Elementary Physics – Numerical Explorations

Blog Entry © Monday, April 20, 2026, by James Pate Williams, Jr., Vector Analysis Continued and Perhaps Corrected

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Blog Entry © Sunday, April 19, 2026, by James Pate Williams, Jr., Scattering from a Spherically Symmetric Potential

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Vector Analysis by James Pate Williams, Jr. Exercises and Supplementary Problems from Introduction to Vector Analysis Fourth Edition© 1979 by Harry F. Davis and Arthur David Snider Selected Exercises from Chapter 1 Pages 48 and 50

Vector Analysis Chapter 1 by James Pate Williams Download

// VectorAnalysis.cpp © Tuesday, April 14, 2026
// by James Pate Williams, Jr.
// Reference: Introduction to Vector Analysis Fourth Edition
// © 1979 by Harry F. Davis and Arthur David Snider 

#include <iostream>
#include <vector>

static double InnerProduct(
	std::vector<double> A,
	std::vector<double> B,
	int n)
{
	double sum = 0.0;

	for (int i = 0; i < n; i++)
		sum += A[i] * B[i];

	return sum;
}

static void VectorProduct(
	std::vector<double> A,
	std::vector<double> B,
	std::vector<double>&C)
{
	C.resize(3);
	C[0] = A[1] * B[2] - A[2] * B[1];
	C[1] = A[2] * B[0] - A[0] * B[2];
	C[2] = A[0] * B[1] - A[1] * B[0];
}

static double TripleProduct(
	std::vector<double> A,
	std::vector<double> B,
	std::vector<double> C)
{
	double sum0 = 0.0, sum1 = 0.0;

	sum0 += A[0] * B[1] * C[2] + A[1] * B[2] * C[0] + A[2] * B[0] * C[1];
	sum1 += A[1] * B[0] * C[2] + A[0] * B[2] * C[1] + A[2] * B[1] * C[0];
	return sum0 - sum1;
}

static void Exercises_Section_1_13_1_Triple_Products()
{
	// triple products (a)
	std::vector<double> A1 = { 2, 0, 0 };
	std::vector<double> B1 = { 0, 3, 0 };
	std::vector<double> C1 = { 0, 0, 5 };
	double tp_1 = TripleProduct(A1, B1, C1);
	std::cout << "Exercise 1 (a)" << '\t';
	std::cout << tp_1 << std::endl;
	// triple products (b)
	std::vector<double> A2 = { 1, 1, 1 };
	std::vector<double> B2 = { 3, 1, 0 };
	std::vector<double> C2 = { 0, -1, 5 };
	std::cout << "Exercise 1 (b)" << '\t';
	double tp_2 = TripleProduct(A2, B2, C2);
	std::cout << tp_2 << std::endl;
	// triple products (c)
	std::vector<double> A3 = { 2, -1, 1 };
	std::vector<double> B3 = { 1, 1, 1 };
	std::vector<double> C3 = { 2, 0, 3 };
	double tp_3 = TripleProduct(A3, B3, C3);
	std::cout << "Exercise 1 (c)" << '\t';
	std::cout << tp_3 << std::endl;
	// triple products (d)
	std::vector<double> A4 = { 0, 0, 1 };
	std::vector<double> B4 = { 1, 0, 0 };
	std::vector<double> C4 = { 0, 1, 0 };
	double tp_4 = TripleProduct(A4, B4, C4);
	std::cout << "Exercise 1 (d)" << '\t';
	std::cout << tp_4 << std::endl;
	// volume of a parallelpipped
	std::vector<double> A5 = { 3, 4, 1 };
	std::vector<double> B5 = { 2, 3, 4 };
	std::vector<double> C5 = { 0, 0, 5 }; 
	double tp_5 = TripleProduct(A5, B5, C5);
	std::cout << "Exercise 2" << '\t';
	std::cout << tp_5 << std::endl;
	// volume of a parallelpipped
	std::vector<double> A6 = { 3, 2, 1 };
	std::vector<double> B6 = { 4, 2, 1 };
	std::vector<double> C6 = { 0, 1, 4 };
	std::vector<double> D6 = { 0, 0, 7 };
	std::vector<double> AB = { -1, 0, 0 };
	std::vector<double> AC = { 3, 1, -3 };
	std::vector<double> AD = { 3, 2, -6 };
	std::cout << "Exercise 3" << '\t';
	double tp_6 = TripleProduct(AB, AC, AD);
	std::cout << tp_6 << std::endl;
	// volume of a tetrahedron
	std::vector<double> AB1 = { 1, 1, 0 };
	std::vector<double> AC1 = { 1, -1, 0 };
	std::vector<double> AD1 = { 0, 0, 2 };
	std::cout << "Exercise 4" << '\t';
	double tp_7 = TripleProduct(AB1, AC1, AD1) / 6.0;
	std::cout << fabs(tp_7) << std::endl;
	std::vector<double> P1 = { 0, 0, 0 };
	std::vector<double> P2 = { 1, 1, 0 };
	std::vector<double> P3 = { 3, 4, 0 };
	std::vector<double> P4 = { 4, 5, 0 };
	std::vector<double> P5 = { 0, 0, 1 };
	std::vector<double> Q1 = { 1, 1, 0 };
	std::vector<double> Q2 = { 2, 3, 0 };
	std::vector<double> Q3 = { 1, 1, 1 };
	std::cout << "Exercise 5" << '\t';
	double tp_8 = TripleProduct(Q1, Q2, Q3);
	std::cout << fabs(tp_8) << std::endl;
	std::vector<double> A10 = { 1, 1, 1 };
	std::vector<double> B10 = { 2, 4, -1 };
	std::vector<double> C10 = { 1, 1, 3 };
	double tp_10 = TripleProduct(A10, B10, C10);
	std::vector<double> D10 = { 0 };
	VectorProduct(A10, B10, D10);
	double magnitude = sqrt(InnerProduct(D10, D10, 3));
	std::cout << "Exercise 10" << '\t';
	std::cout << tp_10 / magnitude << '\t';
	std::cout << 2.0 * sqrt(38.0) / 19.0 << std::endl;
	std::vector<double> A11 = { 1, 1, 1 };
	std::vector<double> B11 = { 2, 4, -1 };
	std::vector<double> C11 = { 1, 1, 3 };
	std::vector<double> D11 = { 3, 2, 1 };
	std::vector<double> AB11(3), BC11(3), CA11(3), BCCA11(3);
	VectorProduct(A11, B11, AB11);
	VectorProduct(B11, C11, BC11);
	VectorProduct(C11, A11, CA11);
	VectorProduct(BC11, CA11, BCCA11);
	double Q11 = InnerProduct(AB11, BCCA11, 3);
	double A_x = A11[0], A_y = A11[1], A_z = A11[2];
	double B_x = B11[0], B_y = B11[1], B_z = B11[2];
	double C_x = C11[0], C_y = C11[1], C_z = C11[2];
	double term1 = +(A_y * B_z - A_z * B_y) * (B_z * C_x - B_x * C_z) * (C_x * A_y - C_y * A_x);
	double term2 = -(A_y * B_z - A_z * B_y) * (B_x * C_y - B_y * C_x) * (C_z * A_x - C_x * A_z);
	double term3 = +(A_z * B_x - A_x * B_z) * (B_x * C_y - B_y * C_x) * (C_y * A_z - C_z * A_y);
	double term4 = -(A_z * B_x - A_x * B_z) * (B_y * C_z - B_z * C_y) * (C_x * A_y - C_y * A_x);
	double term5 = +(A_x * B_y - A_y * B_x) * (B_y * C_z - B_z * C_y) * (C_z * A_x - C_x * A_z);
	double term6 = -(A_x * B_y - A_y * B_x) * (B_z * C_x - B_x * C_z) * (C_y * A_z - C_z * A_y);
	double P11 = term1 + term2 + term3 + term4 + term5 + term6;
	std::cout << "Q = (A x B) . (B x C) x (C x A) = " << Q11 << std::endl;
	std::cout << "P = (A x B) . (B x C) x (C x A) = " << P11 << std::endl;
}

