public static Quaternion rotatePointByAngleAboutAxisVector(Quaternion point, double angle, Quaternion axis)
{
Quaternion result = new Quaternion(0, 0, 0, 0);
// axis (r)
// axis must be a unit vector
axis.setX(axis.getX() / axis.magnitude());
axis.setY(axis.getY() / axis.magnitude());
axis.setZ(axis.getZ() / axis.magnitude());
// angle (a)
// dot product (dp) = cos(a)
double dp = Math.Cos(angle);
if (debugMode)
Console.WriteLine("dot product: " + dp);
// s = sqrt(2*(1+dp))
double s = Math.Sqrt(2 * (1 + dp));
if (debugMode)
Console.WriteLine("s: " + s);
// q
Quaternion q = new Quaternion(0, 0, 0, 0);
q.setW(s/2);
q.setX(axis.getX() / s);
q.setY(axis.getY() / s);
q.setZ(axis.getZ() / s);
if (debugMode)
Console.WriteLine("q: " + q);
// point (p)
// p'= qpq^-1
result = q.multiply(point);
result = result.multiply(q.inverse());
// final round for output (if set)
if (rotationRoundingForOutput)
{
result.setW(Math.Round(result.getW(), 2));
result.setX(Math.Round(result.getX(), 2));
result.setY(Math.Round(result.getY(), 2));
result.setZ(Math.Round(result.getZ(), 2));
}
return result;
}
public Quaternion add(Quaternion other)
{
// (a + e)+i(b + f)+j(c + g)+k(d + h)
Quaternion result = new Quaternion(0, 0, 0, 0);
result.setW(this.getW() + other.getW());
result.setX(this.getX() + other.getX());
result.setY(this.getY() + other.getY());
result.setZ(this.getZ() + other.getZ());
return result;
}
public Quaternion subtract(Quaternion other)
{
// (a - e)+i(b - f)+j(c - g)+k(d - h)
Quaternion result = new Quaternion(0, 0, 0, 0);
result.setW(this.getW() - other.getW());
result.setX(this.getX() - other.getX());
result.setY(this.getY() - other.getY());
result.setZ(this.getZ() - other.getZ());
return result;
}
public Quaternion multiply(Quaternion other)
{
Quaternion result = new Quaternion(0,0,0,0);
// FOIL
Pair myW = new Pair(this.getW(), 0);
Pair myX = new Pair(this.getX(), 1);
Pair myY = new Pair(this.getY(), 2);
Pair myZ = new Pair(this.getZ(), 3);
Pair otherW = new Pair(other.getW(), 0);
Pair otherX = new Pair(other.getX(), 1);
Pair otherY = new Pair(other.getY(), 2);
Pair otherZ = new Pair(other.getZ(), 3);
Dictionary<string, double> expression = new Dictionary<string, double>();
// type, value
expression.Add("w", 0);
expression.Add("i", 0);
expression.Add("j", 0);
expression.Add("k", 0);
expression.Add("ij", 0);
expression.Add("jk", 0);
expression.Add("ki", 0);
expression.Add("ji", 0);
expression.Add("kj", 0);
expression.Add("ik", 0);
expression.Add("i^2", 0);
expression.Add("j^2", 0);
expression.Add("k^2", 0);
// first group
expression["w"] += myW.getX() * otherW.getX();
expression["i"] += myW.getX() * otherX.getX();
expression["j"] += myW.getX() * otherY.getX();
expression["k"] += myW.getX() * otherZ.getX();
// second group
expression["i"] += myX.getX() * otherW.getX();
expression["i^2"] += myX.getX() * otherX.getX();
expression["ij"] += myX.getX() * otherY.getX();
expression["ik"] += myX.getX() * otherZ.getX();
// third group
expression["j"] += myY.getX() * otherW.getX();
expression["ji"] += myY.getX() * otherX.getX();
expression["j^2"] += myY.getX() * otherY.getX();
expression["jk"] += myY.getX() * otherZ.getX();
// fourth group
expression["k"] += myZ.getX() * otherW.getX();
expression["ki"] += myZ.getX() * otherX.getX();
expression["kj"] += myZ.getX() * otherY.getX();
expression["k^2"] += myZ.getX() * otherZ.getX();
// convert ij and ji
expression["k"] += expression["ij"];
expression["k"] += -expression["ji"];
// convert jk and kj
expression["i"] += expression["jk"];
expression["i"] += -expression["kj"];
// convert ki and ik
expression["j"] += expression["ki"];
expression["j"] += -expression["ik"];
// then convert any squared i|j|k to -1 and store result in "w" index
double iSquaredResult = expression["i^2"] * -1;
double jSquaredResult = expression["j^2"] * -1;
double kSquaredResult = expression["k^2"] * -1;
expression["w"] += iSquaredResult;
expression["w"] += jSquaredResult;
expression["w"] += kSquaredResult;
result.setW(expression["w"]);
result.setX(expression["i"]);
result.setY(expression["j"]);
result.setZ(expression["k"]);
if (debugMode)
{
Console.WriteLine("\n\nexpression results:");
foreach (var key in expression.Keys)
{
Console.WriteLine("{0} - {1}", key, expression[key]);
}
}
return result;
}
public Quaternion inverse()
{
double s = this.getW();
Dictionary<string, double> v = new Dictionary<string, double>();
Quaternion result = new Quaternion(0,0,0,0);
v.Add("x", this.getX());
v.Add("y", this.getY());
v.Add("z", this.getZ());
double totalToDivideBy = Math.Pow(s, 2)
+ Math.Pow(v["x"], 2)
+ Math.Pow(v["y"], 2)
+ Math.Pow(v["z"], 2);
result.setW(s / totalToDivideBy);
result.setX(-v["x"] / totalToDivideBy);
result.setY(-v["y"] / totalToDivideBy);
result.setZ(-v["z"] / totalToDivideBy);
return result;
}
public Quaternion inverse()
{
double s = this.getW();
Dictionary<string, double> v = new Dictionary<string, double>();
Quaternion result = new Quaternion(0, 0, 0, 0);
v.Add("x", this.getX());
v.Add("y", this.getY());
v.Add("z", this.getZ());
double totalToDivideBy = Math.Pow(s, 2)
+ Math.Pow(v["x"], 2)
+ Math.Pow(v["y"], 2)
+ Math.Pow(v["z"], 2);
result.setW(s / totalToDivideBy);
result.setX(-v["x"] / totalToDivideBy);
result.setY(-v["y"] / totalToDivideBy);
result.setZ(-v["z"] / totalToDivideBy);
// final round for output (if set)
if (roundingForOutput)
{
result.setW(Math.Round(result.getW(), 4));
result.setX(Math.Round(result.getX(), 4));
result.setY(Math.Round(result.getY(), 4));
result.setZ(Math.Round(result.getZ(), 4));
}
return result;
}
public Quaternion divide(Quaternion other)
{
// multiply q by inverse of other
Quaternion result = new Quaternion(0, 0, 0, 0);
Quaternion inverseOther = other.inverse();
result = this.multiply(inverseOther);
// final round for output (if set)
if (roundingForOutput)
{
result.setW(Math.Round(result.getW(), 4));
result.setX(Math.Round(result.getX(), 4));
result.setY(Math.Round(result.getY(), 4));
result.setZ(Math.Round(result.getZ(), 4));
}
return result;
}