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"Non-Type Based Vector Lib", by world_creator

Basically instead of having to deal with type declarations (ie. the myVector.Vector) you can use handles to banks instead (ie. just myVector). I've written it with some basis on "temporary" vectors which are deleted automatically when used in a non-value-returning vector function. Included are functions to find the pitch and yaw of a vector, two methods of finding the angle between two vectors, and all three projections.

Code

; /////////////////////////////////// VECTORS

; // Create Vector
;    Action: Creates a vector.
;    Return: Vector handle of the new vector.
Function CreateVector(x#=0,y#=0,z#=0)
     Local vectorBank=CreateBank(13)
          PokeFloat vectorBank,0,x#
          PokeFloat vectorBank,4,y#
          PokeFloat vectorBank,8,z#
          PokeByte vectorBank,12,0
     Return vectorBank
End Function

; // Temporary Vector
;    Action: Creates a temporary vector.
;    Return: Vector handle of the new vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TVector(x#=0,y#=0,z#=0)
     Local vectorBank=CreateBank(13)
          PokeFloat vectorBank,0,x#
          PokeFloat vectorBank,4,y#
          PokeFloat vectorBank,8,z#
          PokeByte vectorBank,12,1
     Return vectorBank
End Function

; // Free Vector
;    Action: Deletes a vector.
;    Return: True if successful, False if failed.
Function FreeVector(vectorBank)
     If vectorBank=0
          Return False
          Else
          FreeBank vectorBank
          Return True
     EndIf
End Function

; // Copy Vector
;    Action: Copies the components of Vector 2 onto Vector 1.
;    Return: True if successful, False if failed.
Function CopyVector(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return False
          Else
          PokeFloat vector1Bank,0,PeekFloat#(vector2Bank,0)
          PokeFloat vector1Bank,4,PeekFloat#(vector2Bank,4)
          PokeFloat vector1Bank,8,PeekFloat#(vector2Bank,8)
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return True
     EndIf
End Function

; // Set Vector
;    Action: Set's a vector's components.
;    Return: True if successful, False if failed.
Function SetVector(vectorBank,x#=0,y#=0,z#=0)
     If vectorBank=0
          Return False
          Else
          PokeFloat vectorBank,0,x#
          PokeFloat vectorBank,4,y#
          PokeFloat vectorBank,8,z#
          Return True
     EndIf
End Function

; // Set Vector X
;    Action: Sets the X component of a vector.
;    Return: Nothing.
Function SetVectorX#(vectorBank,tX#)
     PokeFloat vectorBank,0,tX#
End Function

; // Set Vector Y
;    Action: Sets the Y component of a vector.
;    Return: Nothing.
Function SetVectorY#(vectorBank,tY#)
     PokeFloat vectorBank,4,tY#
End Function

; // Set Vector Z
;    Action: Sets the Z component of a vector.
;    Return: Nothing.
Function SetVectorZ#(vectorBank,tZ#)
     PokeFloat vectorBank,8,tZ#
End Function

; // Vector X
;    Action: Returns the X component of a vector.
;    Return: The X component of a vector.
Function VectorX#(vectorBank)
     Return PeekFloat#(vectorBank,0)
End Function

; // Vector Y
;    Action: Returns the Y component of a vector.
;    Return: The Y component of a vector.
Function VectorY#(vectorBank)
     Return PeekFloat#(vectorBank,4)
End Function

; // Vector Z
;    Action: Returns the Z component of a vector.
;    Return: The Z component of a vector.
Function VectorZ#(vectorBank)
     Return PeekFloat#(vectorBank,8)
End Function

; // Vector AX
;    Action: Returns the "pitch" of a vector in Blitz3D space.
;    Return: The "pitch" of a vector in Blitz3D space.
Function VectorAX#(vectorBank)
     Return ATan2(Sqr#(PeekFloat#(vectorBank,0)^2+PeekFloat#(vectorBank,8)^2),PeekFloat#(vectorBank,4))-90
End Function

; // Vector AY
;    Action: Returns the "yaw" of a vector in Blitz3D space.
;    Return: The "yaw" of a vector in Blitz3D space.
Function VectorAY#(vectorBank)
     Return ATan2(-PeekFloat#(vectorBank,0),PeekFloat#(vectorBank,8))
End Function

; // Vector Magnitude
;    Action: Returns the magnitude of a vector.
;    Return: The magnitude of a vector, 0 if failed.
Function VectorMagnitude#(vectorBank)
     If vectorBank=0
          Return 0
          Else
          Return Sqr#(PeekFloat#(vectorBank,0)^2+PeekFloat#(vectorBank,4)^2+PeekFloat#(vectorBank,8)^2)
     EndIf
End Function

; // Add Vectors
;    Action: Vector 1 = Vector 1 + Vector 2
;    Return: True if successful, False if failed.
;    Notes: Directly writes the result onto Vector 1.
Function AddVectors(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return False
          Else
          PokeFloat vector1Bank,0,PeekFloat#(vector1Bank,0)+PeekFloat#(vector2Bank,0)
          PokeFloat vector1Bank,4,PeekFloat#(vector1Bank,4)+PeekFloat#(vector2Bank,4)
          PokeFloat vector1Bank,8,PeekFloat#(vector1Bank,8)+PeekFloat#(vector2Bank,8)
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return True
     EndIf
End Function

; // Subtract Vectors
;    Action: Vector 1 = Vector 1 - Vector 2
;    Return: True if successful, False if failed.
;    Note: Directly writes the result onto Vector 1.
Function SubtractVectors(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return False
          Else
          PokeFloat vector1Bank,0,PeekFloat#(vector1Bank,0)-PeekFloat#(vector2Bank,0)
          PokeFloat vector1Bank,4,PeekFloat#(vector1Bank,4)-PeekFloat#(vector2Bank,4)
          PokeFloat vector1Bank,8,PeekFloat#(vector1Bank,8)-PeekFloat#(vector2Bank,8)
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return True
     EndIf
End Function

; // Temporary Add Vectors
;    Action: Adds Vector 1 and Vector 2 and returns the handle of the new resultant vector.
;    Return: Vector handle of the resultant vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TAddVectors(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tBank=TVector(PeekFloat#(vector1Bank,0)+PeekFloat#(vector2Bank,0),PeekFloat#(vector1Bank,4)+PeekFloat#(vector2Bank,4),PeekFloat#(vector1Bank,8)+PeekFloat#(vector2Bank,8))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Temporary Subtract Vectors
;    Action: Subtracts Vector 2 from Vector 1 and returns the handle of the new resultant vector.
;    Return: Vector handle of the resultant vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TSubtractVectors(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tBank=TVector(PeekFloat#(vector1Bank,0)-PeekFloat#(vector2Bank,0),PeekFloat#(vector1Bank,4)-PeekFloat#(vector2Bank,4),PeekFloat#(vector1Bank,8)-PeekFloat#(vector2Bank,8))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Scale Vector
;    Action: Scales a vector by the second parameter.
;    Return: True if successful, False if failed.
Function ScaleVector(vectorBank,c#)
     If vectorBank=0
          Return False
          Else
          PokeFloat vectorBank,0,PeekFloat#(vectorBank,0)*c#
          PokeFloat vectorBank,4,PeekFloat#(vectorBank,4)*c#
          PokeFloat vectorBank,8,PeekFloat#(vectorBank,8)*c#
          Return True
     EndIf
End Function

; // Unit Vector
;    Action: Scales a vector to a unit vector (vector of length 1).
;    Return: True if successful, False if failed.
Function UnitVector(vectorBank)
     If vectorBank=0
          Return False
          Else
          ScaleVector vectorBank,1.0/VectorMagnitude#(vectorBank)
          Return True
     EndIf
End Function

; // Temporary Scale Vector
;    Action: Scales a vector by the second parameter.
;    Return: Vector handle of resulting scaled vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TScaleVector(vectorBank,c#,freeTemporary=True)
     If vectorBank=0
          Return 0
          Else
          tBank=TVector(PeekFloat#(vectorBank,0)*c#,PeekFloat#(vectorBank,4)*c#,PeekFloat#(vectorBank,8)*c#)
          If PeekByte(vectorBank,12)=1 And freeTemporary=True Then FreeBank vectorBank
          Return tBank
     EndIf
End Function

