Axis-aligned box. Rectangular prism with all sides parallel to basic planes X = 0, Y = 0 and Z = 0. This is sometimes called AABB, "axis-aligned bounding box". Many geometric operations are fast and easy on this type.
The actual box dimensions are stored inside the Data field, as two 3D points. First point has always all the smaller coords, second point has all the larger coords. I.e. always
Data[0, 0] <= Data[1, 0] and
Data[0, 1] <= Data[1, 1] and
Data[0, 2] <= Data[1, 2]
The only exception is the special value EmptyBox3D.
Note that the box may still have all sizes equal 0. Consider a 3D model with only a single 3D point — it's not empty, but all the sizes must be 0.
This is an old-style object (withut any virtual methods). This way there's no need for using constructors / destructors to manage this, you can simply declare TBox3D type and copy / pass around this box to other procedures.
Check is box empty. You can think of this function as "compare Box with EmptyBox3D".
But actually it works a little faster, by utilizing the assumption that EmptyBox3D is the only allowed value that breaks Data[0, 0] <= Data[1, 0] rule.
function AverageSize(const AllowZero: boolean; const EmptyBoxSize: Single): Single; overload;
Average size of TBox3D, or EmptyBoxSize if box is empty.
Parameters
AllowZero
Decides what to do when box is not empty but the result would be zero, which means that the box is infinitely thin in all axes. If True, then result is just 0, otherwise it's EmptyBoxSize.
function MaxSize(const AllowZero: boolean; const EmptyBoxSize: Single): Single; overload;
Largest size of TBox3D, or EmptyBoxSize if box is empty.
Parameters
AllowZero
Decides what to do when box is not empty but the result would be zero, which means that the box is infinitely thin in all axes. If True, then result is just 0, otherwise it's EmptyBoxSize.
function Area(const AllowZero: boolean; const EmptyBoxArea: Single): Single;
Area of the six TBox3D sides, EmptyBoxArea if box is empty.
Parameters
AllowZero
Decides what to do when box is not empty but the result would be zero, which means that the box is infinitely thin in all axes. If True, then result is just 0, otherwise it's EmptyBoxSize.
This decreases Data[0, 0], Data[0, 1], Data[0, 2] by AExpand and increases Data[1, 0], Data[1, 1], Data[1, 2] by AExpand. So you get Box with all sizes increased by 2 * AExpand.
Box must not be empty. Note that AExpand may be negative, but then you must be sure that it doesn't make Box empty.
function PointInside(const Point: TVector3Single): boolean; overload;
Check is the point inside the box. Always false if Box is empty (obviously, no point is inside an empty box).
function PointInside(const Point: TVector3Double): boolean; overload;
function PointInside2D(const Point: TVector3Single; const IgnoreIndex: Integer): boolean;
Is the 2D point inside the 2D projection of the box. 2D projection (of point and box) is obtained by rejecting the IgnoreIndex coordinate (must be 0, 1 or 2).
Transform the Box by given matrix. Since this is still an axis-aligned box, rotating etc. of the box usually makes larger box.
Note that this is very optimized for Matrix with no projection (where last row of the last matrix = [0, 0, 0, 1]). It still works for all matrices (eventually fallbacks to simple "transform 8 corners and get box enclosing them" method).
When the Matrix will transform some point to a direction (vector with 4th component equal zero). In this case we just cannot interpret the result as a 3D point, so we also cannot interpret the final result as a box.
function TryRayClosestIntersection( out Intersection: TVector3Single; out IntersectionDistance: Single; const RayOrigin, RayDirection: TVector3Single): boolean; overload;
TryBoxRayClosestIntersection calculates intersection between the ray (returns closest intersection to RayOrigin) and the box.
The box is treated just like a set of 6 rectangles in 3D. This means that the intersection will always be placed on one of the box sides, even if RayOrigin starts inside the box. See TryBoxRayEntrance for the other version.
Returns also IntersectionDistance, which is the distance to the Intersection relative to RayDirection (i.e. Intersection is always = RayOrigin + IntersectionDistance * RayDirection).
function TryRayClosestIntersection( out Intersection: TVector3Single; const RayOrigin, RayDirection: TVector3Single): boolean; overload;
function TryRayClosestIntersection( out IntersectionDistance: Single; const RayOrigin, RayDirection: TVector3Single): boolean; overload;
function TryRayEntrance( out Entrance: TVector3Single; out EntranceDistance: Single; const RayOrigin, RayDirection: TVector3Single): boolean; overload;
Intersection between the ray (returns closest intersection to RayOrigin) and the box, treating the box as a filled volume.
If RayOrigin is inside the box, TryBoxRayEntrance simply returns RayOrigin. If RayOrigin is outside of the box, the answer is the same as with TryBoxRayClosestIntersection.
function TryRayEntrance( out Entrance: TVector3Single; const RayOrigin, RayDirection: TVector3Single): boolean; overload;
function SegmentCollision( const Segment1, Segment2: TVector3Single): boolean;
Collision between axis-aligned box (TBox3D) and 3D plane. Returns detailed result as TPlaneCollision.
function PlaneCollisionInside(const Plane: TVector4Single): boolean;
Check is axis-aligned box (TBox3D) fully inside/outside the plane.
Inside/outside are defined as for TPlaneCollision: Outside is where plane direction (normal) points. Inside is where the inverted plane direction (normal) points.
They work exactly like Box3DPlaneCollision, except they returns True when box is inside/outside (when Box3DPlaneCollision returned pcInside/pcOutside), and False otherwise.
For example Box3DPlaneCollisionInside doesn't differentiate between case when box is empty, of partially intersects the plane, and is on the outside. But it works (very slightly) faster.
function PlaneCollisionOutside(const Plane: TVector4Single): boolean;
function IsTriangleCollision( const Triangle: TTriangle3Single): boolean;
procedure BoundingSphere( var SphereCenter: TVector3Single; var SphereRadiusSqr: Single);
Smallest possible sphere completely enclosing given Box. When Box is empty we return SphereRadiusSqr = 0 and undefined SphereCenter.
Radius of the minimal sphere that contains this box. Sphere center is assumed to be in (0, 0, 0). 0 if box is empty.
function Radius2D(const IgnoreIndex: Integer): Single;
Radius of the minimal circle that contains the 2D projection of this box. 2D box projection is obtained by rejecting the IgnoreIndex coordinate (must be 0, 1 or 2). Circle center is assumed to be in (0, 0). 0 if box is empty.
function SphereSimpleCollision( const SphereCenter: TVector3Single; const SphereRadius: Single): boolean;
Check for collision between box and sphere, fast but not entirely correct.
This considers a Box enlarged by SphereRadius in each direction. Then checks whether SphereCenter is inside such enlarged Box. So this check will incorrectly report collision while in fact there's no collision in the case when the sphere center is near the corner of the Box.
So this check is not 100% correct. But often this is good enough — in games, if you know that the SphereRadius is going to be relatively small compared to the Box, this may be perfectly acceptable. And it's fast.
function SphereCollision( const SphereCenter: TVector3Single; const SphereRadius: Single): boolean;
Check for box <-> sphere collision. This is a little slower than SphereSimpleCollision, although still damn fast, and it's a precise check.
Calculate a plane in 3D space with direction = given Direction, moved maximally in Direction and still intersecting the given Box.
For example, if Direction = -Z = (0, 0, -1), then this will return the bottom plane of this box. For Direction = (1, 1, 1), this will return a plane intersecting the Data[1] (maximum) point, with slope = (1, 1, 1). The resulting plane always intersects at least one of the 8 corners of the box.
Calculate a plane in 3D space with direction = given Direction, moved such that it touches the Box but takes minimum volume of this box.
For example, if Direction = +Z = (0, 0, 1), then this will return the bottom plane of this box. For Direction = (1, 1, 1), this will return a plane intersecting the Data[0] (minimum) point, with slope = (1, 1, 1). The resulting plane always intersects at least one of the 8 corners of the box.
procedure PointDistances(const P: TVector3Single; out MinDistance, MaxDistance: Single);
Calculate the distances between a given 3D point and a box. MinDistance is the distance to the closest point of the box, MaxDistance is the distance to the farthest point of the box.
Note that always MinDistance <= MaxDistance. Note that both distances are always >= 0.
When the point is inside the box, it works correct too: minimum distance is zero in this case.
TODO: calculation of MinDistance is not perfect now. We assume that the closest/farthest point of the box is one of the 8 box corners. Which may not be true in case of the closest point, because it may lie in the middle of some box face (imagine a sphere with increasing radius reaching from a point to a box). So our minimum may be a *little* too large.
procedure DirectionDistances( const Point, Dir: TVector3Single; out MinDistance, MaxDistance: Single);
Calculate the distances along a direction to a box. The idea is that you have a 3D plane orthogonal to direction Dir and passing through Point. You can move this plane, but you have to keep it's direction constant. MinDistance is the minimal distance along the Dir that you can move this plane, such that it touches the box. MaxDistance is the maximum such distance.
Note that always MinDistance <= MaxDistance. Note that one distance (MinDistance) or both distances may be negative.
As a practical example: imagine a DirectionalLight (light rays are parallel) that has a location. Now MinDistance and MaxDistance give ranges of depth where the Box is, as seen from the light source.