/// <summary>
/// Multiplies two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the product.</returns>
public static Coordinates3D multiply(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X * vector2.X;
sol.Y = vector1.Y * vector2.Y;
sol.Z = vector1.Z * vector2.Z;
return(sol);
}
/// <summary>
/// Subtracts a scalar to all the coordinates of the source vector.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The scalar to substract.</param>
/// <returns>Returs the difference.</returns>
public static Coordinates3D subtract(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X - value;
sol.Y = vector1.Y - value;
sol.Z = vector1.Z - value;
return(sol);
}
/// <summary>
/// Divides two vectors.
/// </summary>
/// <param name="vector1">The dividend.</param>
/// <param name="vector2">The divisor.</param>
/// <returns>Returns the division.</returns>
public static Coordinates3D divide(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X / vector2.X;
sol.Y = vector1.Y / vector2.Y;
sol.Z = vector1.Z / vector2.Z;
return(sol);
}
/// <summary>
/// Multiplies the source vector by a scalar.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The factor.</param>
/// <returns>Returns the product.</returns>
public static Coordinates3D multiply(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X * value;
sol.Y = vector1.Y * value;
sol.Z = vector1.Z * value;
return(sol);
}
/// <summary>
/// Calculates the cross product of two vectors.
/// </summary>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the cross product of the source vectors.</returns>
public static Coordinates3D cross(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.Y * vector2.Z - vector1.Z * vector2.Y;
sol.Y = vector1.Z * vector2.X - vector1.X * vector2.Z;
sol.Z = vector1.X * vector2.Y - vector1.Y * vector2.X;
return(sol);
}
/// <summary>
/// Divides the source vector by an scalar.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The divisor.</param>
/// <returns>Returns the division.</returns>
public static Coordinates3D divide(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X / value;
sol.Y = vector1.Y / value;
sol.Z = vector1.Z / value;
return(sol);
}
/// <summary>
/// Adds two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the sum.</returns>
public static Coordinates3D add(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X + vector2.X;
sol.Y = vector1.Y + vector2.Y;
sol.Z = vector1.Z + vector2.Z;
return(sol);
}
/// <summary>
/// Adds a scalar to all the coordinates of the source vector.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The scalar to add.</param>
/// <returns>Returs the sum.</returns>
public static Coordinates3D add(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X + value;
sol.Y = vector1.Y + value;
sol.Z = vector1.Z + value;
return(sol);
}
// Normalize in the interval [-1, 1] the given 3D point.
// The Z value is in the inverval [-1, 0], being 0 the closest distance.
private Coordinates3D transformTo3DCoord(PointsFingers p, int width, int height, int distance)
{
Coordinates3D v = new Coordinates3D();
v.X = p.Y / (width * 1.0f) * 2 - 1;
v.Y = (1 - p.X / (height * 1.0f)) * 2 - 1;
v.Z = (distance - 400) / -7600.0f;
return(v);
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="vector1">Minuend vector.</param>
/// <param name="vector2">Subtrahend vector.</param>
/// <returns>Returns the difference .</returns>
public static Coordinates3D subtract(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X - vector2.X;
sol.Y = vector1.Y - vector2.Y;
sol.Z = vector1.Z - vector2.Z;
return(sol);
}
/// <summary>
/// Checks if two vectors are equals.
/// </summary>
/// <param name="obj">The vector to compare with.</param>
/// <returns>Returns true if the vectors are equals, or false otherwise.</returns>
public override bool Equals(object obj)
{
Coordinates3D other = (Coordinates3D)obj;
if (this.X == other.X && this.Y == other.Y && this.Z == other.Z)
{
return(true);
}
else
{
return(false);
}
}
// Obtain the 3D normalized point and add it to the list of fingertips
public void calculate3DPoints(int width, int height, int[] distance)
{
if(palm.X != -1 && palm.Y != -1)
palm3D = transformTo3DCoord(palm, width, height, distance[palm.X * width + palm.Y]); // Calculate 3-D position of palm
fingertips3D.Clear(); // Empty any unwanted data.
for(int i = 0; i < fingertips.Count; ++i)
{
PointsFingers f = fingertips[i]; // Store the value of each element in f use it as parameter in transformTo3DCoord
if (palm.X - fingertips[i].X < 20) //reduces the noise, limits fingertips to 20 pixel distance from center.
