Class Plane3

Coefficient of x in ax + by + cz + d = 0.

Coefficient of y in ax + by + cz + d = 0.

Coefficient of z in ax + by + cz + d = 0.

d such that n·p + d = 0 for any point p on the plane.

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

The normal vector (a, b, c). Setting it replaces the vector.

A point of the plane. Setting it accepts a point or a vector.

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

Angle between this plane and another plane, line, or vector.

• Plane3 → dihedral angle (angle between normals).
• Line3 / Vector → angle between the line/vector and the plane (complement of the angle with the normal).

Angle between this plane and another plane, line, or vector.

• Plane3 → dihedral angle (angle between normals).
• Line3 / Vector → angle between the line/vector and the plane (complement of the angle with the normal).

Angle between this plane and another plane, line, or vector.

• Plane3 → dihedral angle (angle between normals).
• Line3 / Vector → angle between the line/vector and the plane (complement of the angle with the normal).

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.

Euclidean distance from a point to this plane, as an exact Root.

Intersection of this plane with a line.

• hasIntersection: line meets the plane at exactly one point.
• isOnPlane: line lies entirely on the plane (direction ⊥ normal AND base point satisfies the equation).
• isParallel: direction ⊥ normal but base point is NOT on the plane.

Intersection of this plane with another plane.

• hasIntersection: planes meet in a unique line.
• isEqual: planes are the same (infinitely many common points).
• isParallel: planes are parallel but distinct.

True when both planes are the same plane, whatever their normal vector and reference point.

True when the plane is parallel to another plane (the normals are parallel) or to a line (the direction is perpendicular to the normal). A plane is parallel to itself.

True when the plane is parallel to another plane (the normals are parallel) or to a line (the direction is perpendicular to the normal). A plane is parallel to itself.

True when the plane is perpendicular to another plane (the normals are perpendicular) or to a line (the direction is parallel to the normal).

True when the plane is perpendicular to another plane (the normals are perpendicular) or to a line (the direction is parallel to the normal).

True when the point satisfies the equation of the plane.

Routes a Plane3Config to the appropriate static factory method.

Orthogonal projection of pt onto this plane.

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

Reduces a, b, c (and implicitly d) by their GCD.

Builds a plane from four cartesian coefficients [a, b, c, d] where the equation is ax + by + cz + d = 0.

Builds a plane from a cartesian equation (string or Equation).

The plane through a point, spanned by two direction vectors (the normal is their cross product).

The plane through a point with a normal vector.

The plane through three points.

The plane of a cartesian equation written in a string, such as "x+2y+3z-6=0".