worked on 3d models within map

adjusted grid factory
adjusted nav mesh factory
minoor changes/fixes
new helper classes
refactoring

math/distribution/ChiSquared.h

@@ -0,0 +1,59 @@
+#ifndef CHISQUARED_H
+#define CHISQUARED_H
+
+#include <cmath>
+
+namespace Distribution {
+
+	/**
+	 * https://en.wikipedia.org/wiki/Chi-squared_distribution
+	 * @brief The ChiSquared class
+	 */
+	template <typename Scalar> class ChiSquared {
+
+	private:
+
+		// degrees of freedom
+		int k;
+
+	public:
+
+		/** ctor */
+		ChiSquared(const int k) : k(k) {
+			;
+		}
+
+		Scalar get(const Scalar val) const {
+
+			const Scalar k2 = k/((Scalar)2);
+			const Scalar k2_1 = k2 - 1;
+			const Scalar gamma = std::tgamma(k2);
+
+			return 1.0 / (std::pow(2, k2)*gamma) * std::pow(val, k2_1) * std::exp(-val/2);
+
+		}
+
+
+		Scalar getInvCDF(const Scalar val) const {
+
+			// brute-force get the inverse CDF...
+
+			const Scalar ss = 0.002;
+			Scalar sum = 0;
+
+			for (float t = 0; t < 20; t += ss) {
+				sum += get(t) * ss;
+				if (sum >= val) {
+					return t;
+				}
+			}
+
+			throw "failed";
+
+		}
+
+	};
+
+}
+
+#endif // CHISQUARED_H

math/distribution/Normal.h

@@ -17,7 +17,7 @@ namespace Distribution {
 		const T sigma;
 		const T _a;
 
-        Random::RandomGenerator gen;
+		Random::RandomGenerator gen;
 		std::normal_distribution<T> dist;
 
 	public:
@@ -32,6 +32,11 @@ namespace Distribution {
 			mu(mu), sigma(sigma), _a(1.0 / (sigma * std::sqrt(2.0 * M_PI))), gen(seed), dist(mu,sigma) {
 		}
 
+		/** mu = 0, sigma = 1 */
+		static Normal unit() {
+			return Normal(0,1);
+		}
+
 		/** do not allow copy. this will not work as expected for std::normal_distribution when using draw() ?! */
 		//Normal(const Normal& o) = delete;
 
@@ -51,15 +56,15 @@ namespace Distribution {
 			gen.seed(seed);
 		}
 
-        /** get the mean value */
-        const T getMu() {
-            return this->mu;
-        }
+		/** get the mean value */
+		const T getMu() {
+			return this->mu;
+		}
 
-        /** get the standard deviation */
-        const T getSigma() {
-            return this->sigma;
-        }
+		/** get the standard deviation */
+		const T getSigma() {
+			return this->sigma;
+		}
 
 		/** get the probability for the given value */
 		static T getProbability(const T mu, const T sigma, const T val) {

math/distribution/NormalN.h

@@ -8,6 +8,8 @@
 
 #include "../../Assertions.h"
 #include "../random/RandomGenerator.h"
+#include "../../geo/Point2.h"
+#include "ChiSquared.h"
 
 namespace Distribution {
 
@@ -96,6 +98,43 @@ namespace Distribution {
                 return NormalDistributionN(mean, cov);
         }
 
+		std::vector<Point2> getContour2(const double percentWithin) {
+
+			const int degreesOfFreedom = 2;	// 2D distribution
+			const ChiSquared<double> chi(degreesOfFreedom);
+
+			// https://people.richland.edu/james/lecture/m170/tbl-chi.html
+			Assert::isNear(0.103, chi.getInvCDF(0.05), 0.01, "error within chi-squared distribution");
+			Assert::isNear(0.211, chi.getInvCDF(0.10), 0.01, "error within chi-squared distribution");
+			Assert::isNear(4.605, chi.getInvCDF(0.90), 0.01, "error within chi-squared distribution");
+			Assert::isNear(5.991, chi.getInvCDF(0.95), 0.03, "error within chi-squared distribution");
+
+			// size of the ellipse using confidence intervals
+			const float mul = chi.getInvCDF(percentWithin);
+
+			std::vector<Point2> res;
+
+			std::cout << sigma << std::endl;
+			Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> solver(this->sigma);
+
+			Eigen::Vector2d evec1 = solver.eigenvectors().col(0);
+			Eigen::Vector2d evec2 = solver.eigenvectors().col(1);
+
+			double eval1 = solver.eigenvalues()(0);
+			double eval2 = solver.eigenvalues()(1);
+
+			for (int deg = 0; deg <= 360; deg += 5) {
+				const float rad = deg / 180.0f * M_PI;
+				Eigen::Vector2d pos =
+						std::cos(rad) * std::sqrt(mul * eval1) * evec1 +
+						std::sin(rad) * std::sqrt(mul * eval2) * evec2;
+				res.push_back(Point2(pos(0), pos(1)));
+			}
+
+			return res;
+
+		}
+
     };
 
 }

math/distribution/Uniform.h

@@ -14,7 +14,7 @@ namespace Distribution {
 
 	private:
 
-        Random::RandomGenerator gen;
+		Random::RandomGenerator gen;
 
 		/** depending on T, Dist is either a uniform_real or uniform_int distribution */
 		typedef typename std::conditional< std::is_floating_point<T>::value, std::uniform_real_distribution<T>, std::uniform_int_distribution<T> >::type Dist;
@@ -33,6 +33,11 @@ namespace Distribution {
 
 		}
 
+		/** -1 to +1 */
+		static Uniform unit() {
+			return Uniform(-1, +1);
+		}
+
 		/** get a uniformaly distributed random number */
 		T draw() {
 			return dist(gen);