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Imports System.Math
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Module Outils_Math
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#Region "calcul matriciel & vectoriel"
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Public Function Addition(ByRef A(,) As Double, ByRef B(,) As Double) As Double(,)
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'additionne deux matrices et le résultat est renvoyé dans la fonction
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' vérification que l'on peut additionner, si toutes les matrices sont de 1 à nb, on devrait pas faire ça car ça bouffe du temps...
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Dim ua1 As Double, ub1 As Double
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Dim ua2 As Double, ub2 As Double
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ua1 = UBound(A, 1)
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ua2 = UBound(A, 2)
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ub1 = UBound(B, 1)
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ub2 = UBound(B, 2)
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If (Not ua1 - ub1 = 0) Or (Not ua2 - ub2 = 0) Then
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MsgBox("deux matrices ne peuvent pas s'additionner")
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Return Nothing
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End If
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Dim matC(ua1, ua2) As Double
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Dim i, j As Integer
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For i = 0 To ub1
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For j = 0 To ub2
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matC(i, j) = A(i, j) + B(i, j)
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Next j
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Next i
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Addition = matC
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End Function
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Public Function addition(ByRef a() As Double, ByRef b() As Double) As Double()
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' addition de vecteurs
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If Not UBound(a) = UBound(b) Then
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MsgBox("Deux vecteurs ne peuvent s'additionner...")
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Return Nothing
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End If
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Dim i As Integer
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Dim c(UBound(a)) As Double
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For i = 0 To UBound(a)
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c(i) = a(i) + b(i)
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Next
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Return c
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End Function
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Public Function multiscal(ByRef A(,) As Double, ByRef c As Double) As Double(,)
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' multiplie la matrice a par le scalaire c
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Dim i As Integer
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Dim j As Integer
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Dim B(UBound(A, 1), UBound(A, 2)) As Double
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For i = 0 To UBound(A, 1)
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For j = 0 To UBound(A, 2)
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B(i, j) = A(i, j) * c
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Next j
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Next i
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multiscal = B
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End Function
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Public Function multiscal(ByRef A() As Double, ByRef c As Double) As Double()
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'multiplie un vecteur par une certaine valeur
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Dim i As Integer
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Dim b(UBound(A)) As Double
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For i = 0 To UBound(A)
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b(i) = A(i) * c
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Next
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multiscal = b
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End Function
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Public Function reduit(ByRef A(,) As Double, Optional ByVal colonne As Integer = -1, Optional ByRef ligne As Integer = -1) As Double(,)
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' fonction qui retire une colonne et /ou une ligne d'une matrice
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Dim temp(UBound(A, 1) - 1, UBound(A, 2) - 1) As Double
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Dim i As Integer, j As Integer, k As Integer, l As Integer
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For l = 0 To UBound(A)
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If Not (l = ligne) Then
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j = 0
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For k = 0 To UBound(A)
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If Not (k = colonne) Then
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temp(i, j) = A(l, k)
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j += 1
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End If
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Next k
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i += 1
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End If
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Next l
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reduit = temp
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End Function
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Public Function reduit(ByRef A() As Double, Optional ByVal colonne As Integer = -1) As Double()
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' fonction qui retire un élément d'un vecteur
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Dim temp(UBound(A)) As Double
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Dim i As Double, l As Double
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While l < UBound(A)
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If Not l = colonne Then
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temp(i) = A(l)
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l = l + 1
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i = i + 1
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Else
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i = i + 1
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End If
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End While
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Return temp
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End Function
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Public Function multiplication(ByVal A(,) As Double, ByVal B(,) As Double) As Double(,)
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' le vecteur C est redimensionné correctement
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' [A]*[B] = [C]
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' si B est un vecteur alors on va à la partie en bas
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Dim i, j, k, n, m As Integer
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Dim c(,) As Double
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m = UBound(B, 2)
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n = UBound(A, 1)
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If UBound(B, 1) <> UBound(A, 2) Then MsgBox(" Incompatibilité de matrices pour la multiplication") : Return Nothing
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ReDim c(n, m)
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For j = 0 To m
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For i = 0 To n
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For k = 0 To UBound(A, 2)
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c(i, j) = c(i, j) + A(i, k) * B(k, j)
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Next k
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Next i
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Next j
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multiplication = c
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End Function
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Public Function multiplication(ByRef A(,) As Double, ByRef b() As Double) As Double()
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' le vecteur C est redimensionné correctement
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' [A]*{B} = {C}
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' B est un vecteur ligne
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Dim i, j, n, m As Integer
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Dim c() As Double
