Vector Projection

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FUNCTION prj3(Point REF AS Vec3, LinePointA REF AS Vec3, LinePointB REF AS Vec3) // "Projection" Get ClosestPoint on Line from Point.
    DeltaAP_X AS FLOAT : DeltaAP_X = Point.x - LinePointA.x
    DeltaAP_Y AS FLOAT : DeltaAP_Y = Point.y - LinePointA.y
    DeltaAP_Z AS FLOAT : DeltaAP_Z = Point.z - LinePointA.z

    DeltaAB_X AS FLOAT : DeltaAB_X = LinePointB.x - LinePointA.x
    DeltaAB_Y AS FLOAT : DeltaAB_Y = LinePointB.y - LinePointA.y
    DeltaAB_Z AS FLOAT : DeltaAB_Z = LinePointB.z - LinePointA.z

    DotAP_AB AS FLOAT : DotAP_AB = (DeltaAP_X * DeltaAB_X) + (DeltaAP_Y * DeltaAB_Y) + (DeltaAP_Z * DeltaAB_Z)
    DotAB_AB AS FLOAT : DotAB_AB = (DeltaAB_X * DeltaAB_X) + (DeltaAB_Y * DeltaAB_Y) + (DeltaAB_Z * DeltaAB_Z) // This is almost Pythagorean.    It's the Squared Length of DeltaAB.

    ProjectedPoint_DistanceFrom_LinePointA_AsMultipleOf_DeltaAB AS FLOAT // lol
    ProjectedPoint_DistanceFrom_LinePointA_AsMultipleOf_DeltaAB = DotAP_AB / DotAB_AB

    Result AS Vec3
    Result.x = LinePointA.x + (DeltaAB_X * ProjectedPoint_DistanceFrom_LinePointA_AsMultipleOf_DeltaAB)
    Result.y = LinePointA.y + (DeltaAB_Y * ProjectedPoint_DistanceFrom_LinePointA_AsMultipleOf_DeltaAB)
    Result.z = LinePointA.z + (DeltaAB_Z * ProjectedPoint_DistanceFrom_LinePointA_AsMultipleOf_DeltaAB)
ENDFUNCTION Result


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FUNCTION prj3n(Point REF AS Vec3, LinePosition REF AS Vec3, LineNormal REF AS Vec3) // "Projection" Get ClosestPointOnLine from Point.
    DeltaAP_X AS FLOAT : DeltaAP_X = Point.x - LinePosition.x
    DeltaAP_Y AS FLOAT : DeltaAP_Y = Point.y - LinePosition.y
    DeltaAP_Z AS FLOAT : DeltaAP_Z = Point.z - LinePosition.z

    DotAP_AB AS FLOAT : DotAP_AB = (DeltaAP_X * LineNormal.x) + (DeltaAP_Y * LineNormal.y) + (DeltaAP_Z * LineNormal.z)

    Result AS Vec3
    Result.x = LinePosition.x + (LineNormal.x * DotAP_AB)
    Result.y = LinePosition.y + (LineNormal.y * DotAP_AB)
    Result.z = LinePosition.z + (LineNormal.z * DotAP_AB)
ENDFUNCTION Result