Option Base 1
Option Explicit
'Option Private Module
'====================================================================================================
' NeedX = get x, ref Y
' x = (-B*y-C)/A
' y = (-A*x-C)/B
Function PRDX_Math_CoordByLineABC(coord#, arrLine, Optional NeedX As Boolean) As Double ' return coord Y or X(if NeedX) by LineABC
    If NeedX Then PRDX_Math_CoordByLineABC = (-arrLine(2) * coord - arrLine(3)) / arrLine(1): Exit Function
    PRDX_Math_CoordByLineABC = (-arrLine(1) * coord - arrLine(3)) / arrLine(2)
End Function
'----------------------------------------------------------------------------------------------------
' https://pro-prof.com/forums/topic/canonical_equation_prolog
Function PRDX_Math_LineABCbyCoords(x1#, y1#, x2#, y2#) As Double() ' return arr(3) A, B, C by equation A*x + B*y + C = 0
Dim aRes(3) As Double
    aRes(1) = y1 - y2            ' A
    aRes(2) = x2 - x1            ' B
    aRes(3) = x1 * y2 - x2 * y1  ' C
    PRDX_Math_LineABCbyCoords = aRes
End Function
'====================================================================================================
' Y=a0+a1*X+a2*X^2
Function PRDX_Math_Polynomial_2ndDegree_Canon_GetY(X#, aKoefs()) As Double
    PRDX_Math_Polynomial_2ndDegree_Canon_GetY = aKoefs(1) + aKoefs(2) * X + aKoefs(3) * X ^ 2
End Function
'----------------------------------------------------------------------------------------------------
'https://4analytics.ru/trendi/3-sposoba-rascheta-polinoma-v-excel.html#:~:text=%D0%9F%D0%BE%D0%BB%D0%B8%D0%BD%D0%BE%D0%BC%20%E2%80%94%20%D1%8D%D1%82%D0%BE%20%D1%81%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D0%BD%D0%B0%D1%8F%20%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F%20y,%D1%8D%D0%BA%D1%81%D1%82%D1%80%D0%B5%D0%BC%D1%83%D0%BC%D0%BE%D0%B2%20(%D0%BF%D0%B8%D0%BA%D0%BE%D0%B2)%2C%20%D1%82.
'http://www.accel.ru/abitur/inform/algorithms/begin_numeth-pr2013/index.php?fname=_1_2_simple_itpl_poly.php
Function PRDX_Math_Polynomial_2ndDegree_Canon_GetKoefs(x0#, y0#, x1#, y1#, x2#, y2#) As Variant()
Dim aRes(3)
    aRes(1) = (1 / (x1 * (x2 - x0))) * ((x0 * (y2 * x1 ^ 2 - y1 * x2 ^ 2) / (x2 - x1)) - (x2 * (y1 * x0 ^ 2 - y0 * x1 ^ 2) / (x1 - x0)))    ' a0
    aRes(2) = (-1 / (x2 - x0)) * (((y2 - y1) * (x1 + x0) / (x2 - x1)) - ((y1 - y0) * (x2 + x1) / (x1 - x0)))                                ' a1
    aRes(3) = (1 / (x2 - x0)) * (((y2 - y1) / (x2 - x1)) - ((y1 - y0) / (x1 - x0)))                                                         ' a2
    PRDX_Math_Polynomial_2ndDegree_Canon_GetKoefs = aRes
End Function
'====================================================================================================
Function PRDX_Math_Polynomial_2ndDegree_Lagrange_GetY(X#, x0#, y0#, x1#, y1#, x2#, y2#) As Double
    PRDX_Math_Polynomial_2ndDegree_Lagrange_GetY = y0 * ((X - x1) * (X - x2)) / ((x0 - x1) * (x0 - x2)) + y1 * ((X - x0) * (X - x2)) / ((x1 - x0) * (x1 - x2)) + y2 * ((X - x0) * (X - x1)) / ((x2 - x0) * (x2 - x1))
End Function
'====================================================================================================
Function PRDX_Math_Polynomial_2ndDegree_Newton_GetY(X#, x0#, y0#, x1#, y1#, x2#, y2#) As Double
    PRDX_Math_Polynomial_2ndDegree_Newton_GetY = y0 + ((y1 - y0) / (x1 - x0)) * (X - x0) + (((y2 - y1) / (x2 - x1)) - ((y1 - y0) / (x1 - x0))) * ((X - x0) * (X - x1) / (x2 - x0))
End Function
'====================================================================================================