; // Temporary Unit Vector
;    Action: Scales a vector to a unit vector (vector of length 1).
;    Return: Vector handle of resulting unit vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TUnitVector(vectorBank,freeTemporary=True)
     If vectorBank=0
          Return 0
          Else
          c#=VectorMagnitude#(vectorBank)
          tBank=TVector(PeekFloat#(vectorBank,0)/c#,PeekFloat#(vectorBank,4)/c#,PeekFloat#(vectorBank,8)/c#)
          If PeekByte(vectorBank,12)=1 And freeTemporary=True Then FreeBank vectorBank
          Return tBank
     EndIf
End Function

; // Dot Product Explanation
;    v1 = <x,y,z>
;    v2 = <a,b,c>
;    v1 * v2 = x*a+y*b+z*c
;    v1 * v2 is a scalar, NOT a vector.
;    If v1 * v2 = 0 Then v1 is orthogonal (perpendicular) to v2.
;    If v1 * v2 > 0 Then angle between v1 and v2 is less than 90 degrees.
;    If v1 * v2 < 0 Then angle between v1 and v2 is greater than 90 degrees.

; // Dot Product
;    Action: Returns the dot product of two vectors.
;    Return: The dot product of the two vectors, 0 if failed.
;    Notes: Last parameter is only for internal library usage (projections).
Function DotProduct#(vector1Bank,vector2Bank,freeTemporary=True)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tDot#=PeekFloat#(vector1Bank,0)*PeekFloat#(vector2Bank,0)+PeekFloat#(vector1Bank,4)*PeekFloat#(vector2Bank,4)+PeekFloat#(vector1Bank,8)*PeekFloat#(vector2Bank,8)
          If PeekByte(vector1Bank,12)=1 And freeTemporary=True Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 And freeTemporary=True Then FreeBank vector2Bank
          Return tDot#
     EndIf
End Function

; // Cross Product Explanation
;    v1 = <x,y,z>
;    v2 = <a,b,c>
;    v1 X v2 = <y*c-z*b,z*a-x*c,x*b-y*a>
;    v1 X v2 is a new vector.
;    v1 X v2 is orthogonal (perpendicular) to v1 AND v2.
;    If v1 X v2 = <0,0,0> Then v1 is parallel to v2.

; // Cross Product
;    Action: Crosses Vector 1 to Vector 2 and returns the handle of the new resultant vector.
;    Return: Vector handle of the resultant vector.
Function CrossProduct(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tBank=CreateVector(PeekFloat#(vector1Bank,4)*PeekFloat#(vector2Bank,8)-PeekFloat#(vector1Bank,8)*PeekFloat#(vector2Bank,4),PeekFloat#(vector1Bank,8)*PeekFloat#(vector2Bank,0)-PeekFloat#(vector1Bank,0)*PeekFloat#(vector2Bank,8),PeekFloat#(vector1Bank,0)*PeekFloat#(vector2Bank,4)-PeekFloat#(vector1Bank,4)*PeekFloat#(vector2Bank,0))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Temporary Cross Product
;    Action: Crosses Vector 1 to Vector 2 and returns the handle of the new resultant vector.
;    Return: Vector handle of the resultant vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TCrossProduct(vector1Bank,vector2Bank,freeTemporary=True)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tBank=TVector(PeekFloat#(vector1Bank,4)*PeekFloat#(vector2Bank,8)-PeekFloat#(vector1Bank,8)*PeekFloat#(vector2Bank,4),PeekFloat#(vector1Bank,8)*PeekFloat#(vector2Bank,0)-PeekFloat#(vector1Bank,0)*PeekFloat#(vector2Bank,8),PeekFloat#(vector1Bank,0)*PeekFloat#(vector2Bank,4)-PeekFloat#(vector1Bank,4)*PeekFloat#(vector2Bank,0))
          If PeekByte(vector1Bank,12)=1 And freeTemporary=True Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 And freeTemporary=True Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Dot Angle Between
;    Action: Returns the absolute angle between Vector 1 and Vector 2 [0,180].
;    Return: Absolute angle between Vector 1 and Vector 2.
;    Notes: The angle returned is between 0 and 180 degrees meaning that it gives no indication of direction.
Function DotAngleBetween#(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tAngle#=ACos(DotProduct#(vector1Bank,vector2Bank,False)/(VectorMagnitude#(vector1Bank)*VectorMagnitude#(vector2Bank)))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tAngle#
     EndIf
End Function

