distance_point_plane

compas.geometry.distance_point_plane(point, plane)

Compute the distance from a point to a plane defined by origin point and normal.

Parameters:

point[float, float, float] | compas.geometry.Point

Point coordinates.

plane[point, vector] | compas.geometry.Plane

A point and a vector defining a plane.

Returns:

float

Distance between point and plane.

Notes

The distance from a point to a plane can be computed from the coefficients of the equation of the plane and the coordinates of the point [1].

The equation of a plane is

\[Ax + By + Cz + D = 0\]

where

\begin{align} D &= - Ax_0 - Bx_0 - Cz_0 \\ Q &= (x_0, y_0, z_0) \\ N &= (A, B, C) \end{align}

with \(Q\) a point on the plane, and \(N\) the normal vector at that point. The distance of any point \(P\) to a plane is the absolute value of the dot product of the vector from \(Q\) to \(P\) and the normal at \(Q\).

References

[1]

Nykamp, D. Distance from point to plane. Available at: http://mathinsight.org/distance_point_plane.

Examples

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