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RonaldoCMP 2020-09-09 09:57:13 +01:00
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@ -142,24 +142,24 @@ function xy_to_polar(x,y=undef) = let(
// Function: project_plane()
// Usage: With 3 Points
// Usage: With the plane defined by 3 Points
// xyz = project_plane(point, a, b, c);
// Usage: With Pointlist
// Usage: With the plane defined by Pointlist
// xyz = project_plane(point, POINTLIST);
// Usage: With Plane Definition [A,B,C,D] Where Ax+By+Cz=D
// Usage: With the plane defined by Plane Definition [A,B,C,D] Where Ax+By+Cz=D
// xyz = project_plane(point, PLANE);
// Description:
// Converts the given 3D point from global coordinates to the 2D planar coordinates of the closest
// point on the plane. This coordinate system can be useful in taking a set of nearly coplanar
// Converts the given 3D points from global coordinates to the 2D planar coordinates of the closest
// points on the plane. This coordinate system can be useful in taking a set of nearly coplanar
// points, and converting them to a pure XY set of coordinates for manipulation, before converting
// them back to the original 3D plane.
// Can be called one of three ways:
// - Given three points, `a`, `b`, and `c`, the planar coordinate system will have `[0,0]` at point `a`, and the Y+ axis will be towards point `b`.
// - Given a list of points, finds three reasonably spaced non-collinear points in the list and uses them as points `a`, `b`, and `c` as above.
// - Given a plane definition `[A,B,C,D]` where `Ax+By+Cz=D`, the closest point on that plane to the global origin at `[0,0,0]` will be the planar coordinate origin `[0,0]`.
// them back to the original 3D plane. The parameter `point` may be a single point or a list of points
// The plane may be given in one of three ways:
// - by three points, `a`, `b`, and `c`, the planar coordinate system will have `[0,0]` at point `a`, and the Y+ axis will be towards point `b`.
// - by a list of points passed by `a`, finds three reasonably spaced non-collinear points in the list and uses them as points `a`, `b`, and `c` as above.
// - by a plane definition `[A,B,C,D]` passed by `a` where `Ax+By+Cz=D`, the closest point on that plane to the global origin at `[0,0,0]` will be the planar coordinate origin `[0,0]`.
// Arguments:
// point = The 3D point, or list of 3D points to project into the plane's 2D coordinate system.
// a = A 3D point that the plane passes through. Used to define the plane.
// a = A 3D point that the plane passes through or a list of points or a plane definition vector.
// b = A 3D point that the plane passes through. Used to define the plane.
// c = A 3D point that the plane passes through. Used to define the plane.
// Example: