for (const BVHNode* sub : node->childNodes) {
-			if (sub->boundingVolume.intersects(ray)) {
+			if (!sub->check || sub->boundingVolume.intersects(ray)) {
 				if (sub->isLeaf) {
-					BVHLeaf* leaf = (BVHLeaf*)(sub);	// TODO: cast
+					const BVHLeaf* leaf = static_cast<const BVHLeaf*>(sub);
 					func(leaf->element);
 				} else {
 					getHits(ray, sub, func);
@@ -82,8 +89,50 @@ public:
 		}
 	}
 
+	/** get the tree's depth */
+	int getDepth() const {
+		return getDepth(&root, 1);
+	}
+
+
 private:
 
+	/** call the given function for each leaf within the given subtree */
+	void forEachLeaf(const BVHNode* n, std::function<void(const BVHNode*)> func) const {
+		if (n->isLeaf) {
+			func(n);
+		} else {
+			for (BVHNode* child : n->childNodes) {
+				forEachLeaf(child, func);
+			}
+		}
+	}
+
+	/** determine/approximate a new bounding volume around n1+n2 */
+	Volume getVolAround(const BVHNode* n1, const BVHNode* n2) const {
+		//return getVolAroundExact(n1, n2);
+		return getVolAroundAPX(n1, n2);
+	}
+
+	/** determine the bounding-volume around n1 and n2 by (slowly) calculating a new, exact volume based on all leaf-elements */
+	Volume getVolAroundExact(const BVHNode* n1, const BVHNode* n2) const {
+		std::vector<Point> verts;
+		auto onLeaf = [&] (const BVHNode* n) {
+			BVHLeaf* leaf = (BVHLeaf*) n;
+			std::vector<Point> subVerts = Wrapper::getVertices(leaf->element);
+			verts.insert(verts.end(),  subVerts.begin(), subVerts.end());
+		};
+		forEachLeaf(n1, onLeaf);
+		forEachLeaf(n2, onLeaf);
+		return Volume::fromVertices(verts);
+	}
+
+	/** approximate the bounding-volume around n1 and n2 by (quickly) joining their current volumes. the result might be unnecessarily large */
+	Volume getVolAroundAPX(const BVHNode* n1, const BVHNode* n2) const {
+		return Volume::join(n1->boundingVolume, n2->boundingVolume);
+	}
+
+
 	bool combineBest() {
 
 		// nothing to do?
@@ -104,7 +153,7 @@ private:
 				BVHNode* n1 = root.childNodes[i];
 				BVHNode* n2 = root.childNodes[j];
 
-				const Volume newVol = Volume::join(n1->boundingVolume, n2->boundingVolume);
+				const Volume newVol = getVolAround(n1,n2);
 				const float newVolSize = newVol.getVolumeSize();
 				if (newVolSize < best.volSize) {
 					best.vol = newVol;
@@ -226,13 +275,32 @@ private:
 
 	}
 
+	int getDepth(const BVHNode* node, const int cur) const {
+		if (node->isLeaf) {
+			return cur;
+		} else {
+			int res = cur;
+			for (const BVHNode* sub : node->childNodes) {
+				const int subDepth = getDepth(sub, cur+1);
+				if (subDepth > res) {res = subDepth;}
+			}
+			return res;
+		}
+	}
+
 	/** get a bounding-volume for the given element */
 	Volume getBoundingVolume(const Element& element) {
-		const std::vector<Point3> verts = Wrapper::getVertices(element);
+		const std::vector<Point> verts = Wrapper::getVertices(element);
 		return Volume::fromVertices(verts);
 	}
 
+};
 
+template <typename Element, typename Volume, typename Wrapper> class BVH3 : public BVH<Element, Ray3, Point3, Volume, Wrapper> {
+
+};
+
+template <typename Element, typename Volume, typename Wrapper> class BVH2 : public BVH<Element, Ray2, Point2, Volume, Wrapper> {
 
 };
 

geo/volume/BVHDebug.h

@@ -2,39 +2,52 @@
 #define BVHDEBUG_H
 
 #include "BVH.h"
+
+
+#include <KLib/misc/gnuplot/Gnuplot.h>
+
 #include <KLib/misc/gnuplot/GnuplotSplot.h>
 #include <KLib/misc/gnuplot/GnuplotSplotElementPoints.h>
 #include <KLib/misc/gnuplot/GnuplotSplotElementColorPoints.h>
 #include <KLib/misc/gnuplot/GnuplotSplotElementLines.h>
-#include <KLib/misc/gnuplot/Gnuplot.h>
+
+#include <KLib/misc/gnuplot/GnuplotPlot.h>
+#include <KLib/misc/gnuplot/GnuplotPlotElementPoints.h>
+#include <KLib/misc/gnuplot/GnuplotPlotElementColorLines.h>
+#include <KLib/misc/gnuplot/GnuplotPlotElementLines.h>
+
 #include "../BBox3.h"
 #include <random>
 
