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JavaScript - calculate distance between two points in 3D space
5 points
In this article, we would like to show you how to calculate the distance between two points in 3D space using a modified Pythagorean equation in JavaScript.
Quick solution:
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// P1 = (x1, y1, z1); P2 = (x2, y2, z2)2
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var a = x2 - x1;4
var b = y2 - y1;5
var c = z2 - z1;6
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var distance = Math.sqrt(a * a + b * b + c * c);
Distance calculation for points requires starting with the transformation of the Pythagorean equation to the point version.
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a^2 + b^2 + c^2 = d^2 => d = sqrt(a^2 + b^2 + c^2)2
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P1 = (x1, y1, z1); P2 = (x2, y2, z2)4
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a = |x2 - x1|6
b = |y2 - y1|7
c = |z2 - z1|8
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d = sqrt(|x2 - x1|^2 + |y2 - y1|^2 + |z2 - z1|^2)what can be transformed to:
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d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)2
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Distance between P1 and P2 is equal to d.Note: absolute values can be avoided because of squares inside Pythagorean equation - squares remove minuses.
Example calculations:
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P1 = (7, 2, 3); P2 = (3, 5, 8)2
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a = |x2 - x1| = |3 - 7| = 44
b = |y2 - y1| = |5 - 2| = 35
c = |z2 - z1| = |8 - 3| = 56
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d = sqrt(4^2 + 3^2 + 5^2) = sqrt(16 + 9 + 25) = sqrt(50)8
d = 7.071067811865475xxxxxxxxxx1
function calculateDistance(p1, p2) {2
var a = p2.x - p1.x;3
var b = p2.y - p1.y;4
var c = p2.z - p1.z;5
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return Math.sqrt(a * a + b * b + c * c);7
}8
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// Example:10
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var p1 = {x: 7, y: 2, z: 3};12
var p2 = {x: 3, y: 5, z: 8};13
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var distance = calculateDistance(p1, p2);15
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console.log(distance);17
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Note:
Math.hypothas been introduced in ECMAScript 2015.
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function calculateDistance(p1, p2) {2
var a = p2.x - p1.x;3
var b = p2.y - p1.y;4
var c = p2.z - p1.z;5
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return Math.hypot(a, b, c);7
}8
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// Example:10
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var p1 = {x: 7, y: 2, z: 3};12
var p2 = {x: 3, y: 5, z: 8};13
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var distance = calculateDistance(p1, p2);15
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console.log(distance);