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m = UBound(b)
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n = UBound(A, 1)
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If UBound(A, 2) <> m Then MsgBox("Impossible de multiplier la matrice avec le vecteur, dimensions incompatibles!") : Return Nothing
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' on multiplie une matrice et un vecteur
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ReDim c(m)
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For i = 0 To UBound(b)
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For j = 0 To UBound(b)
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c(i) = c(i) + A(i, j) * b(j)
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Next j
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Next i
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Return c
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End Function
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Public Function multiplication(ByRef a() As Double, ByRef B(,) As Double) As Double()
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' le vecteur C est redimensionné correctement
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' {A}*[B] = {C}
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' A est un vecteur colonne
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Dim i, j, n, m As Integer
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Dim c() As Double
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m = UBound(a)
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n = UBound(B, 2)
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If m <> UBound(B, 1) Then MsgBox("Impossible de multiplier le veteur par la matrice.") : Return Nothing
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ReDim c(m)
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For i = 0 To UBound(B)
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For j = 0 To UBound(B)
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c(i) = c(i) + a(j) * B(j, i)
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Next j
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Next i
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Return c
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End Function
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Public Function soustraction(ByRef A(,) As Double, ByRef B(,) As Double) As Double(,)
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'C = A - B
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Dim C(,) As Double
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Dim m As Integer, n As Integer
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m = UBound(A, 1)
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n = UBound(A, 2)
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If (m <> UBound(B, 1)) Or (n <> UBound(B, 2)) Then MsgBox("Impossible de soustraire les matrices, dimensions non compatibles") : Return Nothing
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ReDim C(m, n)
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Dim i, j As Integer
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For i = 0 To m
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For j = 0 To n
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C(i, j) = A(i, j) - B(i, j)
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Next j
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Next i
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Return C
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End Function
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Public Function transpose(ByRef A(,) As Double) As Double(,)
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Dim c(,) As Double
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Dim i, j As Integer
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ReDim c(UBound(A, 2), UBound(A, 1))
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For i = 0 To UBound(A, 1)
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For j = 1 To UBound(A, 2)
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c(j, i) = A(i, j)
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Next j
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Next i
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Return c
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End Function
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Public Function gauss(ByRef A(,) As Double, ByRef C() As Double) As Double()
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' [A]{X} = {C}
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' les matrices doivent être déjà dimensionnées
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Dim n As Integer
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Dim i, j, k As Integer
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Dim rapport As Double
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n = UBound(A, 1)
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Dim rep() As Double
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ReDim rep(n)
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For i = 0 To n ' de gauche à droite
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pivoter(i, A, C)
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'Call Form1.affiche(mat(), C())
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'MsgBox i
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For j = i + 1 To n ' les lignes
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rapport = A(j, i) / A(i, i)
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For k = 1 To n ' les colonnes
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A(j, k) = A(j, k) - A(i, k) * rapport
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Next k
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C(j) = C(j) - C(i) * rapport
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Next j
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Next i
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Dim stuff As Double
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For i = n To 0 Step -1
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stuff = 0
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For j = i + 1 To n
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stuff = stuff + A(i, j) * rep(j)
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Next j
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rep(i) = (C(i) - stuff) / A(i, i)
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Next i
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C = rep
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gauss = rep
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End Function
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Private Sub pivoter(ByVal i As Integer, ByRef mat(,) As Double, ByRef C() As Double)
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' sub qui pivote la ligne i de la matrice a ( et du vecteur C). Si et seulement si le pivotage est nécessaire.
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Dim n As Integer
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n = UBound(mat, 1)
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Dim a_pivoter As Integer
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Dim z As Integer
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Dim temp As Double
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Dim tempC As Double
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For z = i To n
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temp = mat(i, i)
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If mat(z, i) > Math.Abs(temp) Then ' on a trouvé une ligneà pivoter
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temp = mat(z, i)
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a_pivoter = z
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End If
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Next z
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'MsgBox a_pivoter
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If a_pivoter <> 0 Then ' on pivote
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' on pivote la ligne i et la ligne a_pivoter
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tempC = C(i)
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C(i) = C(a_pivoter)
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C(a_pivoter) = tempC
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For z = 0 To n
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temp = mat(i, z)
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mat(i, z) = mat(a_pivoter, z)
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mat(a_pivoter, z) = temp
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Next z
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End If
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' fin pivot
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End Sub
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Private Function pivoter(ByVal i As Integer, ByRef mat(,) As Double) As Integer
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' sub qui pivote la ligne i de la matrice a ( et du vecteur C). Si et seulement si le pivotage est nécessaire.