; // Cross Angle Between
;    Action: Returns the absolute angle between the lines drawn by Vector 1 and Vector 2 [0,90].
;    Return: Absolute angle between lines drawn by Vector 1 and Vector 2.
;    Notes: The angle returned is between 0 and 90 degrees meaning that it gives no indication of direction.
Function CrossAngleBetween#(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tAngle#=ASin(VectorMagnitude#(TCrossProduct(vector1Bank,vector2Bank,False))/(VectorMagnitude#(vector1Bank)*VectorMagnitude#(vector2Bank)))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tAngle#
     EndIf
End Function

; // Scalar Projection
;    Action: Returns the length of Vector 2 projected onto Vector 1.
;    Return: Length of projection of Vector 2 onto Vector 1.
;    Notes: The return is a scalar, not a vector. Use vector projection for that.
Function ScalarProjection#(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          tScalar#=DotProduct#(vector1Bank,vector2Bank,False)/VectorMagnitude#(vector1Bank)
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tScalar#
     EndIf
End Function

; // Vector Projection
;    Action: Returns the handle for the vector result of Vector 2 projected onto Vector 1.
;    Return: Vector handle of the resultant vector.
;    Notes: The return is a vector in the direction of Vector 1.
Function VectorProjection(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          c#=DotProduct#(vector1Bank,vector2Bank,False)/DotProduct#(vector1Bank,vector1Bank,False)
          tBank=CreateVector(PeekFloat#(vector1Bank,0)*c#,PeekFloat#(vector1Bank,4)*c#,PeekFloat#(vector1Bank,8)*c#)
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Temporary Vector Projection
;    Action: Returns the handle for the vector result of Vector 2 projected onto Vector 1.
;    Return: Vector handle of the resultant vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TVectorProjection(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          c#=DotProduct#(vector1Bank,vector2Bank,False)/DotProduct#(vector1Bank,vector1Bank,False)
          tBank=TVector(PeekFloat#(vector1Bank,0)*c#,PeekFloat#(vector1Bank,4)*c#,PeekFloat#(vector1Bank,8)*c#)
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Orthogonal Projection
;    Action: Returns the handle for the orthogonal vector result of Vector 2 projected onto Vector 1.
;    Return: Vector handle of the resultant orthogonal vector.
;    Notes: The return is a vector orthogonal (perpendicular) to Vector 1.
Function OrthogonalProjection(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          c#=DotProduct#(vector1Bank,vector2Bank,False)/DotProduct#(vector1Bank,vector1Bank,False)
          tBank=CreateVector()
          CopyVector(tBank,TSubtractVectors(vector2Bank,TVector(PeekFloat#(vector1Bank,0)*c#,PeekFloat#(vector1Bank,4)*c#,PeekFloat#(vector1Bank,8)*c#)))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

; // Temporary Orthogonal Projection
;    Action: Returns the handle for the vector result of Vector 2 projected onto Vector 1.
;    Return: Vector handle of the resultant vector.
;    Notes: Deleted automatically when used in a non-data-returning vector function.
Function TOrthogonalProjection(vector1Bank,vector2Bank)
     If vector1Bank=0 Or vector2Bank=0
          Return 0
          Else
          c#=DotProduct#(vector1Bank,vector2Bank,False)/DotProduct#(vector1Bank,vector1Bank,False)
          tBank=TSubtractVectors(vector2Bank,TVector(PeekFloat#(vector1Bank,0)*c#,PeekFloat#(vector1Bank,4)*c#,PeekFloat#(vector1Bank,8)*c#))
          If PeekByte(vector1Bank,12)=1 Then FreeBank vector1Bank
          If PeekByte(vector2Bank,12)=1 Then FreeBank vector2Bank
          Return tBank
     EndIf
End Function

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