Search results
12 maj 2009 · let p = (lambda |> max 0.0 |> min s) * d / s. (a + p - c).Length. The vector d points from a to b along the line segment. The dot product of d/s with c-a gives the parameter of the point of closest approach between the infinite line and the point c.
8 paź 2020 · I need to calculate the shortest distance from anyplace on this line to a point (X', Y') elsewhere on the coordinate plane. If this is represented by X' in D1, and Y' in D2, I'm using the formula: =ABS ( (SLOPE (B1:B10,A1:A10)*D1-D2+INTERCEPT (B1:B10,A1:A10))/SQRT (SLOPE (B1:B10,A1:A10)2 +1)).
10 gru 2013 · 'Distance from the point (X,Y) to a straight line with equation Y=A0+A1*X 'A0 and A1 are readily calculated by a linear regression from a series of mark points of the line. Dim A0 As Double, A1 As Double. A0 = WorksheetFunction.Intercept(Ys, Xs) A1 = WorksheetFunction.Slope(Ys, Xs) Dist2Line = Abs(A1 * X - Y + A0) / Sqr(A1 * A1 + 1) End Function
Shows how to find the perpendicular distance from a point to a line, and a proof of the formula.
To compute the length of a 2D line given the coordinates of two points on the line, you can use the distance formula, adapted for Excel's formula syntax. In the example shown, the formula in G5, copied down, is: = SQRT ((D5 - B5) ^ 2 + (E5 - C5) ^ 2) where the coordinates of the two points are given in columns B through E. Generic formula.
From the figure above let \(d\) be the perpendicular distance from the point \(Q({ x }_{ 0 },{ y }_{ 0 })\) to the line \(ax+by+c=0.\) We also let \(\vec{n}\) be a vector normal to the line that starts from point \(P({ x }_{ 1 },{ y }_{ 1 })\).
To calculate the perpendicular distance, you need to use the formula =ABS((B1-D1)*E1 - (A1-C1)*F1 + A1*D1 - B1*C1) / SQRT((B1-D1)^2 + (A1-C1)^2). This formula involves the cross product of the line vector and the vector from one of the line's points to the given point, as well as the squared length of the line vector.
