public void TestMethodSolve()
{
QuadraticEquation myQuadraticEquation = new QuadraticEquation();
CollectionAssert.AreEqual(new List<float>() { 2f }, myQuadraticEquation.Solve(0, 2, -4));
CollectionAssert.AreEqual(new List<float>() { 3, -2.5f }, myQuadraticEquation.Solve(2, -1, -15));
CollectionAssert.AreEqual(new List<float>() { 1, 0.6666667f }, myQuadraticEquation.Solve(3, -5, 2));
myQuadraticEquation.Solve(0, 0, 1);
OborotovException ex = Assert.ThrowsException<OborotovException>(() => myQuadraticEquation.Solve(0, 0, 5));
Assert.AreEqual("Такое уравнение не существует", ex.Message);
}
public static bool GetCollisionSphere(Vector3 lineSource, Vector3 lineDestination, Vector3 position, float radius, out float distanceFromSource)
{
// Abs(ベクトルの始点 + a線分ベクトル - 球の中心) = 球の半径
// |E + aD - C| = R
// D^2 x^2 + 2D(E-C)x + (E-C)^2 - R^2 = 0
distanceFromSource = 0;
Vector3 diff = lineSource - position;
Vector3 lineEdge = lineDestination - lineSource;
float coefQuadric = lineEdge.LengthSq();
float coefLinear = 2f * Vector3.Dot(lineEdge, diff);
float coefConst = diff.LengthSq() - radius * radius;
QuadraticEquation qe = QuadraticEquation.Solve(coefQuadric, coefLinear, coefConst);
if (qe.Answers.Length > 0)
{
foreach (var ans in qe.Answers)
{
if (ans >= 0 && ans <= 1)
{
distanceFromSource = ans * lineEdge.Length();
return(true);
}
}
}
return(false);
}
static void Main(string[] args)
{
using (StreamReader sr = new StreamReader("version"))
{
MyLog.Log($"Версия программы {sr.ReadToEnd().Trim()}");
}
QuadraticEquation myQuadraticEquation = new QuadraticEquation();
float a, b, c;
Console.WriteLine("Введите 3 параметра a, b и с");
Console.Write("a = ");
a = Convert.ToSingle(Console.ReadLine());
Console.Write("b = ");
b = Convert.ToSingle(Console.ReadLine());
Console.Write("c = ");
c = Convert.ToSingle(Console.ReadLine());
try
{
MyLog.Log("Корни уравнения: " + String.Join(" ", myQuadraticEquation.Solve(a, b, c)));
}
catch (TrimailovException e)
{
MyLog.Log(e.Message);
}
MyLog.Write();
Console.ReadKey();
}
private void button1_Click(object sender, EventArgs e)
{
if (a.Text.Trim() == string.Empty || a.Text.Trim() == "0")
{
MessageBox.Show("Пожалуйста, проверьте аргумент a", "Ошибка");
return;
}
else if (textBox2.Text.Trim() == string.Empty)
{
MessageBox.Show("Пожалуйста, проверьте аргумент b", "Ошибка");
return;
}
else if (textBox3.Text.Trim() == string.Empty)
{
MessageBox.Show("Пожалуйста, проверьте аргумент с", "Ошибка");
return;
}
else if (textBox1.Text.Trim() == string.Empty)
{
MessageBox.Show("Пожалуйста, проверьте аргумент d", "Ошибка");
return;
}
try
{
QuadraticEquation qe = new QuadraticEquation(a.Text, textBox2.Text, textBox3.Text, textBox1.Text);
double?[] res = qe.Solve();
string result = "";
foreach (double?i in res)
{
result += " " + Math.Round(Convert.ToDecimal(i), 2) + ";";
}
if (res[0] != res[1])
{
label3.Text = "x = " + result;
}
else if (res[0].Equals(null) || res[1].Equals(null))
{
