static void Main()
{
vector3d v = new vector3d(1, 0, 42);
WriteLine($"v = {v}");
vector3d u = new vector3d(42, 42, 42);
WriteLine($"u = {u}");
WriteLine($"v + u = {v+u}");
WriteLine($"v - u = {v-u}");
WriteLine($"3*u = {3*u}");
WriteLine($"u*3 = {u*3}");
WriteLine($"u/3 = {u/3}");
WriteLine($"v * u = {v*u}");
// vector3d s = v.crossP(u);
WriteLine($"s = v x u = {v.crossP(u)}");
WriteLine($"v * s = {v.dotP(v.crossP(u))}");
WriteLine("Update values test");
WriteLine($"Old v: {v}");
v.X = 69; v.Y = 420; v.Z = 100100;
WriteLine($"New v: {v}");
WriteLine($"Dotproduct method test: v*u = {v.dotP(u)}");
}
static int Main()
{
WriteLine("Part A:");
WriteLine("Test of vector3d:");
double c = 2;
double x = 1; double y = 1; double z = 2;
vector3d vec = new vector3d(x, y, z);
vector3d vec2 = new vector3d(3, 2, 1);
vector3d vec1 = c * vec;
WriteLine($"v*c={vec1.x},{vec1.y},{vec1.z}");
vector3d vecplu = vec + vec1;
WriteLine($"v+v1={vecplu.x},{vecplu.y},{vecplu.z}");
vector3d vecmin = vec1 - vec;
WriteLine($"v-v1={vecmin.x},{vecmin.y},{vecmin.z}");
WriteLine($"vdot={dot_product(vec,vec2)}");
vector3d vecpru = vector_product(vec, vec2);
WriteLine($"vpro={vecpru.x},{vecpru.y},{vecpru.z}");
WriteLine($"mag={magnitude(vec)}");
WriteLine("Part B:");
WriteLine("Test ofproperties");
WriteLine($"{vec2.x}");
vec2.xcor = 1;
WriteLine($"{vec2.x}");
WriteLine($"{vec2.ycor}");
return(0);
}
static void Main()
{
double c = 4;
vector3d u = new vector3d(1, 2, 3);
vector3d v = new vector3d(2, -7, 6);
u.print("u = ");
v.print("v = ");
double d = ivector3dfunctions.dot(u, u);
WriteLine($"dot(u,u) = {d}");
double e = ivector3dfunctions.dot(u, v);
WriteLine($"dot(u,v) = {e}");
double f = ivector3dfunctions.magnitude(u);
WriteLine($"|u|= {f}");
vector3d k = ivector3dfunctions.cross(u, u);
k.print("cross(u,u) =");
vector3d l = ivector3dfunctions.cross(v, u);
l.print("cross(u,v) =");
WriteLine($"4*v = {c*v}");
WriteLine($"u+v = {u+v}");
WriteLine($"v+u = {v+u}");
WriteLine($"u-v = {u-v}");
}
public static int Main()
{
vector3d v = new vector3d(1, 2, 3);
vector3d u = new vector3d(7, 5, 8);
v.print("v= ");
u.print("u= ");
vector3d w = u + v;
w.print("w= ");
(v * 2).print("2*v= ");
vector3d A = v.vector_product(u);
A.print("v x u = ");
double B = v.dot_product(u);
System.Console.Write("v dot u ={0}\n", B);
double C = v.magnitude();
System.Console.Write("|v| ={0}\n", C);
return(0);
}
// Vector product
public static vector3d vp(vector3d u, vector3d v)
{
vector3d r = new vector3d(u[1] * v[2] - u[2] * v[1],
u[2] * v[0] - u[0] * v[2],
u[0] * v[1] - u[1] * v[0]);
return(r);
}
// Subtraction
public static vector3d operator-(vector3d u, vector3d v)
{
vector3d r = new vector3d(u[0] - v[0],
u[1] - v[1],
u[2] - v[2]);
return(r);
}
public static double magnitude(vector3d v)
{
double xs = Pow(v.x, 2);
double ys = Pow(v.y, 2);
double zs = Pow(v.z, 2);
return(Sqrt(xs + ys + zs));
}
static void Main()
{
vector3d u = new vector3d(1, 2, 3);
double d = ivector3dfunctions.dot(u, u);