-/** adds some debug helpers to the BVH */
-template <typename Element, typename Volume, typename Wrapper> class BVHDebug : public BVH<Element, Volume, Wrapper> {
+///** adds some debug helpers to the BVH */
+//template <typename Element, typename Ray, typename Point, typename Volume, typename Wrapper> class BVHDebug : public BVH<Element, Ray, Point, Volume, Wrapper> {
+
+
+//};
+
+template <typename Element, typename Volume, typename Wrapper> class BVH3Debug : public BVH<Element, Ray3, Point3, Volume, Wrapper> {
+
+	using BVHNode = typename BVH<Element, Ray3, Point3, Volume, Wrapper>::BVHNode;
+	using BVHLeaf = typename BVH<Element, Ray3, Point3, Volume, Wrapper>::BVHLeaf;
 
-	using BVHNode = typename BVH<Element, Volume, Wrapper>::BVHNode;
-	using BVHLeaf = typename BVH<Element, Volume, Wrapper>::BVHLeaf;
 
 public:
 
-//	std::vecto<std::string> colors {
-//		"#888888", "#888800", "#008888", "#880088", "#ee0000", "#00ee00", "#0000ee"
-//	};
-
 	void show(int maxPts = 1500, bool showLeafs = true) {
 
 		std::stringstream out;
 
 		static K::Gnuplot gp;
 		K::GnuplotSplot plot;
-		K::GnuplotSplotElementColorPoints pVol;		plot.add(&pVol);		//pVol.setColor(K::GnuplotColor::fromRGB(128,128,128));
-		K::GnuplotSplotElementPoints pElemPoints;	plot.add(&pElemPoints);	pElemPoints.setColor(K::GnuplotColor::fromRGB(0,0,255));
-		K::GnuplotSplotElementLines pElemLines;		plot.add(&pElemLines);	pElemLines.getStroke().setColor(K::GnuplotColor::fromRGB(0,0,255));
 
-		const int depth = recurse(maxPts, showLeafs, 0, &this->root, pVol, pElemPoints, pElemLines);
+		K::GnuplotSplotElementColorPoints pVol;			plot.add(&pVol);		//pVol.setColor(K::GnuplotColor::fromRGB(128,128,128));
+		K::GnuplotSplotElementPoints pElemPoints;		plot.add(&pElemPoints);	pElemPoints.setColor(K::GnuplotColor::fromRGB(0,0,255));
+		K::GnuplotSplotElementLines pElemLines;			plot.add(&pElemLines);	pElemLines.getStroke().setColor(K::GnuplotColor::fromRGB(0,0,255));
 
-		plot.getAxisCB().setRange(0, depth);
+		const int maxDepth = this->getDepth();
+		recurse(maxPts, showLeafs, 0, &this->root, pVol, pElemPoints, pElemLines);
+
+		plot.getAxisCB().setRange(0, maxDepth);
 
 		gp << "set view equal xyz\n";
 		gp.draw(plot);
@@ -44,6 +57,31 @@ public:
 
 private:
 
+	Point3 getRandomPoint(BoundingVolumeSphere3 sphere) {
+		static std::minstd_rand gen;
+		std::uniform_real_distribution<float> dist(-1, +1);
+		Point3 dir = Point3(dist(gen), dist(gen), dist(gen)).normalized() * sphere.radius;
+		return sphere.center + dir;
+	}
+
+	void addLines(const Element& elem, K::GnuplotSplotElementLines& elemLines) {
+
+		std::vector<Point3> pts = Wrapper::getDebugLines(elem);
+
+		for (size_t i = 0; i< pts.size(); i+=2) {
+
+			const Point3 p1 = pts[i+0];
+			const Point3 p2 = pts[i+1];
+
+			K::GnuplotPoint3 gp1(p1.x, p1.y, p1.z);
+			K::GnuplotPoint3 gp2(p2.x, p2.y, p2.z);
+
+			elemLines.addSegment(gp1, gp2);
+
+		}
+
+	}
+
 	int recurse(int maxPts, bool showLeafs, int curDepth, const BVHNode* node, K::GnuplotSplotElementColorPoints& vol, K::GnuplotSplotElementPoints& pElemPoints, K::GnuplotSplotElementLines& elemLines) {
 
 		int resDepth = curDepth;
@@ -76,24 +114,53 @@ private:
 