static void Exercises_Section_1_14_Vector_Identities()
{
	std::vector<double> A11 = { 1, 1, 1 };
	std::vector<double> B11 = { 2, 4, -1 };
	std::vector<double> C11 = { 1, 1, 3 };
	std::vector<double> D11 = { 3, 2, 1 };
	std::cout << "Section 1.14 page 50 Exercises Exercise 1" << std::endl;
	std::cout << "A = " << A11[0] << '\t' << A11[1] << '\t' << A11[2] << std::endl;
	std::cout << "B = " << B11[0] << '\t' << B11[1] << '\t' << B11[2] << std::endl;
	std::cout << "C = " << C11[0] << '\t' << C11[1] << '\t' << C11[2] << std::endl;
	std::cout << "D = " << D11[0] << '\t' << D11[1] << '\t' << D11[2] << std::endl;
	std::cout << "TPI1 = (A x B) x (C x D) = [A, B, D]C - [A, B, C]D = " << std::endl;
	double TP1411a = TripleProduct(A11, B11, D11);
	double TP1411b = TripleProduct(A11, B11, C11);
	std::cout << "[A, B, D] = " << TP1411a << std::endl;
	std::cout << "[A, B, C] = " << TP1411b << std::endl;
	std::cout << "TPI1_x = " << TP1411a * C11[0] << std::endl;
	std::cout << "TPI1_y = " << TP1411a * C11[1] << std::endl;
	std::cout << "TPI1_z = " << TP1411a * C11[2] << std::endl;
	std::cout << "TPI2_x = " << TP1411b * D11[0] << std::endl;
	std::cout << "TPI2_y = " << TP1411b * D11[1] << std::endl;
	std::cout << "TPI2_z = " << TP1411b * D11[2] << std::endl;
	std::cout << "RHS1 = [A, B, D]C - [A, B, C]D = " << std::endl;
	std::vector<double> RHS1(3);
	RHS1[0] = TP1411a * C11[0] - TP1411b * D11[0];
	RHS1[1] = TP1411a * C11[1] - TP1411b * D11[1];
	RHS1[2] = TP1411a * C11[2] - TP1411b * D11[2];
	std::cout << "RHS1_x = " << RHS1[0] << std::endl;
	std::cout << "RHS1_y = " << RHS1[1] << std::endl;
	std::cout << "RHS1_z = " << RHS1[2] << std::endl;
	std::vector<double> CD11(3), TD11(3);
	std::vector<double> AB11(3), BC11(3), CA11(3), BCCA11(3);
	VectorProduct(A11, B11, AB11);
	VectorProduct(B11, C11, BC11);
	VectorProduct(C11, A11, CA11);
	VectorProduct(BC11, CA11, BCCA11);
	VectorProduct(A11, B11, AB11);
	VectorProduct(C11, D11, CD11);
	VectorProduct(AB11, CD11, TD11);
	std::cout << "A = " << A11[0] << '\t' << A11[1] << '\t' << A11[2] << std::endl;
	std::cout << "B = " << B11[0] << '\t' << B11[1] << '\t' << B11[2] << std::endl;
	std::cout << "C = " << C11[0] << '\t' << C11[1] << '\t' << C11[2] << std::endl;
	std::cout << "D = " << D11[0] << '\t' << D11[1] << '\t' << D11[2] << std::endl;
	std::cout << "A x B = " << AB11[0] << '\t' << AB11[1] << '\t' << AB11[2] << std::endl;
	std::cout << "C x D = " << CD11[0] << '\t' << CD11[1] << '\t' << CD11[2] << std::endl;
	std::cout << "TD11 = (A x B) x (C x D) = " << std::endl;
	std::cout << "TD11_x = " << TD11[0] << std::endl;
	std::cout << "TD11_y = " << TD11[1] << std::endl;
	std::cout << "TD11_z = " << TD11[2] << std::endl;
	VectorProduct(B11, C11, BC11);
	VectorProduct(C11, A11, CA11);
	VectorProduct(BC11, CA11, D11);
	VectorProduct(A11, B11, AB11);
	double ip12 = InnerProduct(AB11, D11, 3);
	std::cout << "2. Inner Product = " << ip12 << std::endl;
	double tp12 = TripleProduct(A11, B11, C11);
	std::cout << "2. Triple Product ^ 2 = " << tp12 * tp12 << std::endl;
	std::vector<double> ABC11(3), BAC11(3), CAB11(3);
	VectorProduct(A11, BC11, ABC11);
	VectorProduct(B11, CA11, BAC11);
	VectorProduct(C11, AB11, CAB11);
	double zx = ABC11[0] + BAC11[0] + CAB11[0];
	double zy = ABC11[1] + BAC11[1] + CAB11[1];
	double zz = ABC11[2] + BAC11[2] + CAB11[2];
	std::cout << "3. Zero Vector = " << zx << ' ' << zy << ' ' << zz;
	std::cout << std::endl;
}

int main()
{
	Exercises_Section_1_13_1_Triple_Products();
	Exercises_Section_1_14_Vector_Identities();
	return 0;
}

Blog Entry © Tuesday, April 14, 2026, by James Pate Williams, Jr. Exercises and Supplementary Problems from Introduction to Vector Analysis Fourth Edition © 1979 by Harry F. Davis and Arthur David Snider Selected Exercises from Chapter 1 Page 48

Vector Analysis Chapter 1 by James Pate Williams Download

// VectorAnalysis.cpp © Tuesday, April 14, 2026
// by James Pate Williams, Jr.
// Reference: Introduction to Vector Analysis Fourth Edition
// © 1979 by Harry F. Davis and Arthur David Snider 