{
fingertips3D.Add(transformTo3DCoord(f, width, height, distance[f.X * width + f.Y])); // Append the modified elements. The useful set of points are actually in fingertips3D
}
}
}
// Obtain the 3D normalized point and add it to the list of fingertips
public void calculate3DPoints(int width, int height, int[] distance)
{
if (palm.X != -1 && palm.Y != -1)
{
palm3D = transformTo3DCoord(palm, width, height, distance[palm.X * width + palm.Y]); // Calculate 3-D position of palm
}
fingertips3D.Clear(); // Empty any unwanted data.
for (int i = 0; i < fingertips.Count; ++i)
{
PointsFingers f = fingertips[i]; // Store the value of each element in f use it as parameter in transformTo3DCoord
if (palm.X - fingertips[i].X < 20) //reduces the noise, limits fingertips to 20 pixel distance from center.
{
fingertips3D.Add(transformTo3DCoord(f, width, height, distance[f.X * width + f.Y])); // Append the modified elements. The useful set of points are actually in fingertips3D
}
}
}
/// <summary>
/// Calculates the distance between two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the distance between the vectors.</returns>
public static float distance(Coordinates3D vector1, Coordinates3D vector2)
{
return((float)Math.Sqrt((vector1.X - vector2.X) * (vector1.X - vector2.X) + (vector1.Y - vector2.Y) * (vector1.Y - vector2.Y) +
(vector1.Z - vector2.Z) * (vector1.Z - vector2.Z)));
}
/// <summary>
/// Creates a unit vector from the specified vector. The result is a vector one unit in length pointing in the same direction as the original vector.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <returns>The created unit vector.</returns>
public static Coordinates3D normalize(Coordinates3D vector1)
{
float l = length(vector1);
return(divide(vector1, l));
}
/// <summary>
/// Subtracts a scalar to all the coordinates of the source vector.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The scalar to substract.</param>
/// <returns>Returs the difference.</returns>
public static Coordinates3D subtract(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X - value;
sol.Y = vector1.Y - value;
sol.Z = vector1.Z - value;
return sol;
}
// Normalize in the interval [-1, 1] the given 3D point.
// The Z value is in the inverval [-1, 0], being 0 the closest distance.
private Coordinates3D transformTo3DCoord(PointsFingers p, int width, int height, int distance)
{
Coordinates3D v = new Coordinates3D();
v.X = p.Y / (width * 1.0f) * 2 - 1;
v.Y = (1 - p.X / (height * 1.0f)) * 2 - 1;
v.Z = (distance - 400) / -7600.0f;
return v;
}
/// <summary>
/// Calculates the distance between two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the distance between the vectors.</returns>
public static float distance(Coordinates3D vector1, Coordinates3D vector2)
{
return (float)Math.Sqrt((vector1.X - vector2.X) * (vector1.X - vector2.X) + (vector1.Y - vector2.Y) * (vector1.Y - vector2.Y) +
(vector1.Z - vector2.Z) * (vector1.Z - vector2.Z));
}
/// <summary>
/// Divides two vectors.
/// </summary>
/// <param name="vector1">The dividend.</param>
/// <param name="vector2">The divisor.</param>
/// <returns>Returns the division.</returns>
public static Coordinates3D divide(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X / vector2.X;
sol.Y = vector1.Y / vector2.Y;
sol.Z = vector1.Z / vector2.Z;
return sol;
}
/// <summary>
/// Calculates the smaller angle between two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the angle in radians.</returns>
public static float angle(Coordinates3D vector1, Coordinates3D vector2)
{
return((float)Math.Acos((vector1.X * vector2.X + vector1.Y * vector2.Y + vector1.Z * vector2.Z) / (length(vector1) * length(vector2))));
}
/// <summary>
/// Creates a unit vector from the specified vector. The result is a vector one unit in length pointing in the same direction as the original vector.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <returns>The created unit vector.</returns>
public static Coordinates3D normalize(Coordinates3D vector1)
{
float l = length(vector1);
return divide(vector1, l);
}
/// <summary>
/// Calculates the smaller angle between two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the angle in radians.</returns>
public static float angle(Coordinates3D vector1, Coordinates3D vector2)
{
return (float)Math.Acos((vector1.X * vector2.X + vector1.Y * vector2.Y + vector1.Z * vector2.Z) / (length(vector1) * length(vector2)));
}
/// <summary>
/// Calculates the distance between two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the distance between the vectors squared.</returns>
public static float SqauredDistance(Coordinates3D vector1, Coordinates3D vector2)
{
return (vector1.X - vector2.X) * (vector1.X - vector2.X) + (vector1.Y - vector2.Y) * (vector1.Y - vector2.Y) +
(vector1.Z - vector2.Z) * (vector1.Z - vector2.Z);
}
/// <summary>
/// Adds two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the sum.</returns>
public static Coordinates3D add(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X + vector2.X;
sol.Y = vector1.Y + vector2.Y;
sol.Z = vector1.Z + vector2.Z;
return sol;
}
/// <summary>
/// Copy and create a new instance of Vector3FT.