 	}
 
-	Point3 getRandomPoint(BoundingVolumeSphere sphere) {
-		static std::minstd_rand gen;
-		std::uniform_real_distribution<float> dist(-1, +1);
-		Point3 dir = Point3(dist(gen), dist(gen), dist(gen)).normalized() * sphere.radius;
-		return sphere.center + dir;
+};
+
+template <typename Element, typename Volume, typename Wrapper> class BVH2Debug : public BVH<Element, Ray2, Point2, Volume, Wrapper> {
+
+	using BVHNode = typename BVH<Element, Ray2, Point2, Volume, Wrapper>::BVHNode;
+	using BVHLeaf = typename BVH<Element, Ray2, Point2, Volume, Wrapper>::BVHLeaf;
+
+public:
+
+	void show(int maxPts = 1500, bool showLeafs = true) {
+
+		std::stringstream out;
+
+		static K::Gnuplot gp;
+		K::GnuplotPlot plot;
+
+
+		K::GnuplotPlotElementColorLines pVolLines;	plot.add(&pVolLines);
+		K::GnuplotPlotElementPoints pElemPoints;	plot.add(&pElemPoints);	pElemPoints.setColor(K::GnuplotColor::fromRGB(0,0,255));
+		K::GnuplotPlotElementLines pElemLines;		plot.add(&pElemLines);	pElemLines.getStroke().setColor(K::GnuplotColor::fromRGB(0,0,255));
+
+		const int maxDepth = this->getDepth();
+		recurse(maxDepth, showLeafs, 0, &this->root, plot, pVolLines, pElemPoints, pElemLines);
+
+		plot.getObjects().reOrderByZIndex();
+		plot.getAxisCB().setRange(0, maxDepth);
+
+		gp << "set size ratio -1\n";
+		gp.draw(plot);
+		gp.flush();
+
 	}
 
-	void addLines(const Element& elem, K::GnuplotSplotElementLines& elemLines) {
+private:
 
-		std::vector<Point3> pts = Wrapper::getDebugLines(elem);
+
+	void addLines(const Element& elem, K::GnuplotPlotElementLines& elemLines) {
+
+		std::vector<Point2> pts = Wrapper::getDebugLines(elem);
 
 		for (size_t i = 0; i< pts.size(); i+=2) {
 
-			const Point3 p1 = pts[i+0];
-			const Point3 p2 = pts[i+1];
+			const Point2 p1 = pts[i+0];
+			const Point2 p2 = pts[i+1];
 
-			K::GnuplotPoint3 gp1(p1.x, p1.y, p1.z);
-			K::GnuplotPoint3 gp2(p2.x, p2.y, p2.z);
+			K::GnuplotPoint2 gp1(p1.x, p1.y);
+			K::GnuplotPoint2 gp2(p2.x, p2.y);
 
 			elemLines.addSegment(gp1, gp2);
 
@@ -101,6 +168,75 @@ private:
 