#include <iostream>
#include <vector>

static double InnerProduct(
	std::vector<double> A,
	std::vector<double> B,
	int n)
{
	double sum = 0.0;

	for (int i = 0; i < n; i++)
		sum += A[i] * B[i];

	return sum;
}

static void VectorProduct(
	std::vector<double> A,
	std::vector<double> B,
	std::vector<double>&C)
{
	C.resize(3);
	C[0] = A[1] * B[2] - A[2] * B[1];
	C[1] = A[0] * B[2] - A[2] * B[0];
	C[2] = A[0] * B[1] - A[1] * B[0];
}

static double TripleProduct(
	std::vector<double> A,
	std::vector<double> B,
	std::vector<double> C)
{
	double sum0 = 0.0, sum1 = 0.0;

	sum0 += A[0] * B[1] * C[2] + A[1] * B[2] * C[0] + A[2] * B[0] * C[1];
	sum1 += A[1] * B[0] * C[2] + A[0] * B[2] * C[1] + A[2] * B[1] * C[0];
	return sum0 - sum1;
}

static void Exercises_Section_1_13_1_Triple_Products()
{
	// triple products (a)
	std::vector<double> A1 = { 2, 0, 0 };
	std::vector<double> B1 = { 0, 3, 0 };
	std::vector<double> C1 = { 0, 0, 5 };
	double tp_1 = TripleProduct(A1, B1, C1);
	std::cout << "Exercise 1 (a)" << '\t';
	std::cout << tp_1 << std::endl;
	// triple products (b)
	std::vector<double> A2 = { 1, 1, 1 };
	std::vector<double> B2 = { 3, 1, 0 };
	std::vector<double> C2 = { 0, -1, 5 };
	std::cout << "Exercise 1 (b)" << '\t';
	double tp_2 = TripleProduct(A2, B2, C2);
	std::cout << tp_2 << std::endl;
	// triple products (c)
	std::vector<double> A3 = { 2, -1, 1 };
	std::vector<double> B3 = { 1, 1, 1 };
	std::vector<double> C3 = { 2, 0, 3 };
	double tp_3 = TripleProduct(A3, B3, C3);
	std::cout << "Exercise 1 (c)" << '\t';
	std::cout << tp_3 << std::endl;
	// triple products (d)
	std::vector<double> A4 = { 0, 0, 1 };
	std::vector<double> B4 = { 1, 0, 0 };
	std::vector<double> C4 = { 0, 1, 0 };
	double tp_4 = TripleProduct(A4, B4, C4);
	std::cout << "Exercise 1 (d)" << '\t';
	std::cout << tp_4 << std::endl;
	// volume of a parallelpipped
	std::vector<double> A5 = { 3, 4, 1 };
	std::vector<double> B5 = { 2, 3, 4 };
	std::vector<double> C5 = { 0, 0, 5 }; 
	double tp_5 = TripleProduct(A5, B5, C5);
	std::cout << "Exercise 2" << '\t';
	std::cout << tp_5 << std::endl;
	// volume of a parallelpipped
	std::vector<double> A6 = { 3, 2, 1 };
	std::vector<double> B6 = { 4, 2, 1 };
	std::vector<double> C6 = { 0, 1, 4 };
	std::vector<double> D6 = { 0, 0, 7 };
	std::vector<double> AB = { -1, 0, 0 };
	std::vector<double> AC = { 3, 1, -3 };
	std::vector<double> AD = { 3, 2, -6 };
	std::cout << "Exercise 3" << '\t';
	double tp_6 = TripleProduct(AB, AC, AD);
	std::cout << tp_6 << std::endl;
	// volume of a tetrahedron
	std::vector<double> AB1 = { 1, 1, 0 };
	std::vector<double> AC1 = { 1, -1, 0 };
	std::vector<double> AD1 = { 0, 0, 2 };
	std::cout << "Exercise 4" << '\t';
	double tp_7 = TripleProduct(AB1, AC1, AD1) / 6.0;
	std::cout << fabs(tp_7) << std::endl;
	std::vector<double> P1 = { 0, 0, 0 };
	std::vector<double> P2 = { 1, 1, 0 };
	std::vector<double> P3 = { 3, 4, 0 };
	std::vector<double> P4 = { 4, 5, 0 };
	std::vector<double> P5 = { 0, 0, 1 };
	std::vector<double> Q1 = { 1, 1, 0 };
	std::vector<double> Q2 = { 2, 3, 0 };
	std::vector<double> Q3 = { 1, 1, 1 };
	std::cout << "Exercise 5" << '\t';
	double tp_8 = TripleProduct(Q1, Q2, Q3);
	std::cout << fabs(tp_8) << std::endl;
	std::vector<double> A10 = { 1, 1, 1 };
	std::vector<double> B10 = { 2, 4, -1 };
	std::vector<double> C10 = { 1, 1, 3 };
	double tp_10 = TripleProduct(A10, B10, C10);
	std::vector<double> D10 = { 0 };
	VectorProduct(A10, B10, D10);
	double magnitude = sqrt(InnerProduct(D10, D10, 3));
	std::cout << "Exercise 10" << '\t';
	std::cout << tp_10 / magnitude << '\t';
	std::cout << 2.0 * sqrt(38.0) / 19.0 << std::endl;
}

int main()
{
	Exercises_Section_1_13_1_Triple_Products();
	return 0;
}

Blog Entry © Tuesday, April 7, 2026, by James Pate Williams, Jr., Hydrogen-like Atom Polar and Azimuthal Wavefunctions

Blog Entry Tuesday April 7 2026 Download

Blog Entry © Saturday April 4, 2026, by James Pate Williams, Jr., Hydrogen-like Radial Electron Distribution Functions in CPP

Blog Entry Saturday April 4 2026 Download

#pragma once

class RadialWaveFunction
{
private:
	static double Factorial(int n);
	static double Laguerre(double rho, int n, int l);
public:
	static double R(double r, int Z, int n, int l);
};

#include <math.h>
#include "RadialWaveFunction.h"

double RadialWaveFunction::Factorial(int n)
{
	double factorial = 1.0;

	for (int i = 2; i <= n; i++)
		factorial *= i;

	return factorial;
}

double RadialWaveFunction::Laguerre(double rho, int n, int l)
{
	double sum = 0.0;

	for (int k = 0; k <= n - l - 1; k++)
	{
		double factor1 = pow(-1, k + 2 * l + 1);
		double factor2 = pow(Factorial(n + l), 2.0);
		double factor3 = pow(rho, k);
		double numer = factor1 * factor2 * factor3;
		double factor4 = Factorial(n - l - 1 - k);
		double factor5 = Factorial(2 * l + 1 + k);
		double factor6 = Factorial(k);
		double denom = factor4 * factor5 * factor6;

		sum += numer / denom;
	}

	return sum;
}

double RadialWaveFunction::R(double r, int Z, int n, int l)
{
	double rho = 2.0 * Z * r / n;
	double numer1 = pow(2.0 * Z / n, 3.0);
	double numer2 = Factorial(n - l - 1);
	double denom1 = Factorial(n + n);
	double denom2 = pow(Factorial(n + l), 3.0);
	double numer3 = -sqrt(numer1 * numer2 /
		(denom1 * denom2));
	double exp2 = exp(-0.5 * rho);
	double rhol = pow(rho, l);
	return numer3 * exp2 * rhol * Laguerre(rho, n, l);
}

Blog Input © Saturday, March 21, 2026, by James Pate Williams, Jr., Three Model Universes

Blog Entry Saturday March 21 2026 Download

#pragma once

class UniversalModels
{
public:
	static void deSitterUniverse(
		double epsilon, double lambda, double ct,
		double A, double B, double& K);
	static void RadiationUniverse(
		double A, double epsilon,
		double deltaT, double& K);
	static void FriedmannUniverse(
		int epsilon, double M,
		double cT, double& K);
};