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Dim n As Integer
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n = UBound(mat, 1)
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Dim a_pivoter As Integer
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pivoter = 1
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Dim z As Integer
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Dim temp As Double
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For z = i To n
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temp = mat(i, i)
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If mat(z, i) > Math.Abs(temp) Then ' on a trouvé une ligne à pivoter
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temp = mat(z, i)
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a_pivoter = z
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pivoter = -1
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End If
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Next z
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If a_pivoter <> 0 Then ' on pivote
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For z = 0 To n
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temp = mat(i, z)
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mat(i, z) = mat(a_pivoter, z)
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mat(a_pivoter, z) = temp
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Next z
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End If
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' fin pivot
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End Function
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Public Function norme(ByRef u() As Double) As Double
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' calcul la norme (longueur) d'un vecteur à xDimensions
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Dim i As Integer
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Dim temp As Double
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For i = 0 To UBound(u)
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temp = temp + u(i) ^ 2
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Next i
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Return Math.Sqrt(temp)
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End Function
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Public Function Prod_scalaire(ByRef u() As Double, ByRef v() As Double) As Double
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' fait le produit scalaire entre deux vecteurs
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' en notation indicielle: w = uivi
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Dim i As Integer
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For i = 0 To UBound(u)
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Prod_scalaire = Prod_scalaire + u(i) * v(i)
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Next i
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End Function
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Public Function prod_vect3D(ByRef u() As Double, ByRef v() As Double) As Double()
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' fait le produit vectoriel entre les vecteur 3D u et v
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' [ i j k ]
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' | u1 u2 u3 |
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' [ v1 v2 v3 ]
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'
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' w = (u2*v3 - u3*v2) i - (u1*v3 - u3*v1) j + (u1*v2-u2*v1) k
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Dim w(2) As Double
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w(0) = u(2) * v(3) - u(3) * v(2)
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w(1) = -(u(1) * v(3) - u(3) * v(1))
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w(2) = u(1) * v(2) - u(2) * v(1)
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prod_vect3D = w
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End Function
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Public Function unitaire(ByRef u() As Double) As Double()
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' prend le vecteur u et son vecteur unitaire v
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Dim longueur As Double
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Dim i As Integer
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Dim v() As Double
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ReDim v(UBound(u))
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Dim temp As Double
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For i = 0 To UBound(u)
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temp = temp + u(i) ^ 2
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Next i
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longueur = Math.Sqrt(temp)
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For i = 0 To UBound(u)
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v(i) = u(i) / longueur
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Next i
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unitaire = v
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End Function
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Public Function cosdir(ByRef u() As Double, ByRef v() As Double) As Double
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' retourne le cosinus entre deux vecteurs, u et v
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cosdir = Prod_scalaire(u, v) / norme(u) / norme(v)
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End Function
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Public Function projection(ByVal u() As Double, ByVal e() As Double) As Double
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' projette le vecteur u sur e et retourne
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' le résultat est la longueur sur le vecteur e
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projection = norme(u) * cosdir(u, e)
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End Function
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Public Function det(ByRef A(,) As Double) As Double
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' calcule le détrminant de la matrice A
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Dim i As Long
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Dim temp As Double
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' contrôle d'erreur:
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If UBound(A, 1) <> UBound(A, 2) Then
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MsgBox("Impossible de calculer le déterminant, la matrice n'est pas carrée")
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End If
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Dim n As Integer
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Dim j As Integer, k As Integer
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Dim rapport As Double
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n = UBound(A, 1)
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Dim rep() As Double
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ReDim rep(n)
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temp = 1
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For i = 0 To n ' de gauche à droite
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temp *= pivoter(i, A)
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For j = i + 1 To n ' les lignes
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rapport = A(j, i) / A(i, i)
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For k = 1 To n ' les colonnes
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A(j, k) = A(j, k) - A(i, k) * rapport
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Next k
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Next j
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Next i
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' à partir d'ici on a une matrice triangulaire suppérieure. (mais je me casse pas la tête à mettre des 0...)