 	}
 
+	std::vector<std::string> colors = {
+		"#888800", "#444400", "#008888", "#004444", "#880088", "#440044", "#ee0000", "#880000", "#00ee00", "#008800", "#0000ee", "#000088",
+		"#888800", "#444400", "#008888", "#004444", "#880088", "#440044", "#ee0000", "#880000", "#00ee00", "#008800", "#0000ee", "#000088",
+		"#888800", "#444400", "#008888", "#004444", "#880088", "#440044", "#ee0000", "#880000", "#00ee00", "#008800", "#0000ee", "#000088"
+	};
+
+	void showVolume(const BoundingVolumeCircle2& circle, int maxDepth, int curDepth, K::GnuplotPlot& plot, K::GnuplotPlotElementColorLines& pVolLines) {
+		K::GnuplotObjectPolygon* poly = new K::GnuplotObjectPolygon();
+		for (int i = 0; i < 20; ++i) {
+			const float f = M_PI*2 * i / 19;
+			const Point2 p = circle.getPointAt(f);
+			poly->add(K::GnuplotCoordinate2(p.x, p.y, K::GnuplotCoordinateSystem::FIRST));
+			poly->getFill().setColor(K::GnuplotColor::fromHexStr(colors[maxDepth-curDepth]));
+			poly->getFill().setStyle(K::GnuplotFillStyle::SOLID);
+			poly->setZIndex(curDepth);
+		}
+		plot.getObjects().add(poly);
+	}
+
+	void showVolume(const BoundingVolumeAABB2& _aabb, int maxDepth, int curDepth, K::GnuplotPlot& plot, K::GnuplotPlotElementColorLines& pVolLines) {
+		BBox2 bbox2 = _aabb;
+		bbox2.grow( (10-curDepth) / 100.0f );
+//		pVolLines.add(K::GnuplotPoint2(bbox2.getMin().x, bbox2.getMin().y), curDepth);
+//		pVolLines.add(K::GnuplotPoint2(bbox2.getMax().x, bbox2.getMin().y), curDepth);
+//		pVolLines.add(K::GnuplotPoint2(bbox2.getMax().x, bbox2.getMax().y), curDepth);
+//		pVolLines.add(K::GnuplotPoint2(bbox2.getMin().x, bbox2.getMax().y), curDepth);
+//		pVolLines.add(K::GnuplotPoint2(bbox2.getMin().x, bbox2.getMin().y), curDepth);
+//		pVolLines.splitFace();
+		K::GnuplotObjectPolygon* poly = new K::GnuplotObjectPolygon();
+		poly->getStroke().setColor(K::GnuplotColor::fromHexStr(colors[maxDepth-curDepth]));
+		//poly->getFill().setColor(K::GnuplotColor::fromHexStr(colors[maxDepth-curDepth]));
+		//poly->getFill().setStyle(K::GnuplotFillStyle::SOLID);
+		poly->add(K::GnuplotCoordinate2(bbox2.getMin().x, bbox2.getMin().y, K::GnuplotCoordinateSystem::FIRST));
+		poly->add(K::GnuplotCoordinate2(bbox2.getMax().x, bbox2.getMin().y, K::GnuplotCoordinateSystem::FIRST));
+		poly->add(K::GnuplotCoordinate2(bbox2.getMax().x, bbox2.getMax().y, K::GnuplotCoordinateSystem::FIRST));
+		poly->add(K::GnuplotCoordinate2(bbox2.getMin().x, bbox2.getMax().y, K::GnuplotCoordinateSystem::FIRST));
+		poly->close();
+		poly->setZIndex(curDepth);
+		plot.getObjects().add(poly);
+	}
+
+	int recurse(int maxDepth, bool showLeafs, int curDepth, const BVHNode* node, K::GnuplotPlot& plot, K::GnuplotPlotElementColorLines& pVolLines, K::GnuplotPlotElementPoints& pElemPoints, K::GnuplotPlotElementLines& elemLines) {
+
+		int resDepth = curDepth;
+
+		for (BVHNode* sub : node->childNodes) {
+			resDepth = recurse(maxDepth, showLeafs, curDepth+1, sub, plot, pVolLines, pElemPoints, elemLines);
+		}
+
+		if (!node->isLeaf || showLeafs) {
+			if (node != &this->root) {
+				//const int numPts = maxPts / (curDepth+1);
+				showVolume(node->boundingVolume, maxDepth, curDepth, plot, pVolLines);
+			}
+		}
+
+		if (node->isLeaf) {
+			BVHLeaf* leaf = (BVHLeaf*) node;
+			std::vector<Point2> verts = Wrapper::getVertices(leaf->element);
+			for (const Point2 p : verts) {
+				pElemPoints.add(K::GnuplotPoint2(p.x, p.y));
+			}
+			addLines(leaf->element, elemLines);
+		}
+
+		return resDepth;
+
+	}
+
 };
 
 #endif // BVHDEBUG_H

geo/volume/BoundingVolumeAABB2.h

@@ -0,0 +1,36 @@
+#ifndef BOUNDINGVOLUMEAABB2_H
+#define BOUNDINGVOLUMEAABB2_H
+
+#include <vector>
+
+#include "BoundingVolume.h"
+#include "../BBox2.h"
+
+class BoundingVolumeAABB2 : public BBox2 {
+
+public:
+
+	BoundingVolumeAABB2() {;}
+
+	BoundingVolumeAABB2(const BBox2& bb) : BBox2(bb) {;}
+
+	float getVolumeSize() const  {
+		const float dx = getMax().x - getMin().x;
+		const float dy = getMax().y - getMin().y;
+		return (dx*dy);
+	}
+
+	/** construct a volume around the given point-set */
+	static BoundingVolumeAABB2 fromVertices(const std::vector<Point2>& verts) {
+		BoundingVolumeAABB2 bvs;
+		for (const Point2 p : verts) {bvs.add(p);}
+		return bvs;
+	}
+
+	static BoundingVolumeAABB2 join(const BoundingVolumeAABB2 a, const BoundingVolumeAABB2 b) {
+		return BoundingVolumeAABB2(BBox2::join(a, b));
+	}
+
+};
+
+#endif // BOUNDINGVOLUMEAABB2_H