#include "UniversalModels.h"
#include <math.h>

void UniversalModels::deSitterUniverse(
	double epsilon, double lambda,
	double ct, double A, double B, double& K)
{
	if (lambda > 0)
	{
		if (epsilon == +1)
		{
			K = cosh(B * ct) / B;
		}

		else if (epsilon == -1)
		{
			K = sinh(B * ct) / B;
		}

		else
		{
			K = A * exp(B * ct);
		}
	}

	else if (lambda < 0)
	{
		if (epsilon == -1)
		{
			lambda = -3.0 * B * B;
			K = cos(B * ct) / B;
		}
	}
}

void UniversalModels::RadiationUniverse(
	double A, double epsilon,
	double deltaT, double& K)
{
	double c = 1.0, kappa = 1.0;

	if (epsilon == 0)
	{
		K = sqrt(2.0 * c * sqrt(kappa * A / 3.0) * deltaT);
	}

	else if (epsilon == -1)
	{
		K = sqrt(c * c * pow(deltaT, 2.0) + 2 * c *
			sqrt(kappa * A / 3.0) * deltaT);
	}

	else if (epsilon == +1)
	{
		K = sqrt(-c * c * pow(deltaT, 2.0) + 2 * c *
			sqrt(kappa * A / 3.0) * deltaT);
	}
}

void UniversalModels::FriedmannUniverse(
	int epsilon, double M, double cT, double& K)
{
	if (epsilon == 0)
	{
		K = M * cT * cT / 12.0;
	}

	else if (epsilon == -1)
	{
		K = M * (cosh(cT) - 1.0) / 6.0;
	}

	else if (epsilon == +1)
	{
		K = M * (1.0 - cos(cT)) / 6.0;
	}
}

// ModelUniverses.cpp (c) Thursday, March 19, 2026
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Reference: "General Relativity An Introduction
// to the theory of the gravitational field "
// (c) 1982 by Hans Stephani translated by Martin
// Pollack and John Stewart

#include "framework.h"
#include "ModelUniverses.h"
#include "UniversalModels.h"
#include <math.h>
#include <string>
#include <vector>

#define MAX_LOADSTRING 100

typedef struct tagPoint2dDeSitter
{
    double ct, K;
} Point2dDeSitter, * PPoint2dDeSitter;

typedef struct tagPoint2dRadiation
{
    double deltaT, K;
} Point2dRadiation, * PPoint2dRadiation;

typedef struct tagPoint2dFriedmann
{
    double cT, K;
} Point2dFriedmann, * PPoint2dFriedmann;


// Global Variables:
HINSTANCE hInst;                                // current instance
WCHAR szTitle[MAX_LOADSTRING];                  // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING];            // the main window class name
bool deSitter, radiation, friedmann;            // universal model type
std::wstring fTitle, xTitle, yTitle;            // graph titles
std::vector<Point2dDeSitter> pointsDeSitter;    // graph points
std::vector<Point2dRadiation> pointsRadiation;  // graph points
std::vector<Point2dFriedmann> pointsFriedmann;  // graph points

// Forward declarations of functions included in this code module:
ATOM                MyRegisterClass(HINSTANCE hInstance);
BOOL                InitInstance(HINSTANCE, int);
LRESULT CALLBACK    WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    About(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogDeSitter(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogDeSitter(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogRadiation(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogRadiation(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DataInputDialogFriedmann(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK    DrawGraphDialogFriedmann(HWND, UINT, WPARAM, LPARAM);

int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
                     _In_opt_ HINSTANCE hPrevInstance,
                     _In_ LPWSTR    lpCmdLine,
                     _In_ int       nCmdShow)
{
    UNREFERENCED_PARAMETER(hPrevInstance);
    UNREFERENCED_PARAMETER(lpCmdLine);

    // TODO: Place code here.

    // Initialize global strings
    LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
    LoadStringW(hInstance, IDC_MODELUNIVERSES, szWindowClass, MAX_LOADSTRING);
    MyRegisterClass(hInstance);

    // Perform application initialization:
    if (!InitInstance (hInstance, nCmdShow))
    {
        return FALSE;
    }

    HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_MODELUNIVERSES));

    MSG msg;

    // Main message loop:
    while (GetMessage(&msg, nullptr, 0, 0))
    {
        if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
        {
            TranslateMessage(&msg);
            DispatchMessage(&msg);
        }
    }

    return (int) msg.wParam;
}

//
//  FUNCTION: MyRegisterClass()
//
//  PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
    WNDCLASSEXW wcex = { 0 };

    wcex.cbSize = sizeof(WNDCLASSEX);

    wcex.style          = CS_HREDRAW | CS_VREDRAW;
    wcex.lpfnWndProc    = WndProc;
    wcex.cbClsExtra     = 0;
    wcex.cbWndExtra     = 0;
    wcex.hInstance      = hInstance;
    wcex.hIcon          = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_MODELUNIVERSES));
    wcex.hCursor        = LoadCursor(nullptr, IDC_ARROW);
    wcex.hbrBackground  = (HBRUSH)(COLOR_WINDOW+1);
    wcex.lpszMenuName   = MAKEINTRESOURCEW(IDC_MODELUNIVERSES);
    wcex.lpszClassName  = szWindowClass;
    wcex.hIconSm        = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));

    return RegisterClassExW(&wcex);
}

//
//   FUNCTION: InitInstance(HINSTANCE, int)
//
//   PURPOSE: Saves instance handle and creates main window
//
//   COMMENTS:
//
//        In this function, we save the instance handle in a global variable and
//        create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
   hInst = hInstance; // Store instance handle in our global variable

   HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
      CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);

   if (!hWnd)
   {
      return FALSE;
   }

   ShowWindow(hWnd, nCmdShow);
   UpdateWindow(hWnd);

   return TRUE;
}

//
//  FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
//  PURPOSE: Processes messages for the main window.
//
//  WM_COMMAND  - process the application menu
//  WM_PAINT    - Paint the main window
//  WM_DESTROY  - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
    switch (message)
    {
    case WM_COMMAND:
        {
            int wmId = LOWORD(wParam);
            // Parse the menu selections:
            switch (wmId)
            {
            case IDM_ABOUT:
                DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
                break;
            case IDM_DE_SITTER:
                deSitter = true;
                fTitle = L"de Sitter Universe";
                xTitle = L"Bct";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_DE_SITTER), 
                    hWnd, DataInputDialogDeSitter);
                break;
            case IDM_RADIATION:
                radiation = true;
                fTitle = L"Radiation Universe";
                xTitle = L"t - t0";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_RADIATION), hWnd,
                    DataInputDialogRadiation);
                break;
            case IDM_FRIEDMANN:
                friedmann = true;
                fTitle = L"Friedmann Universe";
                xTitle = L"cT";
                yTitle = L"K";
                DialogBox(hInst, MAKEINTRESOURCE(IDD_DATA_INPUT_DIALOG_FRIEDMANN), hWnd,
                    DataInputDialogFriedmann);
                break;
            case IDM_EXIT:
                DestroyWindow(hWnd);
                break;
            default:
                return DefWindowProc(hWnd, message, wParam, lParam);
            }
        }
        break;
    case WM_PAINT:
        {
            PAINTSTRUCT ps;
            HDC hdc = BeginPaint(hWnd, &ps);
            // TODO: Add any drawing code that uses hdc here...
            EndPaint(hWnd, &ps);
        }
        break;
    case WM_DESTROY:
        PostQuitMessage(0);
        break;
    default:
        return DefWindowProc(hWnd, message, wParam, lParam);
    }
    return 0;
}

// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    switch (message)
    {
    case WM_INITDIALOG:
        return (INT_PTR)TRUE;

    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    }
    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogDeSitter(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_A = GetDlgItem(hDlg, IDC_COMBO_A_1);
    static HWND hCombo_B = GetDlgItem(hDlg, IDC_COMBO_B);
    static HWND hCombo_ct = GetDlgItem(hDlg, IDC_COMBO_CT);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_1);
    static HWND hCombo_lambda = GetDlgItem(hDlg, IDC_COMBO_LAMBDA);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_B, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-5");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-4");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-3");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-2");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_LAMBDA, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_DE_SITTER)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_A_1, line, 128);
            double A = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_B, line, 128);
            double B = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_CT, line, 128);
            double CT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_1, FALSE, TRUE);
            GetDlgItemTextA(hDlg, IDC_COMBO_LAMBDA, line, 128);
            double lambda = atof(line);
			double ct = 0.0, K = 0.0;
			double delta_ct = CT / 256.0;
			int index = 0;

            pointsDeSitter.clear();

			while (ct <= CT)
			{
                UniversalModels::deSitterUniverse(
                    epsilon, lambda, ct, A, B, K);
				Point2dDeSitter pt = { 0 };
				pt.ct = ct;
				pt.K = K;
				ct += delta_ct;
                pointsDeSitter.push_back(pt);
			}

			DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_DE_SITTER),
				hDlg, DrawGraphDialogDeSitter);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxDeSitter(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsDeSitter[0].ct;
    xmax = pointsDeSitter[0].ct;
    ymin = pointsDeSitter[0].K;
    ymax = pointsDeSitter[0].K;

    for (int i = 1; i < pointsDeSitter.size(); i++)
    {
        Point2dDeSitter pt = pointsDeSitter[i];

        if (pt.ct < xmin)
            xmin = pt.ct;
        if (pt.ct > xmax)
            xmax = pt.ct;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static void DrawTitles(
    HDC hdc, RECT clientRect,
    const std::wstring& fTitle,
    const std::wstring& xTitle,
    const std::wstring& yTitle,
    int sx0, int sx1, int sy0, int sy1)
{
    HFONT hCustomFont = CreateFont(
        -MulDiv(10, GetDeviceCaps(hdc, LOGPIXELSY), 72), // Height in logical units
        0,                      // Width (0 = default)
        0,                      // Escapement
        0,                      // Orientation
        FW_BOLD,                // Weight (700 = bold)
        FALSE,                  // Italic
        FALSE,                  // Underline
        FALSE,                  // StrikeOut
        DEFAULT_CHARSET,        // Charset
        OUT_DEFAULT_PRECIS,     // Output precision
        CLIP_DEFAULT_PRECIS,    // Clipping precision
        DEFAULT_QUALITY,        // Quality
        FIXED_PITCH | FF_MODERN,// Pitch and family
        L"Courier New"          // Typeface name
    );

    HFONT hOldFont = (HFONT)SelectObject(hdc, hCustomFont);

    SIZE sz;
    int width = clientRect.right - clientRect.left;

    // Title: fTitle
    GetTextExtentPoint32W(hdc, fTitle.c_str(), (int)fTitle.length(), &sz);
    int w = sz.cx;
    int h = sz.cy;
    TextOutW(hdc, (width - w) / 2, h, fTitle.c_str(), (int)fTitle.length());
    // draw x-axis title
    GetTextExtentPoint32W(hdc, xTitle.c_str(), (int)xTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx0 + (sx1 - sx0 - w) / 2, sy1 + 2 * h, 
        xTitle.c_str(), (int)xTitle.length());
    // draw y-axis title
    GetTextExtentPoint32W(hdc, yTitle.c_str(), (int)yTitle.length(), &sz);
    w = sz.cx;
    TextOutW(hdc, sx1 + w / 5, sy0 + (sy1 - sy0) / 2 - h / 2, 
        yTitle.c_str(), (int)yTitle.length());
    SelectObject(hdc, hOldFont); // Restore original font
}

static void DrawFormattedText(HDC hdc, char loctext[], RECT rect)
{
    // Draw the text with formatting options
    DrawTextA(hdc, loctext, (int)strlen(loctext), &rect, DT_SINGLELINE | DT_NOCLIP);
}

static INT_PTR CALLBACK DrawGraphDialogDeSitter(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog deSitter Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxDeSitter(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsDeSitter[0].ct;
        py = (float)pointsDeSitter[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsDeSitter[0].ct;
        py = (float)pointsDeSitter[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsDeSitter.size(); j++)
        {
            px = (float)pointsDeSitter[j].ct;
            py = (float)pointsDeSitter[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogRadiation(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_B = GetDlgItem(hDlg, IDC_COMBO_B);
    static HWND hCombo_ct = GetDlgItem(hDlg, IDC_COMBO_DELTA_T);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_2);
    static HWND hCombo_lambda = GetDlgItem(hDlg, IDC_COMBO_LAMBDA);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e1");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e2");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e3");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e4");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"1e5");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_A_2, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-5");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-4");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-3");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-2");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+0");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+2");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+3");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+4");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_ADDSTRING, 0, (LPARAM)L"1.0e+5");
        SendDlgItemMessage(hDlg, IDC_COMBO_DELTA_T, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_2, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_RADIATION)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_A_2, line, 128);
            double A = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_DELTA_T, line, 128);
            double deltaT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_2, FALSE, TRUE);
            double step = deltaT / 256.0, t = 0.0, K = 0.0;
            int index = 0;

            pointsRadiation.clear();

            while (t <= deltaT)
            {
                UniversalModels::RadiationUniverse(
                    A, epsilon, t, K);
                Point2dRadiation pt = { 0 };
                pt.deltaT = t;
                pt.K = K;
                t += step;
                pointsRadiation.push_back(pt);
            }

            DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_RADIATION),
                hDlg, DrawGraphDialogRadiation);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxRadiation(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsRadiation[0].deltaT;
    xmax = pointsRadiation[0].deltaT;
    ymin = pointsRadiation[0].K;
    ymax = pointsRadiation[0].K;

    for (int i = 1; i < pointsRadiation.size(); i++)
    {
        Point2dRadiation pt = pointsRadiation[i];

        if (pt.deltaT < xmin)
            xmin = pt.deltaT;
        if (pt.deltaT > xmax)
            xmax = pt.deltaT;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static INT_PTR CALLBACK DrawGraphDialogRadiation(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog Radiation Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxRadiation(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsRadiation[0].deltaT;
        py = (float)pointsRadiation[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsRadiation[0].deltaT;
        py = (float)pointsRadiation[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsRadiation.size(); j++)
        {
            px = (float)pointsRadiation[j].deltaT;
            py = (float)pointsRadiation[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