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For i = 0 To UBound(A)
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temp *= A(i, i)
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Next
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Return temp
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End Function
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Public Function det2(ByRef A(,) As Double) As Double
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' calcul du déterminant à l'aide du cofacteur
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Dim i As Long
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Dim temp As Double
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' contrôle d'erreur:
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| 458 |
If UBound(A, 1) <> UBound(A, 2) Then
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MsgBox("Impossible de calculer le déterminant, la matrice n'est pas carrée")
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End If
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If UBound(A) = 0 Then det2 = A(0, 0) : Exit Function
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Dim B(,) As Double
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ReDim B(UBound(A) - 1, UBound(A) - 1)
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For i = 0 To UBound(A)
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B = (reduit(A, i, 0))
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temp += (-1) ^ i * det2(reduit(A, i, 0)) * A(0, i)
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Next i
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det2 = temp
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End Function
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'Function qui compare 2 vecteurs. retourne 0 si non alignés. 1 si dans le même sens, 2 si de sens opposé.
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Public Function CompareSens(ByRef u() As Double, ByRef v() As Double, Optional ByVal Epsilon As Double = 0.000000001) As Integer
|
| 479 |
If ((u(0) - v(0)) < Epsilon) And ((u(1) - v(1)) < Epsilon) And ((u(2) - v(2)) < Epsilon) Then Return 1
|
| 480 |
If ((u(0) + v(0)) < Epsilon) And ((u(1) + v(1)) < Epsilon) And ((u(2) + v(2)) < Epsilon) Then Return 2
|
| 481 |
Return 0
|
| 482 |
End Function
|
| 483 |
|
| 484 |
#End Region
|
| 485 |
|
| 486 |
#Region "calcul intégral"
|
| 487 |
|
| 488 |
|
| 489 |
Function rectangles(ByRef dx As Double, Optional ByVal a As Double = 0, Optional ByVal b As Double = 1) As Double
|
| 490 |
' function qui calcule l'intégrale de f par la méthode des rectangles
|
| 491 |
Dim ecart As Double
|
| 492 |
Dim i As Integer
|
| 493 |
Dim nb As Long
|
| 494 |
Dim x As Double
|
| 495 |
Dim aire As Double
|
| 496 |
|
| 497 |
ecart = b - a
|
| 498 |
|
| 499 |
nb = CLng(ecart / dx)
|
| 500 |
dx = ecart / nb
|
| 501 |
|
| 502 |
If nb < 100 Then MsgBox("Attention, moins de 100 rectangles seront utilisés pour calculer l'intégrale")
|
| 503 |
|
| 504 |
x = a
|
| 505 |
For i = 1 To nb
|
| 506 |
aire += f(x + dx / 2) * dx
|
| 507 |
x += dx
|
