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Math Help - Straight line in 3D space (equation for ~)

  1. #1
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    Straight line in 3D space (equation for ~)

    I know two points in 3D space:
    {x1, y1, z1} and {x2, y2, z2}

    How do I find the coordinates of a third point at y=y3 on a straight line through those two points?

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  2. #2
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    Quote Originally Posted by Dirlewanger View Post
    I know two points in 3D space:
    {x1, y1, z1} and {x2, y2, z2}

    How do I find the coordinates of a third point at y=y3 on a straight line through those two points?

    The equation of the line is:

    (x,y,z) = (x_1, y_1, z_1)+r \cdot \left((x_2, y_2, z_2) - (x_1, y_1, z_1)\right)

    If you know the value of y_3 then you can determine the value of r by solving the equation:

    y_3 = y_1 + r \cdot (y_2 - y_1)

    Once you know the value of r you can plug it into the equation of the line to calculate the missing coordinates of the point.
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