INT_PTR CALLBACK DataInputDialogFriedmann(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    static WCHAR data[128] = L"";
    static HWND hCombo_M = GetDlgItem(hDlg, IDC_COMBO_M);
    static HWND hCombo_CT1 = GetDlgItem(hDlg, IDC_COMBO_CT1);
    static HWND hCombo_epsilon = GetDlgItem(hDlg, IDC_COMBO_EPSILON_3);

    switch (message)
    {
    case WM_INITDIALOG:
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_M, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"1");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"2");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"3");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"4");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"5");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"6");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"7");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"8");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"9");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_ADDSTRING, 0, (LPARAM)L"10");
        SendDlgItemMessage(hDlg, IDC_COMBO_CT1, CB_SETCURSEL, 0, 0);
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"-1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"0");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_ADDSTRING, 0, (LPARAM)L"+1");
        SendDlgItemMessage(hDlg, IDC_COMBO_EPSILON_3, CB_SETCURSEL, 0, 0);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
    {
        if (LOWORD(wParam) == IDC_BUTTON_DRAW_FRIEDMANN)
        {
            char line[128] = "";
            GetDlgItemTextA(hDlg, IDC_COMBO_M, line, 128);
            double M = atof(line);
            GetDlgItemTextA(hDlg, IDC_COMBO_CT1, line, 128);
            double cT = atof(line);
            int epsilon = GetDlgItemInt(hDlg, IDC_COMBO_EPSILON_3, FALSE, TRUE);
            double step = cT / 256.0, t = 0.0, K = 0.0;
            int index = 0;

            pointsFriedmann.clear();

            while (t <= cT)
            {
                UniversalModels::FriedmannUniverse(
                    epsilon, M, t, K);
                Point2dFriedmann pt = { 0 };
                pt.cT = t;
                pt.K = K;
                t += step;
                pointsFriedmann.push_back(pt);
            }

            DialogBox(hInst, MAKEINTRESOURCE(IDD_DRAW_GRAPH_DIALOG_FRIEDMANN),
                hDlg, DrawGraphDialogFriedmann);
            return (INT_PTR)TRUE;
        }

        else if (LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
    }
    }

    return (INT_PTR)FALSE;
}

static void FindMinMaxFriedmann(
    double& xmin,
    double& xmax,
    double& ymin,
    double& ymax)
{
    xmin = pointsFriedmann[0].cT;
    xmax = pointsFriedmann[0].cT;
    ymin = pointsFriedmann[0].K;
    ymax = pointsFriedmann[0].K;

    for (int i = 1; i < pointsFriedmann.size(); i++)
    {
        Point2dFriedmann pt = pointsFriedmann[i];

        if (pt.cT < xmin)
            xmin = pt.cT;
        if (pt.cT > xmax)
            xmax = pt.cT;
        if (pt.K < ymin)
            ymin = pt.K;
        if (pt.K > ymax)
            ymax = pt.K;
    }
}

static INT_PTR CALLBACK DrawGraphDialogFriedmann(
    HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
    UNREFERENCED_PARAMETER(lParam);
    char line[256] = "";
    switch (message)
    {
    case WM_INITDIALOG:
        strcpy_s(line, 256, "Drawing Dialog Friedmann Universe");
        SetWindowTextA(hDlg, line);
        return (INT_PTR)TRUE;
    case WM_COMMAND:
        if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
        {
            EndDialog(hDlg, LOWORD(wParam));
            return (INT_PTR)TRUE;
        }
        break;
    case WM_PAINT:
        double xmax = 0, xmin = 0;
        double ymax = 0, ymin = 0;
        FindMinMaxFriedmann(xmin, xmax, ymin, ymax);
        double h = 0, pi = 0, plm = 0, theta = 0;
        float xSpan = (float)(xmax - xmin);
        float ySpan = (float)(ymax - ymin);
        RECT rect = { };
        GetClientRect(hDlg, &rect);
        float width = (float)(rect.right - rect.left + 1);
        float height = (float)(rect.bottom - rect.top - 32 + 1);
        float sx0 = 2.0f * width / 16.0f;
        float sx1 = 14.0f * width / 16.0f;
        float sy0 = 2.0f * height / 16.0f;
        float sy1 = 14.0f * height / 16.0f;
        float deltaX = xSpan / 8.0f;
        float deltaY = ySpan / 8.0f;
        float xSlope = (sx1 - sx0) / xSpan;
        float xInter = (float)(sx0 - xSlope * xmin);
        float ySlope = (sy0 - sy1) / ySpan;
        float yInter = (float)(sy0 - ySlope * ymax);
        float px = 0, py = 0, sx = 0, sy = 0;
        PAINTSTRUCT ps;
        POINT wPt = { };
        HDC hdc = BeginPaint(hDlg, &ps);
        int i = 0;
        float x = (float)xmin;
        float y = (float)ymax;
        DrawTitles(hdc, rect, fTitle, xTitle, yTitle,
            (int)sx0, (int)sx1, (int)sy0, (int)sy1);
        px = (float)pointsFriedmann[0].cT;
        py = (float)pointsFriedmann[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        MoveToEx(hdc, (int)sx, (int)sy0, &wPt);

        while (i <= 8)
        {
            sx = xSlope * x + xInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx, (int)sy0, &wPt);
            LineTo(hdc, (int)sx, (int)sy1);
            char numberStr[128] = "";
            sprintf_s(numberStr, 128, "%5.4lf", x);
            SIZE size = { };
            GetTextExtentPoint32A(
                hdc,
                numberStr,
                (int)strlen(numberStr),
                &size);
            RECT textRect = { };
            textRect.left = (long)(sx - size.cx / 2.0f);
            textRect.right = (long)(sx + size.cx / 2.0f);
            textRect.top = (long)sy1;
            textRect.bottom = (long)(sy1 + size.cy / 2.0f);
            DrawFormattedText(hdc, numberStr, textRect);
            x += deltaX;
            i++;
        }

        i = 0;
        y = (float)ymin;

        while (i <= 8)
        {
            sy = ySlope * y + yInter;
            wPt.x = wPt.y = 0;
            MoveToEx(hdc, (int)sx0, (int)sy, &wPt);
            LineTo(hdc, (int)sx, (int)sy);

            if (i != 0)
            {
                char numberStr[128] = "";
                sprintf_s(numberStr, 128, "%+5.3lf", y);
                SIZE size = { };
                GetTextExtentPoint32A(
                    hdc,
                    numberStr,
                    (int)strlen(numberStr),
                    &size);
                RECT textRect = { 0 };
                textRect.left = (long)(sx0 - size.cx - size.cx / 2.0f);
                textRect.right = (long)(sx0 - size.cx / 2.0f);
                textRect.top = (long)(sy - size.cy / 2.0f);
                textRect.bottom = (long)(sy + size.cy / 2.0f);
                DrawFormattedText(hdc, numberStr, textRect);
            }

            y += deltaY;
            i++;
        }

        HGDIOBJ bPenNew = NULL;
        HGDIOBJ hPenOld = NULL;

        bPenNew = CreatePen(PS_SOLID, 2, RGB(0, 0, 255));
        hPenOld = SelectObject(hdc, bPenNew);