| 508 |
Next
|
| 509 |
|
| 510 |
rectangles = aire
|
| 511 |
|
| 512 |
End Function
|
| 513 |
|
| 514 |
|
| 515 |
Function trapezes(ByRef dx As Double, Optional ByVal a As Double = 0, Optional ByVal b As Double = 1) As Double
|
| 516 |
' function qui calcule l'intégrale de f par la méthode des trapezes
|
| 517 |
Dim ecart As Double
|
| 518 |
Dim i As Integer
|
| 519 |
Dim nb As Long
|
| 520 |
Dim x As Double
|
| 521 |
Dim aire As Double
|
| 522 |
|
| 523 |
ecart = b - a
|
| 524 |
nb = CLng(ecart / dx)
|
| 525 |
dx = ecart / nb
|
| 526 |
|
| 527 |
If nb < 100 Then MsgBox("Attention, moins de 100 trapezes seront utilisés pour calculer l'intégrale")
|
| 528 |
|
| 529 |
x = a
|
| 530 |
For i = 1 To nb
|
| 531 |
aire += (f(x) + f(x + dx)) / 2 * dx
|
| 532 |
x += dx
|
| 533 |
Next
|
| 534 |
|
| 535 |
trapezes = aire
|
| 536 |
End Function
|
| 537 |
|
| 538 |
|
| 539 |
|
| 540 |
Function IntegrationGauss(ByRef n As Integer, Optional ByRef noFunction As Integer = 1) As Double
|
| 541 |
Dim i As Integer
|
| 542 |
Dim temp As Double
|
| 543 |
Dim t() As Double
|
| 544 |
Dim w() As Double
|
| 545 |
ReDim w(0)
|
| 546 |
ReDim t(0)
|
| 547 |
|
| 548 |
Select Case n
|
| 549 |
Case 1 ' un seul point d'intégration
|
| 550 |
ReDim t(0)
|
| 551 |
ReDim w(0)
|
| 552 |
|
| 553 |
t(0) = 0
|
| 554 |
w(0) = 2
|
| 555 |
|
| 556 |
Case 2 ' deux points d'intégration
|
| 557 |
' somme wi f(ri)
|
| 558 |
ReDim t(1)
|
| 559 |
ReDim w(1)
|
| 560 |
|
| 561 |
t(0) = -0.57735027
|
| 562 |
t(1) = 0.57735027
|
| 563 |
|
| 564 |
w(0) = 1
|
| 565 |
w(1) = 1
|
| 566 |
|
| 567 |
Case 3 ' trois points
|
| 568 |
ReDim t(2)
|
| 569 |
ReDim w(2)
|
| 570 |
|
| 571 |
t(0) = -0.77459667
|
| 572 |
t(1) = 0
|
| 573 |
t(2) = 0.77459667
|
| 574 |
|
| 575 |
w(0) = 5 / 9
|
| 576 |
w(1) = 8 / 9
|
| 577 |
w(2) = 5 / 9
|
| 578 |
|
| 579 |
Case 4
|
| 580 |
|
| 581 |
ReDim t(3)
|
| 582 |
ReDim w(3)
|
| 583 |
|
| 584 |
t(0) = -0.86113631
|
| 585 |
t(1) = -0.33998104
|
| 586 |
t(2) = 0.33998104
|
| 587 |
t(3) = 0.86113631
|
| 588 |
|
| 589 |
w(0) = 0.34785485
|
| 590 |
w(1) = 0.65214515
|
| 591 |
w(2) = 0.65214515
|
| 592 |
w(3) = 0.34785485
|
| 593 |
|
| 594 |
|
| 595 |
Case 5
|
| 596 |
ReDim t(4)
|
| 597 |
ReDim w(4)
|
| 598 |
|
| 599 |
t(0) = -0.90617975
|
| 600 |
t(1) = -0.53846931
|
| 601 |
t(2) = 0
|
| 602 |
t(3) = 0.53846931
|
| 603 |
t(4) = 0.90617975
|
| 604 |
|
| 605 |
w(0) = 0.23692689
|
| 606 |
w(1) = 0.47862867
|
| 607 |
w(2) = 0.56888889
|
| 608 |
w(3) = 0.47862867
|
| 609 |
w(4) = 0.23692689
|
| 610 |
|
| 611 |
Case Else
|
| 612 |
MsgBox("Problème dans l'intégration de Gauss, nb de points d'intégration non reconnu!?!")
|
| 613 |
End Select
|
| 614 |
|
| 615 |
|
| 616 |
For i = 0 To n - 1
|
| 617 |
temp = temp + w(i) * Choose(noFunction, f1(t(i)), f2(t(i)), f3(t(i)), f4(t(i)), f5(t(i)))
|
| 618 |
Next
|
| 619 |
|
| 620 |
IntegrationGauss = temp
|
| 621 |
End Function
|
| 622 |
|
| 623 |
|
| 624 |
Function simpson(ByRef dx As Double, Optional ByVal a As Double = 0, Optional ByVal b As Double = 1) As Double
|
| 625 |
|
| 626 |
|
| 627 |
End Function
|
| 628 |
|
| 629 |
#End Region
|
| 630 |
|
| 631 |
|
| 632 |
|
| 633 |
|
