Imports System
Namespace GeomLib
' the 3d matrix class
Public Class Matrix3D
' storing the members of the matrix as array
Public matrix As Array
' constructor - create instance of the array variable and
' and fill with values of a idendity matrix
Public Sub New()
matrix = Array.CreateInstance(GetType(Double), 4, 4)
Dim i As Integer
For i = matrix.GetLowerBound(0) To matrix.GetUpperBound(0)
Dim j As Integer
For j = matrix.GetLowerBound(1) To matrix.GetUpperBound(1)
matrix.SetValue(0, i, j)
Next j
Next i
matrix.SetValue(1, 0, 0)
matrix.SetValue(1, 1, 1)
matrix.SetValue(1, 2, 2)
matrix.SetValue(1, 3, 3)
End Sub
' copy constructor
Public Sub New(ByVal Mat As Matrix3D)
matrix.CreateInstance(GetType(Double), 4, 4)
Dim i As Integer
For i = matrix.GetLowerBound(0) To matrix.GetUpperBound(0)
Dim j As Integer
For j = matrix.GetLowerBound(1) To matrix.GetUpperBound(1)
matrix.SetValue(Mat.matrix.GetValue(i, j), i, j)
Next j
Next i
End Sub
' set the current matrix to identity matrix
Public Sub SetToIdentity()
Dim i As Integer
For i = matrix.GetLowerBound(0) To matrix.GetUpperBound(0)
Dim j As Integer
For j = matrix.GetLowerBound(1) To matrix.GetUpperBound(1)
matrix.SetValue(0, i, j)
Next j
Next i
matrix.SetValue(1, 0, 0)
matrix.SetValue(1, 1, 1)
matrix.SetValue(1, 2, 2)
matrix.SetValue(1, 3, 3)
End Sub
' rotate the current matrix along the axis specified
Public Sub SetToRotation(ByVal Angle As Double, ByVal Axis As Vector3D)
Dim SinAng As Double = Math.Sin(Angle)
Dim CosAng As Double = Math.Cos(Angle)
If Axis.IsZAxis() Then
matrix.SetValue(CosAng, 0, 0)
matrix.SetValue(-SinAng, 0, 1)
matrix.SetValue(SinAng, 1, 0)
matrix.SetValue(CosAng, 1, 1)
End If
If Axis.IsXAxis() Then
matrix.SetValue(CosAng, 1, 1)
matrix.SetValue(-SinAng, 1, 2)
matrix.SetValue(SinAng, 2, 1)
matrix.SetValue(CosAng, 2, 2)
End If
If Axis.IsYAxis() Then
matrix.SetValue(CosAng, 0, 0)
matrix.SetValue(SinAng, 0, 2)
matrix.SetValue(-SinAng, 2, 0)
matrix.SetValue(CosAng, 2, 2)
End If
End Sub
' scale the current matrix
Public Sub SetToScaling(ByVal ScaleFac As Double)
matrix.SetValue(ScaleFac, 0, 0)
matrix.SetValue(ScaleFac, 1, 1)
matrix.SetValue(ScaleFac, 2, 2)
End Sub
' translate the current matrix
Public Sub SetToTranslation(ByVal TransVec As Vector3D)
matrix.SetValue(TransVec.X, 0, 3)
matrix.SetValue(TransVec.Y, 1, 3)
matrix.SetValue(TransVec.Z, 2, 3)
End Sub
' multiply matrix 1 and 2 and return the resultant matrix
Private Function Multiply(ByVal Mat1 As Matrix3D, ByVal Mat2 As Matrix3D) As Matrix3D
Dim Mat = New Matrix3D
Dim ii As Integer = 0
Dim jj As Integer = 0
Dim kk As Integer = 0
Dim sum As Double = 0
For ii = 0 To 3
For jj = 0 To 3
sum = 0
For kk = 0 To 3
sum = sum + (Mat1.matrix.GetValue(ii, kk) * Mat2.matrix.GetValue(kk, jj))
Next kk
Mat.matrix.SetValue(sum, ii, jj)
Next jj
Next ii
Return Mat
End Function
' find the determinant of the current matrix
Public Function Determinant() As Double
Dim det As Double = 0.0
Dim m = New Matrix2D
For j1 As Integer = 0 To 3
For i As Integer = 1 To 3
Dim j2 As Integer = 0
For j As Integer = 0 To 3
If j <> j1 Then
m.Matrix.SetValue(matrix.GetValue(i, j), i - 1, j2)
j2 = j2 + 1
End If
Next j
Next i
Dim d As Double = System.Math.Pow(-1.0, j1 + 2)
d *= matrix.GetValue(0, j1) * m.Determinant()
det += d
Next j1
m = Nothing
Return det
End Function
' find the transpose
Public Sub Transpose()
Dim i As Integer = 0
Dim j As Integer = 0
Dim tmp As Double = 0.0
For i = 1 To 3
For j = 0 To i
tmp = matrix.GetValue(i, j)
matrix.SetValue(matrix.GetValue(j, i), i, j)
matrix.SetValue(tmp, j, i)
Next j
Next i
End Sub
' find the cofactor matrix and return the same
Public Function CoFactor() As Matrix3D
Dim i, j, ii, jj, i1, j1 As Integer
Dim det As Double
Dim m = New Matrix3D
Dim CMat = New Matrix3D
For j = 0 To 3
For i = 0 To 3
i1 = 0
For ii = 0 To 3
If ii <> i Then
j1 = 0
For jj = 0 To 3
If jj <> j Then
m.matrix.SetValue(matrix.GetValue(ii, jj), i1, j1)
j1 = +j1 + 1
End If
Next jj
i1 = i1 + 1
End If
Next ii
det = m.Determinant()
CMat.Matrix.SetValue(System.Math.Pow(-1.0, i + j + 2.0) * det, i, j)
Next i
Next j
m = Nothing
Return CMat
End Function
' multiply the currnet matrix with the parameter
Public Sub PreMultiplyBy(ByVal Mat As Matrix3D)
Dim ThisMat = New Matrix3D
Dim CMat = New Matrix3D
ThisMat.matrix = matrix
CMat = Multiply(Mat, ThisMat)
matrix = CMat.matrix
ThisMat = Nothing
CMat = Nothing
End Sub
' multiply the currnet matrix with the parameter
Public Sub PostMultiplyBY(ByVal Mat As Matrix3D)
Dim Thismat = New Matrix3D
Dim CMat = New Matrix3D
Thismat.matrix = matrix
CMat = Multiply(Thismat, Mat)
matrix = CMat.matrix
Thismat = Nothing
CMat = Nothing
End Sub
' get the inverse matrix of the current matrix and return it
Public Function GetInverse() As Matrix3D
Dim NewMatrix As Matrix3D
Dim det As Double = Determinant()
det = 1 / det
NewMatrix = CoFactor()
NewMatrix.Transpose()
For i As Integer = 0 To 3
For j As Integer = 0 To 3
NewMatrix.matrix.SetValue(NewMatrix.matrix.GetValue(i, j) * det, i, j)
Next j
Next i
Return NewMatrix
End Function
' find the inverse matrix of the current matrix and set that as current matrix
Public Sub Invert()
Dim NewMatrix As Matrix3D
Dim det As Double = Determinant()
det = 1 / det
NewMatrix = CoFactor()
NewMatrix.Transpose()
For i As Integer = 0 To 3
For j As Integer = 0 To 3
matrix.SetValue(NewMatrix.matrix.GetValue(i, j) * det, i, j)
Next j
Next i
NewMatrix = Nothing
End Sub
End Class
End Namespace
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