Vegard: shortest distance from point to line

2020-01-28T10:00:33Z

shortest distance from point to line

← Older revision		Revision as of 10:00, 28 January 2020
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	To obtain a line equation of the form <math>Ax + By + C = 0</math> from two points <math>a</math> and <math>b</math>, set:		To obtain a line equation of the form <math>Ax + By + C = 0</math> from two points <math>a</math> and <math>b</math>, set:

	<math>		:<math>
	\begin{align}		\begin{align}
	A &= a_y - b_y \\		A &= a_y - b_y \\
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	Source: https://bobobobo.wordpress.com/2008/01/07/solving-linear-equations-ax-by-c-0/		Source: https://bobobobo.wordpress.com/2008/01/07/solving-linear-equations-ax-by-c-0/

	=== ~~Distance~~ from point to line ~~segment~~ ===		=== Shortest distance from point to line ===

			Given a line <math>Ax + By + C = 0</math> and a point <math>p</math>, the shortest distance from the point to the line is given by:

			:<math>
			\frac{\left \| A \cdot p_x + B \cdot p_y + C \right \|}{\sqrt{A^2 + B^2}}
			</math>

			Source: https://www.toppr.com/guides/maths/straight-lines/distance-of-point-from-a-line/

			=== Shortest distance from point to line segment ===

	<source lang="C++">		<source lang="C++">

Vegard: new page

2020-01-28T09:37:25Z

new page

New page

=== Line equation from two points ===

To obtain a line equation of the form <math>Ax + By + C = 0</math> from two points <math>a</math> and <math>b</math>, set:

<math>
\begin{align}
A &= a_y - b_y \\
B &= b_x - a_x \\
C &= a_x \cdot b_y - b_x \cdot a_y
\end{align}
</math>

Source: https://bobobobo.wordpress.com/2008/01/07/solving-linear-equations-ax-by-c-0/

=== Distance from point to line segment ===

<source lang="C++">
// https://www.iquilezles.org/www/articles/distfunctions2d/distfunctions2d.htm
static float sdLineSegment(glm::vec2 p, glm::vec2 a, glm::vec2 b)
{
auto pa = p - a;
auto ba = b - a;
auto h = glm::clamp(glm::dot(pa, ba) / glm::dot(ba, ba), 0.f, 1.f);
return glm::length(pa - ba * h);
}
</source>

[[Category:Programming]]
[[Category:Geometry]]

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Vegard: shortest distance from point to line

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