| 634 |
Public Function f(ByVal x As Double) As Double
|
| 635 |
f = x ^ 2
|
| 636 |
End Function
|
| 637 |
Public Function f1(ByVal r As Double) As Double
|
| 638 |
f1 = -0.04 * (-3 + r) * r ^ 2
|
| 639 |
End Function
|
| 640 |
Public Function f2(ByVal r As Double) As Double
|
| 641 |
f2 = -0.04 * (-3 + r) * r ^ 2
|
| 642 |
End Function
|
| 643 |
Public Function f3(ByVal r As Double) As Double
|
| 644 |
f3 = -0.04 * (-3 + r) * r ^ 2
|
| 645 |
End Function
|
| 646 |
Public Function f4(ByVal r As Double) As Double
|
| 647 |
f4 = -0.04 * (-3 + r) * r ^ 2
|
| 648 |
End Function
|
| 649 |
Public Function f5(ByVal r As Double) As Double
|
| 650 |
f5 = -0.04 * (-3 + r) * r ^ 2
|
| 651 |
End Function
|
| 652 |
|
| 653 |
|
| 654 |
' Secant
|
| 655 |
Public Function Sec(ByVal X As Double) As Double
|
| 656 |
Sec = 1 / Math.Cos(X)
|
| 657 |
End Function
|
| 658 |
|
| 659 |
' Cosecant
|
| 660 |
Public Function CoSec(ByVal X As Double) As Double
|
| 661 |
CoSec = 1 / Math.Sin(X)
|
| 662 |
End Function
|
| 663 |
|
| 664 |
' Cotangent
|
| 665 |
Public Function CoTan(ByVal X As Double) As Double
|
| 666 |
CoTan = 1 / Math.Tan(X)
|
| 667 |
End Function
|
| 668 |
|
| 669 |
' Inverse Sine
|
| 670 |
Public Function ArcSin(ByVal X As Double) As Double
|
| 671 |
ArcSin = Math.Atan(X / Math.Sqrt(-X * X + 1))
|
| 672 |
End Function
|
| 673 |
|
| 674 |
' Inverse Cosine
|
| 675 |
Public Function ArcCos(ByVal X As Double) As Double
|
| 676 |
ArcCos = Math.Atan(-X / Math.Sqrt(-X * X + 1)) + 2 * Math.Atan(1)
|
| 677 |
End Function
|
| 678 |
|
| 679 |
' Inverse Secant
|
| 680 |
Public Function ArcSec(ByVal X As Double) As Double
|
| 681 |
ArcSec = Math.Atan(X / Math.Sqrt(X * X - 1)) + Math.Sign(X - 1) * (2 * Math.Atan(1))
|
| 682 |
End Function
|
| 683 |
|
| 684 |
' Inverse Cosecant
|
| 685 |
Public Function ArcCoSec(ByVal X As Double) As Double
|
| 686 |
ArcCoSec = Math.Atan(X / Math.Sqrt(X * X - 1)) + (Math.Sign(X) - 1) * (2 * Math.Atan(1))
|
| 687 |
End Function
|
| 688 |
|
| 689 |
' Inverse Cotangent
|
| 690 |
Public Function ArcCoTan(ByVal X As Double) As Double
|
| 691 |
ArcCoTan = Math.Atan(X) + 2 * Math.Atan(1)
|
| 692 |
End Function
|
| 693 |
|
| 694 |
|
| 695 |
' Hyperbolic Secant
|
| 696 |
Public Function HSec(ByVal X As Double) As Double
|
| 697 |
HSec = 2 / (Math.Exp(X) + Math.Exp(-X))
|
| 698 |
End Function
|
| 699 |
|
| 700 |
' Hyperbolic Cosecant
|
| 701 |
Public Function HCoSec(ByVal X As Double) As Double
|
| 702 |
HCoSec = 2 / (Math.Exp(X) - Math.Exp(-X))
|
| 703 |
End Function
|
| 704 |
|
| 705 |
' Hyperbolic Cotangent
|
| 706 |
Public Function HCotan(ByVal X As Double) As Double
|
| 707 |
HCotan = (Math.Exp(X) + Math.Exp(-X)) / (Math.Exp(X) - Math.Exp(-X))
|
| 708 |
End Function
|
| 709 |
|
| 710 |
' Inverse Hyperbolic Sine
|
| 711 |
Public Function HArcSin(ByVal X As Double) As Double
|
| 712 |
HArcSin = Math.Log(X + Math.Sqrt(X * X + 1))
|
| 713 |
End Function
|
| 714 |
|
| 715 |
' Inverse Hyperbolic Cosine
|
| 716 |
Public Function HArcCos(ByVal X As Double) As Double
|
| 717 |
HArcCos = Math.Log(X + Math.Sqrt(X * X - 1))
|
| 718 |
End Function
|
| 719 |
|
| 720 |
' Inverse Hyperbolic Tangent
