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Mathematics Geometry Wolfram Language

How to optimize the program for calculating the distance between points and straight lines?

Lee Tao

Posted 10 months ago

How to optimize the calculation from point to line? Clear["Global`*"] line = a x + b y + c == 0 pt = {x0, y0} pol = Apply[Subtract, line] Flatten@CoefficientList[pol, {x, y}] A1 = Coefficient[Apply[Subtract, line], x] B1 = Coefficient[Apply[Subtract, line], y] C1 = Select[Apply[Subtract, line], FreeQ[x \| y]] distance = Abs[A1 pt[[1]] + B1 pt[[2]] + C1]/Sqrt[A1^2 + B1^2]

How to optimize the calculation from point to line?

Clear["Global`*"]

line = a x + b y + c == 0

pt = {x0, y0}

pol = Apply[Subtract, line]

Flatten@CoefficientList[pol, {x, y}]

A1 = Coefficient[Apply[Subtract, line], x]

B1 = Coefficient[Apply[Subtract, line], y]

C1 = Select[Apply[Subtract, line], FreeQ[x | y]]

distance = Abs[A1 pt[[1]] + B1 pt[[2]] + C1]/Sqrt[A1^2 + B1^2]

POSTED BY: Lee Tao

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 10 months ago

Here is a way to shorten it a little: line = a x + b y + c == 0; pt = {x0, y0}; pol = Apply[Subtract, line]; A1 = Coefficient[pol, x] B1 = Coefficient[pol, y] distance = Abs[pol /. Thread[{x, y} -> pt]]/Sqrt[A1^2 + B1^2]