label3.Font = new System.Drawing.Font("Leelawadee", 8);
label3.Text = "Уравнение имеет комплексные корни.";
}
else
{
label3.Text = "x = " + res[0];
}
}
catch (Exception)
{
MessageBox.Show("Проверьте введенные данные.");
}
}
static void Main(string[] args)
{
var quadraticEquation = new QuadraticEquation();
Console.WriteLine("Digite A");
var a = double.Parse(Console.ReadLine());
Console.WriteLine("Digite B");
var b = double.Parse(Console.ReadLine());
Console.WriteLine("Digite C");
var c = double.Parse(Console.ReadLine());
var x = quadraticEquation.Solve(a, b, c);
Console.WriteLine($"X1: {x.x1:N}");
Console.WriteLine($"X2: {x.x2:N}");
}
/// <summary>
/// 線分と円筒が交点を持つかを返します．
/// </summary>
/// <param name="lineSource">線分の始点</param>
/// <param name="lineDestination">線分の終点</param>
/// <param name="end1">円筒の一方の側面の中心</param>
/// <param name="end2">円筒の他方の側面の中心</param>
/// <param name="radius">円筒の半径</param>
/// <param name="distanceFromSource">線分の始点から円筒までの最短距離</param>
/// <returns></returns>
public static bool GetCollisionCylinder(Vector3 lineSource, Vector3 lineDestination, Vector3 end1, Vector3 end2, float radius, out float distanceFromSource)
{
distanceFromSource = 0;
// B:line.end T:line.lineDir E:cylinder.End N:cylinder.lineDir R:cylinder.radius
// |(B+aT)-E - ((B+aT)-E) . N * N| = R
// [(T-T.N N)a + (B-E-B.N N+E.N N)]^2 = R
Vector3 lineEdge = lineDestination - lineSource;
Vector3 axis = end2 - end1;
Vector3 axisDir = Vector3.Normalize(axis);
float axisLength = axis.Length();
Vector3 position = end1 - axisDir * radius;
Vector3 coefQuadricVec = lineEdge - Vector3.Dot(lineEdge, axisDir) * axisDir;
Vector3 endDiff = lineSource - end1;
Vector3 coefConstVec = endDiff - Vector3.Dot(endDiff, axisDir) * axisDir;
float A = coefQuadricVec.LengthSq();
float B = 2f * Vector3.Dot(coefQuadricVec, coefConstVec);
float C = coefConstVec.LengthSq() - radius * radius;
QuadraticEquation eq = QuadraticEquation.Solve(A, B, C);
if (eq.Indefinite)
{
distanceFromSource = 0;
return(true);
}
foreach (var ans in eq.Answers)
{
if (ans < 0)
{
continue;
}
Vector3 point = lineSource + lineEdge * ans;
Vector3 toPoint = point - end1;
float horiz = Vector3.Dot(toPoint, axisDir);
if (0 <= horiz && horiz <= axisLength)
{
distanceFromSource = ans * lineEdge.LengthSq();
return(true);
}
}
return(false);
}
public PointF[] Intersect(CircleEquation circle)
{
var cx = circle.Center.X;
var cy = circle.Center.Y;
var r = circle.Radius;
if (isVertical)
{
var distance = Math.Abs(cx - xConstForVertical);
if (distance > r)
{
return(new PointF[0]);
}
if (distance == r)
{
return new[] { new PointF(xConstForVertical, cy) }
}
;
// two intersections
var dx = cx - xConstForVertical;
var qe = new QuadraticEquation(
1,
-2 * cy,
r * r - dx * dx);
return(qe.Solve());
}
var t = b - cy;
var q = new QuadraticEquation(
1 + a * a,
2 * a * t - 2 * cx,
cx * cx + t * t - r * r);
var solutions = q.Solve();
for (var i = 0; i < solutions.Length; i++)
{
solutions[i] = Intersect(solutions[i].X).Value;
}