|
| 721 |
Function HArcTan(ByVal X As Double) As Double
|
| 722 |
HArcTan = Math.Log((1 + X) / (1 - X)) / 2
|
| 723 |
End Function
|
| 724 |
|
| 725 |
' Inverse Hyperbolic Secant
|
| 726 |
Public Function HArcSec(ByVal X As Double) As Double
|
| 727 |
HArcSec = Math.Log((Math.Sqrt(-X * X + 1) + 1) / X)
|
| 728 |
End Function
|
| 729 |
|
| 730 |
' Inverse Hyperbolic Cosecant
|
| 731 |
Public Function HArcCoSec(ByVal X As Double) As Double
|
| 732 |
HArcCoSec = Math.Log((Math.Sign(X) * Math.Sqrt(X * X + 1) + 1) / X)
|
| 733 |
End Function
|
| 734 |
|
| 735 |
' Inverse Hyperbolic Cotangent
|
| 736 |
Public Function HArcCoTan(ByVal X As Double) As Double
|
| 737 |
HArcCoTan = Math.Log((X + 1) / (X - 1)) / 2
|
| 738 |
End Function
|
| 739 |
|
| 740 |
' Logarithm to base N
|
| 741 |
Public Function LogN(ByVal X As Double, ByVal n As Double) As Double
|
| 742 |
LogN = Math.Log(X) / Math.Log(n)
|
| 743 |
End Function
|
| 744 |
|
| 745 |
' function qui effectue la rotation d'un point Pt par la matrice Mat
|
| 746 |
Public Function Rotation2D(ByRef Mat(,) As Double, ByVal Pt() As Double) As Double()
|
| 747 |
Dim temp(1) As Double
|
| 748 |
|
| 749 |
temp(0) = Mat(0, 0) * Pt(0) + Mat(0, 1) * Pt(1)
|
| 750 |
temp(1) = Mat(0, 1) * Pt(0) + Mat(1, 1) * Pt(1)
|
| 751 |
|
| 752 |
Return temp
|
| 753 |
|
| 754 |
End Function
|
| 755 |
|
| 756 |
' function qui effectue la rotation d'un point Pt par le vecteur UNITAIRE u
|
| 757 |
Public Function Rotation2D(ByRef u() As Double, ByVal Pt() As Double) As Double()
|
| 758 |
Dim temp(1) As Double
|
| 759 |
'Dim longueur As Double = Math.Sqrt(u(0) * u(0) + u(1) * u(1))
|
| 760 |
'u(0) /= longueur
|
| 761 |
'u(1) /= longueur
|
| 762 |
|
| 763 |
Dim test(2) As Double
|
| 764 |
test(0) = 1
|
| 765 |
'Debug.Print(Outils_Math.Angle2Vecteurs(test, u))
|
| 766 |
'Debug.Print(Outils_Math.Angle2Vecteurs(test, Pt))
|
| 767 |
|
| 768 |
'temp(0) = u(0) * Pt(0) - u(1) * Pt(1)
|
| 769 |
'temp(1) = u(1) * Pt(0) + u(0) * Pt(1)
|
| 770 |
|
| 771 |
'Debug.Print(Outils_Math.Angle2Vecteurs(test, temp))
|
| 772 |
|
| 773 |
Dim u2(2) As Double
|
| 774 |
u2(0) = u(0)
|
| 775 |
u2(1) = u(1)
|
| 776 |
Dim angleInit As Double = Math.Atan2(u(1), u(0))
|
| 777 |
Dim anglePt As Double = Math.Atan2(Pt(1), Pt(0))
|
| 778 |
Dim longueur As Double = Math.Sqrt(Pt(0) * Pt(0) + Pt(1) * Pt(1))
|
| 779 |
|
| 780 |
Dim anglefinal As Double = anglePt + angleInit
|
| 781 |
temp(0) = Math.Cos(anglefinal) * longueur
|
| 782 |
temp(1) = Math.Sin(anglefinal) * longueur
|
| 783 |
|
| 784 |
Return temp
|
| 785 |
|
| 786 |
End Function
|
| 787 |
|
| 788 |
|
| 789 |
'Private Function Angle2D(ByRef u() As Double) As Double
|
| 790 |
' If Math.Sign(u(0)) = 1 AndAlso Math.Sign(u(1)) = 1 Then
|
| 791 |
' Return (Math.Atan(u(1) / u(0)))
|
| 792 |
' ElseIf Math.Sign(u(0)) = -1 AndAlso Math.Sign(u(1)) = 1 Then ' 2nd quadrant
|
| 793 |
' Return (Math.Atan(u(1) / u(0)))
|
| 794 |
' ElseIf Math.Sign(u(0)) = -1 AndAlso Math.Sign(u(1)) = 1 Then ' 3ieme quadrant
|
| 795 |
' Return (Math.Atan(u(1) / u(0))) + 2 * Math.PI
|
| 796 |
' Else
|
| 797 |
' Return (Math.Atan(u(1) / u(0))) + 2 * Math.PI
|
| 798 |
' math.
