# LPlaned

class LPlaned

Bases: `LVecBase4d`

An abstract mathematical description of a plane. A plane is defined by the equation Ax + By + Cz + D = 0.

Inheritance diagram

LPlaned(void)
LPlaned(LVecBase4d const &copy)
LPlaned(LPoint3d const &a, LPoint3d const &b, LPoint3d const &c)
LPlaned(LVector3d const &normal, LPoint3d const &point)
LPlaned(double a, double b, double c, double d)
LPlaned(LPlaned const&) = default

Creates a default plane. This plane happens to intersect the origin, perpendicular to the Z axis. It’s not clear how useful a default plane is.

Constructs a plane given three counter-clockwise points, as seen from the front of the plane (that is, viewed from the end of the normal vector, looking down).

Constructs a plane given a surface normal vector and a point within the plane.

Constructs a plane given the four terms of the plane equation.

double dist_to_plane(LPoint3d const &point) const

Returns the straight-line shortest distance from the point to the plane. The returned value is positive if the point is in front of the plane (on the side with the normal), or negative in the point is behind the plane (on the opposite side from the normal). It’s zero if the point is exactly in the plane.

void flip(void)

Convenience method that flips the plane in-place. This is done by simply flipping the normal vector.

LVector3d get_normal(void) const

Returns the surface normal of the plane.

LPoint3d get_point(void) const

Returns an arbitrary point in the plane. This can be used along with the normal returned by `get_normal()` to reconstruct the plane.

LMatrix4d get_reflection_mat(void) const

This computes a transform matrix that reflects the universe to the other side of the plane, as in a mirror.

bool intersects_line(LPoint3d &intersection_point, LPoint3d const &p1, LPoint3d const &p2) const
bool intersects_line(double &t, LPoint3d const &from, LVector3d const &delta) const

Returns true if the plane intersects the infinite line passing through points p1 and p2, false if the line is parallel. The points p1 and p2 are used only to define the Euclidean line; they have no other bearing on the intersection test. If true, sets intersection_point to the point of intersection.

This flavor of intersects_line() returns a bit more information about the nature of the intersecting point. The line is defined via the parametric equation from + t * delta for all real values of t.

If there is no intersection with the plane, the function returns false and leaves t undefined. If there is an intersection with the plane, the function returns true and sets t to the parametric value that defines the point of intersection. That is, t == 0.0f implies that the intersection occurred exactly at point from, and t == 1.0f implies at point from + delta, with other values of t accordingly.

bool intersects_parabola(double &t1, double &t2, LParabolad const &parabola) const

Determines whether and where the indicated parabola intersects with the plane.

If there is no intersection with the plane, the function returns false and leaves t1 and t2 undefined. If there is an intersection with the plane, the function returns true and sets t1 and t2 to the parametric value that defines the two points of intersection. If the parabola is exactly tangent to the plane, then t1 == t2.

bool intersects_plane(LPoint3d &from, LVector3d &delta, LPlaned const &other) const

Returns true if the two planes intersect, false if they do not. If they do intersect, then from and delta are filled in with the parametric representation of the line of intersection: that is, from is a point on that line, and delta is a vector showing the direction of the line.

bool normalize(void)

Normalizes the plane in place. Returns true if the plane was normalized, false if the plane had a zero-length normal vector.

LPlaned normalized(void) const

Normalizes the plane and returns the normalized plane as a copy. If the plane’s normal was a zero-length vector, the same plane is returned.

void output(std::ostream &out) const
LPoint3d project(LPoint3d const &point) const

Returns the point within the plane nearest to the indicated point in space.

void write(std::ostream &out, int indent_level = 0) const
void xform(LMatrix4d const &mat)

Transforms the plane by the indicated matrix.