geo/volume/BoundingVolumeBox.h

@@ -1,4 +0,0 @@
-#ifndef BOUNDINGVOLUMEBOX_H
-#define BOUNDINGVOLUMEBOX_H
-
-#endif // BOUNDINGVOLUMEBOX_H

geo/volume/BoundingVolumeCircle2.h

@@ -0,0 +1,38 @@
+#ifndef BOUDINGVOLUMECIRCLE2_H
+#define BOUDINGVOLUMECIRCLE2_H
+
+#include <vector>
+
+#include "BoundingVolume.h"
+#include "../Circle2.h"
+
+class BoundingVolumeCircle2 : public Circle2 {
+
+public:
+
+	BoundingVolumeCircle2() {;}
+
+	BoundingVolumeCircle2(const Circle2& c) : Circle2(c) {;}
+
+	float getVolumeSize() const  {
+		return M_PI * (radius*radius);
+	}
+
+	bool intersects(const Ray2 ray) const {
+		return Circle2::intersects(ray);
+	}
+
+	/** construct a volume around the given point-set */
+	static BoundingVolumeCircle2 fromVertices(const std::vector<Point2>& verts) {
+		BoundingVolumeCircle2 bvs;
+		bvs.adjustToPointSet(verts);
+		return bvs;
+	}
+
+	static BoundingVolumeCircle2 join(const BoundingVolumeCircle2 a, const BoundingVolumeCircle2 b) {
+		return BoundingVolumeCircle2(Circle2::join(a, b));
+	}
+
+};
+
+#endif // BOUDINGVOLUMECIRCLE2_H

geo/volume/BoundingVolumeHierarchy.h

@@ -1,4 +0,0 @@
-#ifndef BOUNDINGVOLUMEHIERARCHY_H
-#define BOUNDINGVOLUMEHIERARCHY_H
-
-#endif // BOUNDINGVOLUMEHIERARCHY_H

geo/volume/BoundingVolumeSphere3.h

@@ -5,13 +5,13 @@
 #include "../Sphere3.h"
 #include "../Point3.h"
 
-class BoundingVolumeSphere : public BoundingVolume, public Sphere3 {
+class BoundingVolumeSphere3 : public BoundingVolume, public Sphere3 {
 
 public:
 
-	BoundingVolumeSphere() {;}
+	BoundingVolumeSphere3() {;}
 
-	BoundingVolumeSphere(const Sphere3& s) : Sphere3(s) {;}
+	BoundingVolumeSphere3(const Sphere3& s) : Sphere3(s) {;}
 
 	float getVolumeSize() const  {
 		return (4.0f / 3.0f) * M_PI * (radius*radius*radius);
@@ -27,25 +27,25 @@ public:
 
 	/** does the volume intersect with the given volume? */
 	bool intersects(const BoundingVolume& other) const  {
-		const BoundingVolumeSphere& sphere = (const BoundingVolumeSphere&) other;
+		const BoundingVolumeSphere3& sphere = (const BoundingVolumeSphere3&) other;
 		return Sphere3::intersects(sphere);
 	}
 
 	/** does the volume contain the given volume? */
 	bool contains(const BoundingVolume& other) const {
-		const BoundingVolumeSphere& sphere = (const BoundingVolumeSphere&) other;
+		const BoundingVolumeSphere3& sphere = (const BoundingVolumeSphere3&) other;
 		return Sphere3::contains(sphere);
 	}
 
 	/** construct a volume around the given point-set */
-	static BoundingVolumeSphere fromVertices(const std::vector<Point3>& verts) {
-		BoundingVolumeSphere bvs;
+	static BoundingVolumeSphere3 fromVertices(const std::vector<Point3>& verts) {
+		BoundingVolumeSphere3 bvs;
 		bvs.adjustToPointSet(verts);
 		return bvs;
 	}
 
-	static BoundingVolumeSphere join(const BoundingVolumeSphere a, const BoundingVolumeSphere b) {
-		return BoundingVolumeSphere(Sphere3::join(a, b));
+	static BoundingVolumeSphere3 join(const BoundingVolumeSphere3 a, const BoundingVolumeSphere3 b) {
+		return BoundingVolumeSphere3(Sphere3::join(a, b));
 	}
 
 };