|
| 799 |
' End If
|
| 800 |
'End Function
|
| 801 |
|
| 802 |
|
| 803 |
Public Sub Rotation2D(ByRef u() As Double, ByRef Ptx As Double, ByRef Pty As Double)
|
| 804 |
Dim temp(1) As Double
|
| 805 |
Dim longueur As Double = Math.Sqrt(u(0) * u(0) + u(1) * u(1))
|
| 806 |
u(0) /= longueur
|
| 807 |
u(1) /= longueur
|
| 808 |
|
| 809 |
temp(0) = u(0) * Ptx - u(1) * Pty
|
| 810 |
temp(1) = u(1) * Ptx + u(0) * Pty
|
| 811 |
|
| 812 |
Ptx = temp(0)
|
| 813 |
Pty = temp(1)
|
| 814 |
|
| 815 |
End Sub
|
| 816 |
|
| 817 |
|
| 818 |
''' <summary>
|
| 819 |
''' Retourne l'angle entre 2 vecteurs
|
| 820 |
''' </summary>
|
| 821 |
''' <param name="u">Le premier vecteur</param>
|
| 822 |
''' <param name="v">Le second vecteur</param>
|
| 823 |
''' <returns>Un angle en radian</returns>
|
| 824 |
''' <remarks>Retourne Pi si les 2 vecteurs sont d'orientation identique mais de direction opposés</remarks>
|
| 825 |
Public Function Angle2Vecteurs(ByRef u() As Double, ByRef v() As Double) As Double
|
| 826 |
Dim temp As Double
|
| 827 |
temp = Outils_Math.Prod_scalaire(u, v) / norme(u) / norme(v)
|
| 828 |
If Math.Abs(temp - 1) < 0.000000000001 Or Math.Abs(temp + 1) < 0.000000000001 Then
|
| 829 |
Return Pi
|
| 830 |
Else
|
| 831 |
Return Math.Acos(temp)
|
| 832 |
End If
|
| 833 |
End Function
|
| 834 |
|
| 835 |
|
| 836 |
''' <summary>
|
| 837 |
''' Compare 2 vecteur de dimension 3
|
| 838 |
''' </summary>
|
| 839 |
''' <param name="u">Premier Vecteur</param>
|
| 840 |
''' <param name="v">Second vecteur</param>
|
| 841 |
''' <returns>0 si sans rapport, 1 si identiques, 2 si sens inverse, 3 si même sens mais norme différente, 4 si norme et sens différent</returns>
|
| 842 |
''' <remarks>Non optimisé pour les vecteurs unitaires</remarks>
|
| 843 |
Public Function ComparerVecteurs3D(ByRef u() As Double, ByRef v() As Double) As Byte
|
| 844 |
|
| 845 |
If u.GetUpperBound(0) <> 2 AndAlso v.GetUpperBound(0) <> 2 Then Return 0
|
| 846 |
If Math.Abs(u(0) - v(0)) < 0.0005 AndAlso Math.Abs(u(1) - v(1)) < 0.0005 AndAlso Math.Abs(u(1) - v(1)) < 0.0005 Then Return 1
|
| 847 |
If Math.Abs(u(0) + v(0)) < 0.0005 AndAlso Math.Abs(u(1) + v(1)) < 0.0005 AndAlso Math.Abs(u(1) + v(1)) < 0.0005 Then Return 2
|
| 848 |
|
| 849 |
Dim u2() As Double = unitaire(u)
|
| 850 |
Dim v2() As Double = unitaire(v)
|
| 851 |
|
| 852 |
If Math.Abs(u2(0) - v2(0)) < 0.0005 AndAlso Math.Abs(u2(1) - v2(1)) < 0.0005 AndAlso Math.Abs(u2(1) - v2(1)) < 0.0005 Then Return 3
|
| 853 |
If Math.Abs(u2(0) + v2(0)) < 0.0005 AndAlso Math.Abs(u2(1) + v2(1)) < 0.0005 AndAlso Math.Abs(u2(1) + v2(1)) < 0.0005 Then Return 4
|
| 854 |
|
| 855 |
Return 0
|
| 856 |
|
| 857 |
End Function
|
| 858 |
|
| 859 |
''' <summary>
|
| 860 |
''' Fonction qui inverse le sens d'un vecteur
|
| 861 |
''' </summary>
|
| 862 |
''' <param name="u">Le vecteur</param>
|
| 863 |
''' <returns>Un vecteur de direction inverse</returns>
|
| 864 |
''' <remarks></remarks>
|
| 865 |
Public Function InverserVecteur(ByRef u() As Double) As Double()
|
| 866 |
Dim v() As Double
|
| 867 |
ReDim v(u.GetUpperBound(0))
|
| 868 |
|
| 869 |
For i As Integer = 0 To u.GetUpperBound(0)
|
| 870 |
v(i) = -u(i)
|
| 871 |
Next
|
| 872 |
Return v
|
| 873 |
End Function
|
| 874 |
|
| 875 |
|
| 876 |
|
| 877 |
End Module
|