return(solutions);
}
}
/// <summary>
/// 给定初始速度大小，目标位置，求角度（复数解），不考虑重力xz方向分力和阻力
/// </summary>
/// <param name="initialPosition">初始位置</param>
/// <param name="targetPosition">目标位置</param>
/// <param name="v">初始速度</param>
/// <param name="gravity">重力</param>
/// <returns></returns>
public static ProjectileMotion[] CalculateAngle(Vector3 initialPosition, Vector3 targetPosition, float v, Vector3 gravity)
{
var distance = targetPosition - initialPosition;
var dirXZ = new Vector3(distance.x, 0f, distance.z).normalized;
var x = distance.SetValue(null, 0, null).magnitude;
var y = distance.y;
var item = gravity.y * x * x / (2 * v * v);
float a = item, b = x, c = item - y;
var result = QuadraticEquation.Solve(a, b, c);
if (result == null)
{
Debug.LogWarning("给定力度无法达到目标位置");
return(null);
}
var angle1 = Mathf.Atan(result[0]) * Mathf.Rad2Deg;
var angle2 = Mathf.Atan(result[1]) * Mathf.Rad2Deg;
//var root = b * b - (4f * a * c);
//if (root < 0)
//{
// Debug.LogWarning("给定力度无法达到目标位置");
// return null;
//}
//var angle1 = Mathf.Atan((-b + Mathf.Sqrt(root)) / (2f * a)) * Mathf.Rad2Deg;
//var angle2 = Mathf.Atan((-b - Mathf.Sqrt(root)) / (2f * a)) * Mathf.Rad2Deg;
var asix = Vector3.Cross(dirXZ, Vector3.up);
var v0_1 = v * (Quaternion.AngleAxis(angle1, asix) * dirXZ);
var v0_2 = v * (Quaternion.AngleAxis(angle2, asix) * dirXZ);
return(new ProjectileMotion[] { new ProjectileMotion(initialPosition, v0_1, Vector3.zero, Vector3.zero, gravity), new ProjectileMotion(initialPosition, v0_2, Vector3.zero, Vector3.zero, gravity) });
}
protected virtual void OnQuadraticValueChanged(double oldValue, double newValue)
{
if (QuadraticValue > 0)
{
QuadraticEquation quadraticEquation = new QuadraticEquation(a, b, c - QuadraticValue);
quadraticEquation.Solve();
double rootRealPart;
double derivate = 2 * a * Value + b;
if (derivate > 0)
{
rootRealPart = quadraticEquation.Root1RealPart;
}
else
{
rootRealPart = quadraticEquation.Root2RealPart;
}
Debug.WriteLine(derivate);
if (Math.Abs(Value - rootRealPart) > 0.5)
{
Value = rootRealPart;
}
}
}
public void QuadraticEquation()
{
var eq = new QuadraticEquation("A".Parse(), "B".Parse(), "C".Parse());
var roots = eq.Solve();
var context = ImmutableContext.Empty
.RegisterValue("A".Parse(), 1)
.RegisterValue("B".Parse(), -2)
.RegisterValue("C".Parse(), -3);
Assert.AreEqual(3, roots.Item1.ToReal(context));
Assert.AreEqual(-1, roots.Item2.ToReal(context));
context = ImmutableContext.Empty
.RegisterValue("A".Parse(), 2)
.RegisterValue("B".Parse(), -4)
.RegisterValue("C".Parse(), -6);
Assert.AreEqual(3, roots.Item1.ToReal(context));
Assert.AreEqual(-1, roots.Item2.ToReal(context));
eq = new QuadraticEquation("X + 1".Parse(), "Y - 2".Parse(), "Z / 2".Parse());
roots = eq.Solve();
context = ImmutableContext.Empty
.RegisterValue("X".Parse(), 0)
.RegisterValue("Y".Parse(), 0)
.RegisterValue("Z".Parse(), -6);
Assert.AreEqual(3, roots.Item1.ToReal(context));
Assert.AreEqual(-1, roots.Item2.ToReal(context));
}