        HRGN clipRegion = CreateRectRgn(
            (int)sx0, (int)sy0,              // Left, Top
            (int)(sx1), (int)(sy1)           // Right, Bottom
        );

        // Apply clipping region

        SelectClipRgn(hdc, clipRegion);

        px = (float)pointsFriedmann[0].cT;
        py = (float)pointsFriedmann[0].K;
        sx = xSlope * px + xInter;
        sy = ySlope * py + yInter;
        wPt.x = wPt.y = 0;
        MoveToEx(hdc, (int)sx, (int)sy, &wPt);

        for (size_t j = 1; j < pointsFriedmann.size(); j++)
        {
            px = (float)pointsFriedmann[j].cT;
            py = (float)pointsFriedmann[j].K;
            sx = xSlope * px + xInter;
            sy = ySlope * py + yInter;
            LineTo(hdc, (int)sx, (int)sy);
        }

        DeleteObject(bPenNew);
        bPenNew = NULL;

        SelectObject(hdc, hPenOld);
        DeleteObject(clipRegion);
        EndPaint(hDlg, &ps);
        return (INT_PTR)TRUE;
    }

    return (INT_PTR)FALSE;
}

//Microsoft Visual C++ generated resource script.
//
#include "resource.h"

#define APSTUDIO_READONLY_SYMBOLS
/////////////////////////////////////////////////////////////////////////////
//
// Generated from the TEXTINCLUDE resource.
//
#ifndef APSTUDIO_INVOKED
#include "targetver.h"
#endif
#define APSTUDIO_HIDDEN_SYMBOLS
#include "windows.h"
#undef APSTUDIO_HIDDEN_SYMBOLS
/////////////////////////////////////////////////////////////////////////////
#undef APSTUDIO_READONLY_SYMBOLS

#if !defined(AFX_RESOURCE_DLL) || defined(AFX_TARG_ENU)
LANGUAGE 9, 1

/////////////////////////////////////////////////////////////////////////////
//
// Icon
//

// Icon with lowest ID value placed first to ensure application icon
// remains consistent on all systems.

IDI_MODELUNIVERSES       ICON         "ModelUniverses.ico"
IDI_SMALL               ICON         "small.ico"

/////////////////////////////////////////////////////////////////////////////
//
// Menu
//

IDC_MODELUNIVERSES MENU
BEGIN
    POPUP "&Begin"
    BEGIN
        MENUITEM "&de Sitter Universe", IDM_DE_SITTER
        MENUITEM "&Radiation Universe", IDM_RADIATION
        MENUITEM "&Friedmann Universe", IDM_FRIEDMANN
        MENUITEM SEPARATOR
        MENUITEM "E&xit",               IDM_EXIT
    END
    POPUP "&Help"
    BEGIN
        MENUITEM "&About ...",          IDM_ABOUT
    END
END


/////////////////////////////////////////////////////////////////////////////
//
// Accelerator
//

IDC_MODELUNIVERSES ACCELERATORS
BEGIN
    "?",            IDM_ABOUT,              ASCII,  ALT
    "/",            IDM_ABOUT,              ASCII,  ALT
END


/////////////////////////////////////////////////////////////////////////////
//
// Dialog
//

IDD_ABOUTBOX DIALOGEX 0, 0, 170, 62
STYLE DS_SETFONT | DS_MODALFRAME | DS_FIXEDSYS | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "About ModelUniverses"
FONT 8, "MS Shell Dlg"
BEGIN
    ICON            IDI_MODELUNIVERSES,IDC_STATIC,14,14,21,20
    LTEXT           "ModelUniverses, Version 1.0",IDC_STATIC,42,14,114,8,SS_NOPREFIX
    LTEXT           "Copyright (c) 2026",IDC_STATIC,42,26,114,8
    DEFPUSHBUTTON   "OK",IDOK,113,41,50,14,WS_GROUP
END

IDD_DATA_INPUT_DIALOG_DE_SITTER DIALOGEX 0, 0, 280, 200
STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "Data Input Dialog de Sitter Universe"
FONT 10, "Courier New", 700
BEGIN
LTEXT       "A:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_A_1, 120, 10, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "B:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_B, 120, 40, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "ct:", IDC_STATIC, 10, 70, 100, 10
COMBOBOX    IDC_COMBO_CT, 120, 70, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "epsilon:",
IDC_STATIC, 10, 100, 50, 60
COMBOBOX    IDC_COMBO_EPSILON_1, 120, 100, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "Lambda:",
IDC_STATIC, 10, 130, 50, 60
COMBOBOX    IDC_COMBO_LAMBDA, 120, 130, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_DE_SITTER, 10, 160, 50, 16
PUSHBUTTON  "Cancel", IDCANCEL, 210, 160, 50, 16
END

IDD_DRAW_GRAPH_DIALOG_DE_SITTER DIALOGEX 0, 0, 600, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog de Sitter Universe"
FONT 10, "Courier New", 700
BEGIN
END

IDD_DATA_INPUT_DIALOG_RADIATION DIALOGEX 0, 0, 280, 170
STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "Data Input Dialog Radiation Universe"
FONT 10, "Courier New", 700
BEGIN
LTEXT       "A:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_A_2, 120, 10, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "t - t0:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_DELTA_T, 120, 40, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "epsilon:",
IDC_STATIC, 10, 70, 50, 60
COMBOBOX    IDC_COMBO_EPSILON_2, 120, 70, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_RADIATION, 10, 100, 50, 16
PUSHBUTTON  "Cancel", IDCANCEL, 210, 100, 50, 16
END

IDD_DRAW_GRAPH_DIALOG_RADIATION DIALOGEX 0, 0, 600, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog Radiation Universe"
FONT 10, "Courier New", 700
BEGIN
END

IDD_DATA_INPUT_DIALOG_FRIEDMANN DIALOGEX 0, 0, 280, 170
STYLE DS_SETFONT | WS_POPUP | WS_CAPTION | WS_SYSMENU
CAPTION "Data Input Dialog Friedmann Universe"
FONT 10, "Courier New", 700
BEGIN
LTEXT       "M:", IDC_STATIC, 10, 10, 100, 10
COMBOBOX    IDC_COMBO_M, 120, 10, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "cT:", IDC_STATIC, 10, 40, 100, 10
COMBOBOX    IDC_COMBO_CT1, 120, 40, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
LTEXT       "epsilon:",
IDC_STATIC, 10, 70, 50, 60
COMBOBOX    IDC_COMBO_EPSILON_3, 120, 70, 50, 60, CBS_DROPDOWNLIST
| WS_VSCROLL | WS_TABSTOP
PUSHBUTTON  "Draw", IDC_BUTTON_DRAW_FRIEDMANN, 10, 100, 50, 16
PUSHBUTTON  "Cancel", IDCANCEL, 210, 100, 50, 16
END