/// </summary>
/// <param name="other">The Vector3FT to copy.</param>
public Coordinates3D(Coordinates3D other)
{
this.X = other.X;
this.Y = other.Y;
this.Z = other.Z;
}
/// <summary>
/// Calculates the distance between two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the distance between the vectors squared.</returns>
public static float SqauredDistance(Coordinates3D vector1, Coordinates3D vector2)
{
return((vector1.X - vector2.X) * (vector1.X - vector2.X) + (vector1.Y - vector2.Y) * (vector1.Y - vector2.Y) +
(vector1.Z - vector2.Z) * (vector1.Z - vector2.Z));
}
/// <summary>
/// Multiplies the source vector by a scalar.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The factor.</param>
/// <returns>Returns the product.</returns>
public static Coordinates3D multiply(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X * value;
sol.Y = vector1.Y * value;
sol.Z = vector1.Z * value;
return sol;
}
/// <summary>
/// Calculates the dot product of two vectors. Returns a floating point value between -1 and 1.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the dot product of the source vectors.</returns>
public static float dot(Coordinates3D vector1, Coordinates3D vector2)
{
return((vector1.X * vector2.X + vector1.Y * vector2.Y + vector1.Z * vector2.Z) / (length(vector1) * length(vector2)));
}
/// <summary>
/// Multiplies two vectors.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the product.</returns>
public static Coordinates3D multiply(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X * vector2.X;
sol.Y = vector1.Y * vector2.Y;
sol.Z = vector1.Z * vector2.Z;
return sol;
}
/// <summary>
/// Divides the source vector by an scalar.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The divisor.</param>
/// <returns>Returns the division.</returns>
public static Coordinates3D divide(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X / value;
sol.Y = vector1.Y / value;
sol.Z = vector1.Z / value;
return sol;
}
/// <summary>
/// Returns the length of the source vector.
/// </summary>
/// <returns>The length of the vector.</returns>
public static float length(Coordinates3D vector1)
{
return (float)Math.Sqrt(vector1.X * vector1.X + vector1.Y * vector1.Y + vector1.Z * vector1.Z);
}
/// <summary>
/// Copy and create a new instance of Vector3FT.
/// </summary>
/// <param name="other">The Vector3FT to copy.</param>
public Coordinates3D(Coordinates3D other)
{
this.X = other.X;
this.Y = other.Y;
this.Z = other.Z;
}
/// <summary>
/// Calculates the dot product of two vectors. Returns a floating point value between -1 and 1.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the dot product of the source vectors.</returns>
public static float dot(Coordinates3D vector1, Coordinates3D vector2)
{
return (vector1.X * vector2.X + vector1.Y * vector2.Y + vector1.Z * vector2.Z) / (length(vector1) * length(vector2));
}
/// <summary>
/// Calculates the cross product of two vectors.
/// </summary>
/// <param name="vector2">Source vector.</param>
/// <returns>Returns the cross product of the source vectors.</returns>
public static Coordinates3D cross(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.Y * vector2.Z - vector1.Z * vector2.Y;
sol.Y = vector1.Z * vector2.X - vector1.X * vector2.Z;
sol.Z = vector1.X * vector2.Y - vector1.Y * vector2.X;
return sol;
}
/// <summary>
/// Returns the length of the source vector.
/// </summary>
/// <returns>The length of the vector.</returns>
public static float length(Coordinates3D vector1)
{
return((float)Math.Sqrt(vector1.X * vector1.X + vector1.Y * vector1.Y + vector1.Z * vector1.Z));
}
/// <summary>
/// Adds a scalar to all the coordinates of the source vector.
/// </summary>
/// <param name="vector1">Source vector.</param>
/// <param name="value">The scalar to add.</param>
/// <returns>Returs the sum.</returns>
public static Coordinates3D add(Coordinates3D vector1, float value)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X + value;
sol.Y = vector1.Y + value;
sol.Z = vector1.Z + value;
return sol;
}
/// <summary>
/// Subtracts two vectors.
/// </summary>
/// <param name="vector1">Minuend vector.</param>
/// <param name="vector2">Subtrahend vector.</param>
/// <returns>Returns the difference .</returns>
public static Coordinates3D subtract(Coordinates3D vector1, Coordinates3D vector2)
{
Coordinates3D sol = new Coordinates3D();
sol.X = vector1.X - vector2.X;
sol.Y = vector1.Y - vector2.Y;
sol.Z = vector1.Z - vector2.Z;
return sol;
}
