public BladeDecomposition AnalyzeBlade(Operand operand, Context context)
{
BladeDecomposition decomposition;
decomposition.weight = null;
decomposition.center = null;
decomposition.radius = null;
decomposition.normal = null;
decomposition.analysisList = new List <string>();
using (var pushPopper = new ContextPushPopper(context))
{
int grade = operand.Grade;
if (grade < 0)
{
decomposition.analysisList.Add("Could not identify grade of given element.");
}
else
{
OuterProduct blade = null;
try
{
blade = FactorBlade.Factor(operand, context);
}
catch (MathException)
{
}
if (blade == null)
{
decomposition.analysisList.Add("The given element was not a blade.");
}
else
{
context.operandStorage.SetStorage("__blade__", operand);
Evaluate("del(@weight, @center, @radius, @normal)", context);
switch (grade)
{
case 0:
{
if (operand.IsAdditiveIdentity)
{
decomposition.analysisList.Add("The blade is all of space.");
}
else
{
decomposition.analysisList.Add("The blade is the empty set.");
}
break;
}
case 1:
{
decomposition.weight = Evaluate("@weight = mag(ni . @__blade__)", context).output;
if (decomposition.weight.IsAdditiveIdentity)
{
decomposition.analysisList.Add("The blade is a plane.");
decomposition.weight = Evaluate("@weight = mag(no . ni ^ @__blade__)", context).output;
Evaluate("@__blade__ = @__blade__ / @weight", context);
decomposition.normal = Evaluate("@normal = -no . ni ^ @__blade__", context).output;
decomposition.center = Evaluate("@center = (-no . @__blade__) * @normal", context).output;
}
else
{
Evaluate("@__blade__ = @__blade__ / @weight", context);
decomposition.center = Evaluate("@center = ni^no . ni^no ^ @__blade__", context).output;
Operand squareRadius = Evaluate("@__square_radius__ = @__blade__ . @__blade__", context).output;
if (squareRadius.IsAdditiveIdentity)
{
decomposition.analysisList.Add("The blade is a point.");
}
else if (!(squareRadius is NumericScalar numericScalar))
{
decomposition.analysisList.Add("The blade is a sphere.");
decomposition.radius = Evaluate("@radius = sqrt(@__square_radius__)", context).output;
}
public VersorDecomposition AnalyzeVersor(Operand operand, Context context)
{
VersorDecomposition decomposition;
decomposition.analysisList = new List <string>();
using (var pushPopper = new ContextPushPopper(context))
{
int grade = operand.Grade;
if (grade == 0)
{
if (operand.IsAdditiveIdentity)
{
decomposition.analysisList.Add("Zero is not a versor because it is not invertible.");
}
else
{
decomposition.analysisList.Add("Non-zero scalars act as the identity transformation.");
}
}
else
{
GeometricProduct versor = null;
try
{
versor = FactorVersor.Factor(operand, context);
}
catch (MathException)
{
}
if (versor == null)
{
decomposition.analysisList.Add("The given element was not a versor.");
}
else
{
// The reflections and rotations of conformal space give us the conformal transformations in the embedded 3D euclidean sub-space.
int i = versor.operandList.Count - 1;
while (i >= 0)
{
if (i - 1 >= 0 && AnalyzeRotation(versor.operandList[i - 1], versor.operandList[i], ref decomposition, context))
{
i -= 2;
}
else if (AnalyzeReflection(versor.operandList[i], ref decomposition, context))
{
i--;
}
else
{
decomposition.analysisList.Add("Failed to recognize transformation performed by vector.");
i--;
}
}
}
}
}
return(decomposition);
}