IDD_DRAW_GRAPH_DIALOG_FRIEDMANN DIALOGEX 0, 0, 600, 310
STYLE DS_SETFONT | WS_POPUP | WS_VISIBLE | WS_CAPTION | WS_SYSMENU
CAPTION "Draw Graph Dialog Friedmann Universe"
FONT 10, "Courier New", 700
BEGIN
END

/////////////////////////////////////////////////////////////////////////////
//
// DESIGNINFO
//

#ifdef APSTUDIO_INVOKED
GUIDELINES DESIGNINFO
BEGIN
    IDD_ABOUTBOX, DIALOG
    BEGIN
        LEFTMARGIN, 7
        RIGHTMARGIN, 163
        TOPMARGIN, 7
        BOTTOMMARGIN, 55
    END
END
#endif    // APSTUDIO_INVOKED

#ifdef APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// TEXTINCLUDE
//
1 TEXTINCLUDE
BEGIN
    "resource.h\0"
END

2 TEXTINCLUDE
BEGIN
    "#ifndef APSTUDIO_INVOKED\r\n"
    "#include ""targetver.h""\r\n"
    "#endif\r\n"
    "#define APSTUDIO_HIDDEN_SYMBOLS\r\n"
    "#include ""windows.h""\r\n"
    "#undef APSTUDIO_HIDDEN_SYMBOLS\r\n"
    "\0"
END

3 TEXTINCLUDE
BEGIN
    "\r\n"
    "\0"
END

#endif    // APSTUDIO_INVOKED

/////////////////////////////////////////////////////////////////////////////
//
// String Table
//

STRINGTABLE
BEGIN
   IDC_MODELUNIVERSES   "MODELUNIVERSES"
   IDS_APP_TITLE       "ModelUniverses"
END

#endif
/////////////////////////////////////////////////////////////////////////////



#ifndef APSTUDIO_INVOKED
/////////////////////////////////////////////////////////////////////////////
//
// Generated from the TEXTINCLUDE resource.
//

/////////////////////////////////////////////////////////////////////////////
#endif    // not APSTUDIO_INVOKED

//{{NO_DEPENDENCIES}}
// Microsoft Visual C++ generated include file.
// Used by ModelUniverses.rc

#define IDS_APP_TITLE			103

#define IDR_MAINFRAME			128
#define IDD_MODELUNIVERSES_DIALOG	102
#define IDD_ABOUTBOX			103
#define IDM_ABOUT				104
#define IDM_EXIT				105
#define IDI_MODELUNIVERSES		107
#define IDI_SMALL				108
#define IDC_MODELUNIVERSES		109
#define IDC_MYICON				2
#ifndef IDC_STATIC
#define IDC_STATIC				-1
#endif
// Next default values for new objects
//
#ifdef APSTUDIO_INVOKED
#ifndef APSTUDIO_READONLY_SYMBOLS

#define _APS_NO_MFC					130
#define _APS_NEXT_RESOURCE_VALUE	129
#define _APS_NEXT_COMMAND_VALUE		32771
#define _APS_NEXT_CONTROL_VALUE		1000
#define _APS_NEXT_SYMED_VALUE		110
#endif
#endif

#define IDD_DATA_INPUT_DIALOG_DE_SITTER	1000
#define IDC_COMBO_A_1				1010
#define IDC_COMBO_B					1020
#define IDC_COMBO_CT				1030
#define IDC_COMBO_EPSILON_1			1040
#define IDC_COMBO_LAMBDA			1050
#define IDC_BUTTON_DRAW_DE_SITTER	1060
#define IDD_DRAW_GRAPH_DIALOG_DE_SITTER	2000
#define IDD_DATA_INPUT_DIALOG_RADIATION	3000
#define IDC_COMBO_A_2				3010
#define IDC_COMBO_DELTA_T			3020
#define IDC_COMBO_EPSILON_2			3030
#define IDC_BUTTON_DRAW_RADIATION	3040
#define IDD_DRAW_GRAPH_DIALOG_RADIATION	4000
#define IDD_DATA_INPUT_DIALOG_FRIEDMANN 5000
#define IDC_COMBO_M					5010
#define IDC_COMBO_CT1				5020
#define IDC_COMBO_EPSILON_3			5030
#define IDC_BUTTON_DRAW_FRIEDMANN	5040
#define IDD_DRAW_GRAPH_DIALOG_FRIEDMANN	6000
#define IDM_DE_SITTER				32771
#define IDM_RADIATION				32772
#define IDM_FRIEDMANN				32773

Blog Entry © Thursday, March 5, 2026, by James Pate Williams, Jr., Simple Filtering of a Noisy Signal in the Programming Language C

Blog Entry Thursday March 5 2026 Download

Blog Entry (c) Tuesday February 3, 2026, by James Pate Williams, Jr. Derivation of the Classical Kinetic Energy Formula

Derivation of the Classical Kinetic Energy Equation from Einstein Download

// KineticEnergy.cpp
// Author: James Pate Williams, Jr. and NIST
// Copyright Monday February 2, 2026

#include <iomanip>
#include <iostream>
#include <vector>

const double c = 2.99792458E8;
const double mass0 = 1.67492750056E-27;

static double KineticEnergy(
    double v, size_t number,
    double& kilotonsTNT,
    std::vector<double>& terms)
{
    double c2 = c * c, ke = 0;;
    
    if (number >= 0)
        terms[0] = mass0 * c2;
    if (number >= 1)
        terms[1] = 0.5 * mass0 * v * v;
    if (number >= 2)
        terms[2] = 3.0 * mass0 * pow(v, 4.0) / (8.0 * c2);
    if (number >= 3)
        terms[3] = 225.0 * mass0 * pow(v, 6.0) / (720.0 * c2 * c2);

    for (size_t i = 0; i <= number; i++)
        ke += terms[i];

    kilotonsTNT = 2.3900573613767E-13 * ke;
    return ke;
}

int main()
{
    char line[128] = "";

    while (true)
    {
        double ke = 0.0, kilotonsTNT = 0.0, v = 0.0;
        size_t number = 0;

        std::cout << "Enter v = ";
        std::cin.getline(line, 128);
        v = atof(line);

        if (v == 0)
            break;

        std::cout << "# Terms = ";
        std::cin.getline(line, 128);
        number = static_cast<size_t>(atoi(line));
        std::vector<double> terms(number + 1);
        ke = KineticEnergy(v, number, kilotonsTNT, terms);
        std::cout << "KE = " << ke << " joules" << std::endl;
        std::cout << "KE = " << kilotonsTNT << " kilotons TNT";
        std::cout << std::endl;
        std::cout << std::scientific;

        for (size_t i = 0; i <= number; i++)
        {
            std::cout << "KE[" << i << "] = " << terms[i];
            std::cout << " joules" << std::endl;
            kilotonsTNT = 2.3900573613767E-13 * terms[i];
            std::cout << "KE[" << i << "] = " << kilotonsTNT;
            std::cout << " kilotons TNT" << std::endl;
        }
    }
}

Blog Entry © Sunday, January 25, 2026, by James Pate Williams, Jr., Schwarzschild Solution of Einstein’s General Relativity Gravitational Field Equation

Blog Entry Sunday January 25 2026 Download