Class Line3

Creates an empty line, or a line through two points, or a line through a point with a direction.

Output option for the next tex or display: the symmetric form (x-a)/p = (y-b)/q = (z-c)/r. Chainable.

Output option for the next tex or display: a point and a direction vector (default). Chainable.

Output option for the next tex or display: the parametric system of x, y and z. Chainable.

The direction vector (a copy, see direction). Setting it replaces the direction.

The direction vector, as a copy.

ASCIIMath rendering of the current state (terminal output, not chainable).

The reference point of the line. The getter returns the point itself, not a copy.

The reference point, as a copy.

LaTeX rendering of the current state (terminal output, not chainable).

Full duplicate of this instance, including display state (selected form and options set via as*** / with***). Distinct from copy.

Copy the mathematical state of another instance into this (display state is NOT transferred — the receiver keeps its own formatting). Entry point used when constructing/parsing from a same-type input. Distinct from clone. Classes without a real implementation throw NotImplementedError.

Distance from this line to pt, as an exact Root (simplified radical).

Returns true when this line intersects the closed segment [A, B].

Computes the relationship between this line and line.

• isSame: coincident lines (infinitely many common points).
• isParallel: parallel non-coincident lines.
• hasIntersection + point: lines meet at exactly one point.
• all false: skew lines (non-coplanar, no intersection).

True when both lines are the same line, whatever their reference point and direction vector.

Returns true when the direction vectors are orthogonal (90°), regardless of whether the lines intersect.

True when the directions are parallel and the lines are not the same.

Returns true when the lines are both orthogonal and intersecting (strict perpendicularity).

True when the point is on the line.

Replace the line with the line through two points, or through a point with a direction vector.

Replace the line with the line through two points, or through a point with a direction vector.

Orthogonal projection of pt onto this line.

A random point close to the line but not on it.

A random point of the line: the reference point moved along the direction vector by a non-zero integer between -max and max.

Reflection of pt through this line (proj is the midpoint of [pt, reflect(pt)]).

Give the direction vector the smallest integer coordinates, with a positive first coordinate.

The line through a point with a direction vector.

The line through two points.