WriteLine($"test of dot function calleds using iterface dot(u,u)={d}, with u=(1,2,3)");
}
public vector3d vector_product(vector3d v)
{
double a = y * v.z - z * v.y;
double b = z * v.x - x * v.z;
double c = x * v.y - y * v.x;
return(new vector3d(a, b, c));
}
static void Main()
{
double a = 2;
double b = 3;
double c = 4;
double d = 8;
vector3d u = new vector3d(a, b, c);
vector3d v = new vector3d(2 * a, b, c);
vector3d w = u + v;
vector3d y = u - v;
vector3d x = d * u;
Write("The vector u is: ");
Write(u);
Write("The vector v is: ");
Write(v);
Write("The vector w = u + v is: ");
Write(w);
Write("The vector y = u - v is: ");
Write(y);
Write("The vector x = 8*u is: ");
Write(x);
WriteLine("\nAttempt at dot product:");
double dot = dot_product(u, v);
WriteLine("The dot product of u and v is = {0}", dot);
WriteLine("Correct dot product: 33\n");
vector3d cross = new vector3d(0, 0, 0);
WriteLine("Attempt at cross product:");
cross = cross_product(u, v);
Write("The cross product of u and v is = {0}", cross);
WriteLine("Correct cross product: (0, 8, -6)\n");
WriteLine("Attempt at calculating the magnitude:");
double magni = magnitude(u);
double magniCorrect = 5.385;
WriteLine("The magnitude of u is {0:f3}", magni);
WriteLine("Correct magnitude: {0}\n", magniCorrect);
WriteLine("Let's try to change the x-value of the u vector to 5");
u.xval = 5;
Write("The vector u is: ");
Write(u);
WriteLine("\nLet's try to read the z-value of the u vector");
double zvalue = u.zval;
Write("The z-value of the u-vector is: ");
WriteLine("{0}", zvalue);
}
public static void Main()
{
vector3d v = new vector3d(1, 1, 1);
vector3d u = new vector3d(1, 2, 3);
Write($"{v}*{u} = " + v * u + "\n");
Write($" {v} - {u} = " + (v - u) + "\n");
Write($"|{v}| = " + v.magnitude() + "\n");
}
public static vector3d operator*(double a, vector3d b)
{
vector3d result = new vector3d(0, 0, 0);
result.x = b.x * a;
result.y = b.y * a;
result.z = b.z * a;
return(result);
}
public static vector3d operator-(vector3d a, vector3d b)
{
vector3d result = new vector3d(0, 0, 0);
result.x = a.x - b.x;
result.y = a.y - b.y;
result.z = a.z - b.z;
return(result);
}
// Subtraction
public static vector3d operator-(vector3d u, vector3d v)
{
double i = u.x - v.x;
double j = u.y - v.y;
double k = u.z - v.z;
vector3d w = new vector3d(i, j, k);
return(w);
}
// Cross product
public static vector3d cross_product(vector3d u, vector3d v)
{
double i = u.y * v.z - u.z * v.y;
double j = u.z * v.x - u.x * v.z;
double k = u.x * v.y - u.y * v.x;
vector3d w = new vector3d(i, j, k);
return(w);
}
public static int Main()
{
vector3d v = new vector3d(2, 2, 3);
vector3d u = new vector3d(1, 1, 1);
vector3d w = vector3d.vp(v, u);
w.print();
double a = w.x; double b = w.y; double c = w.z;
Write($"{a},{b},{c}\n");
return(0);
}
public static void Main()
{
vector3d m = new vector3d(4, 5, 3);
WriteLine($"test vector: {m}");
WriteLine($"to String: {m.ToString()}");
vector3d n = m * 2;
WriteLine($"multiplication by 2, {n}");
double a = n.dot_product(m);
WriteLine($"dot_product, {a}");
}
static void Main()
{
vector3d u = new vector3d(9, 9, 9);
vector3d v = new vector3d(1, 2, 3);
u.print("vector3d u =");
v.print("vector3d v =");
double d = ivector3dfunctions.dot(u, u);
vector3d c = ivector3dfunctions.Cross(u, v);
WriteLine($"The dot product of u with u is {d}");
WriteLine($"The cross product og u with v is ({c.x},{c.y},{c.z})");
}
static int Main()
{
vector3d v = new vector3d(1, 1, 2);
vector3d u = new vector3d(0, 1, 0);
Console.WriteLine($"Dot product of v = (1,1,2) and u = (0,1,0)");
Console.WriteLine($"v*u = {vector3d.dotproduct(u,v)}");
Console.WriteLine("Vector product:");
Console.WriteLine($"v x u = {vector3d.vectorproduct(v,u)}");
Console.WriteLine("Magnitude of v:");
Console.WriteLine($"|v| = {v.magnitude()}");
return(0);
}
static int Main()
{
vector3d v = new vector3d(1, 1, 1);
vector3d u = new vector3d(0, 2, 4);
v.print("v=");
u.print("u=");
vector3d w1 = u + v;
w1.print("u+v=");
vector3d w2 = v + u;
w2.print("v+u=");
vector3d w3 = u - v;
w3.print("u-v=");
vector3d w4 = v - u;
w4.print("v-u=");
vector3d w5 = 3 * v;
w5.print("3*v=");
vector3d w6 = u * 3;
w6.print("u*3=");
double w7 = vector3d.dot_product(u, v);
w7.print("u.v=");
vector3d w8 = vector3d.vector_product(u, v);
w8.print("uxv=");
double magv = vector3d.magnitude(v);
magv.print("|v|=");
return(0);
}
public static int Main()
{
var v = new vector3d(1, 2, 3);
var u = new vector3d(3, 4, 5);
WriteLine($"{v} + {u} = {v+u}");
WriteLine($"{v} - {u} = {v-u}");
WriteLine($"{v} * {2} = {v*2}");
WriteLine($"{2} * {v} = {2*v}");
WriteLine($"{v} dot {u} = {v.dot_product(u)}");
WriteLine($"{v} cross {u} = {v.cross_product(u)}");
WriteLine($"The magnitude of the vector {v} is {vector3d.magnitude(v)}");
WriteLine($"{v} / {2} = {v/2}");
v.x = 9;
WriteLine(v);
return(0);
}
static void Main()
{
vector3d v = new vector3d(1, 2, 3);
Write("v = {0}\n", v);
ivector3d iv = new vector3d(4, 5, 6);
Write("iv = {0}\n", iv);
ivector3d iv2 = new vector3d_array(7, 8, 9);
Write("iv2 = {0}\n", iv2);
iv2 = v.cross_product(iv);
Write("iv2 = v x iv = {0}\n", iv2);
}
static int Main()
{
vector3d v = new vector3d(1, 2, 3);
vector3d u = new vector3d(4, 5, 6);
double c = 1.5;
WriteLine($"v = {v}");
WriteLine($"u = {u}");
WriteLine($"c = {c}");
WriteLine($"c*v = {c*v} & v*c = {v*c} ");
WriteLine($"v+u = {v+u}");
WriteLine($"v-u = {v-u}");
WriteLine($"v*u = {v.dot_product(u)}");
WriteLine($"vxu = {v.vector_product(u)}");
WriteLine($"||v|| = {v.magnitude()}");
return(0);
}
static int Main()
{
vector3d v1 = new vector3d(1, 2, 3);
vector3d v2 = new vector3d(2, 2, 1);
Write("v1 = "); v1.ToString();
Write("v2 = "); v2.ToString();
Write("v1.magnitude() = {0}\n", v1.magnitude());
vector3d v3 = v1 * 2;
Write("v1*2 = "); v3.ToString();
Write("2*v1 = "); (2 * v1).ToString();
Write("v1+v2 = "); (v1 + v2).ToString();
Write("v1-v2 = "); (v1 - v2).ToString();
Write("v1.dot_product(v2) = {0}\n", v1.dot_product(v2));
Write("v1.vector_product(v2) = "); v1.vector_product(v2).ToString();
WriteLine($" v1.x={v1.x}, v1.y={v1.y}, v1.z={v1.z}");
return(0);
}
static int Main()
{
vector3d a = new vector3d(1, 1, 0);
vector3d b = new vector3d(0, 0, 1);
string str_a = a.ToString();
string str_b = b.ToString();
string str_b_minus_a = (b - a).ToString();
string str_a_dot_b = (vector3d.dot_product(a, b)).ToString();
string str_a_X_b = (vector3d.vector_product(a, b)).ToString();
string str_mag_a = (vector3d.magnitude(a)).ToString();
Write("a = " + str_a + "\n");
Write("b = " + str_b + "\n");
Write("b-a = " + str_b_minus_a + "\n");
Write("a dot b = " + str_a_dot_b + "\n");
Write("a X b = " + str_a_X_b + "\n");
Write("magnitude(a) = " + str_mag_a + "\n");
return(0);
}
static int Main()
{
vector3d v = new vector3d(1, 2, 3);
vector3d u = new vector3d(5, 4, 3);
v.print("v= ");
u.print("u= ");
(v + u).print("u+v= ");
(v - u).print("u-v= ");
(2 * v).print("2*v= ");
System.Console.Write("v.x = {0}\n", v.x);
v.x = 5.0;
System.Console.Write("v.x = {0}\n", v.x);
System.Console.Write("v@u= {0}\n", v.dot_product(u));
v.vector_product(u).print("v cross u= ");
System.Console.Write("|v|= {0}\n", v.magnitude());
return(0);
}
public static int Main()
{
vector3d v = new vector3d(2, 427, -17);
vector3d u = new vector3d(351, -379, 1);
double c = System.Math.PI;
v.print("v=");
u.print("u=");
(v + u).print("v+u=");
(v - u).print("v-u=");
double vu = v.dot_product(u);
Write($"v.u={vu}\n");
(v.vector_product(u)).print("v x u =");
Write("|v|={0}\n", v.magnitude());
(v * c).print($"v*{c}=");
return(0);
}
public static void Main()
{
vector3d a = new vector3d(1, 2, 3);
vector3d b = new vector3d(4, 5, 6);
WriteLine("The vectors are: " + a.ToString() + " and " + b.ToString());
vector3d c = a + b;
WriteLine("Their sum is: " + c.ToString());
vector3d d = a - b;
WriteLine("Their difference is: " + d.ToString());
double e = dotProduct(a, b);
WriteLine("Their dot is: " + e.ToString());
vector3d f = vectorProduct(a, b);
WriteLine("Their cross is: " + f.ToString());
double g = magnitude(a);
double h = magnitude(b);
WriteLine("Their magnitudes are: " + g.ToString() + " and " + h.ToString());
}
static int Main()
{
System.Console.Write("Example with vector v:\n");
vector3d v = new vector3d(1.2, 1.5, 2.0);
System.Console.Write("v = " + v + "\n");
System.Console.Write("v_x = " + v.x + "\n");
System.Console.Write("Changing v_x to 10 and v_y to 3.\n");
v.x = 10;
v.y = 3;
System.Console.Write("v_x = " + v.x + "\n");
v.print("v=");
System.Console.Write("Defining new vector u:");
vector3d u = new vector3d(2, 5, 7);
double a = 2;
u.print("u=");
System.Console.Write("Calculating 2*u, u+v and cross-product of u and v \n");
vector3d w = u * a;
w.print("2*u = ");
vector3d q = u + v;
q.print("u+v = ");
vector3d t = v.vectorProduct(u);
t.print("u x v = ");
System.Console.Write("Magnitude v = {0:f3}\n", v.magnitude());
return(0);
}
public vector3d vector_product(vector3d other)
{
return(new vector3d(this.y * other.z - this.z * other.y, this.z * other.x - this.x * other.z, this.x * other.y - this.y * other.x));
}
