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Bounding boxes trees

Name

Bounding boxes trees -- implementation of axis-aligned bounding-box trees.

Synopsis


#include <gts.h>


#define     GTS_BBOX_CLASS                  (klass)
#define     GTS_BBOX                        (obj)
#define     GTS_IS_BBOX                     (obj)
struct      GtsBBoxClass;
struct      GtsBBox;

GtsBBoxClass* gts_bbox_class                (void);
GtsBBox*    gts_bbox_new                    (GtsBBoxClass *klass,
                                             gpointer bounded,
                                             gdouble x1,
                                             gdouble y1,
                                             gdouble z1,
                                             gdouble x2,
                                             gdouble y2,
                                             gdouble z2);
void        gts_bbox_set                    (GtsBBox *bbox,
                                             gpointer bounded,
                                             gdouble x1,
                                             gdouble y1,
                                             gdouble z1,
                                             gdouble x2,
                                             gdouble y2,
                                             gdouble z2);
GtsBBox*    gts_bbox_segment                (GtsBBoxClass *klass,
                                             GtsSegment *s);
GtsBBox*    gts_bbox_triangle               (GtsBBoxClass *klass,
                                             GtsTriangle *t);
GtsBBox*    gts_bbox_surface                (GtsBBoxClass *klass,
                                             GtsSurface *surface);
GtsBBox*    gts_bbox_points                 (GtsBBoxClass *klass,
                                             GSList *points);
GtsBBox*    gts_bbox_bboxes                 (GtsBBoxClass *klass,
                                             GSList *bboxes);
void        gts_bbox_draw                   (GtsBBox *bb,
                                             FILE *fptr);
#define     gts_bbox_point_is_inside        (bbox, p)
gboolean    gts_bboxes_are_overlapping      (GtsBBox *bb1,
                                             GtsBBox *bb2);
gdouble     gts_bbox_diagonal2              (GtsBBox *bb);
void        gts_bbox_point_distance2        (GtsBBox *bb,
                                             GtsPoint *p,
                                             gdouble *min,
                                             gdouble *max);
gboolean    gts_bbox_is_stabbed             (GtsBBox *bb,
                                             GtsPoint *p);

void        (*GtsBBTreeTraverseFunc)        (GtsBBox *bb1,
                                             GtsBBox *bb2,
                                             gpointer data);
GNode*      gts_bb_tree_new                 (GSList *bboxes);
GNode*      gts_bb_tree_surface             (GtsSurface *s);
GSList*     gts_bb_tree_overlap             (GNode *tree,
                                             GtsBBox *bbox);
gboolean    gts_bb_tree_is_overlapping      (GNode *tree,
                                             GtsBBox *bbox);
void        gts_bb_tree_traverse_overlapping
                                            (GNode *tree1,
                                             GNode *tree2,
                                             GtsBBTreeTraverseFunc func,
                                             gpointer data);
void        gts_bb_tree_draw                (GNode *tree,
                                             guint depth,
                                             FILE *fptr);
void        gts_bb_tree_destroy             (GNode *tree,
                                             gboolean free_leaves);

gdouble     (*GtsBBoxDistFunc)              (GtsPoint *p,
                                             gpointer bounded);
GtsPoint*   (*GtsBBoxClosestFunc)           (GtsPoint *p,
                                             gpointer bounded);
gdouble     gts_bb_tree_point_distance      (GNode *tree,
                                             GtsPoint *p,
                                             GtsBBoxDistFunc distance,
                                             GtsBBox **bbox);
GtsPoint*   gts_bb_tree_point_closest       (GNode *tree,
                                             GtsPoint *p,
                                             GtsBBoxClosestFunc closest,
                                             gdouble *distance);
void        gts_bb_tree_segment_distance    (GNode *tree,
                                             GtsSegment *s,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);
void        gts_bb_tree_triangle_distance   (GNode *tree,
                                             GtsTriangle *t,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);
GSList*     gts_bb_tree_point_closest_bboxes
                                            (GNode *tree,
                                             GtsPoint *p);
void        gts_bb_tree_surface_boundary_distance
                                            (GNode *tree,
                                             GtsSurface *s,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);
void        gts_bb_tree_surface_distance    (GNode *tree,
                                             GtsSurface *s,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);

GSList*     gts_bb_tree_stabbed             (GNode *tree,
                                             GtsPoint *p);

Description

Axis-aligned bounding box trees can be used for intersection/collision detection using gts_bb_tree_traverse_overlapping(), or to compute the minimum distance between an object and a collection of others using gts_bb_tree_point_distance(), gts_bb_tree_segment_distance(), gts_bb_tree_triangle_distance() or gts_bb_tree_surface_distance().

Details

GTS_BBOX_CLASS()

#define     GTS_BBOX_CLASS(klass)

Casts klass to GtsBBoxClass.

klass :a descendant of GtsBBoxClass.


GTS_BBOX()

#define     GTS_BBOX(obj)

Casts obj to GtsBBox.

obj :a descendant of GtsBBox.


GTS_IS_BBOX()

#define     GTS_IS_BBOX(obj)

Evaluates to TRUE if obj is a GtsBBox, FALSE otherwise.

obj :a pointer to test.


struct GtsBBoxClass

struct GtsBBoxClass;

The bounding box class derived from GtsObjectClass.


struct GtsBBox

struct GtsBBox {
  GtsObject object;
  gpointer bounded;
  gdouble x1, y1, z1;
  gdouble x2, y2, z2;
};

The bounding box structure.

GtsObject objectParent object.
gpointer boundedBounded object.
gdouble x1x coordinate of the lower-left front corner.
gdouble y1y coordinate of the lower-left front corner.
gdouble z1z coordinate of the lower-left front corner.
gdouble x2x coordinate of the upper-right back corner.
gdouble y2y coordinate of the upper-right back corner.
gdouble z2z coordinate of the upper-right back corner.


gts_bbox_class ()

GtsBBoxClass* gts_bbox_class                (void);

Returns : the GtsBBoxClass.


gts_bbox_new ()

GtsBBox*    gts_bbox_new                    (GtsBBoxClass *klass,
                                             gpointer bounded,
                                             gdouble x1,
                                             gdouble y1,
                                             gdouble z1,
                                             gdouble x2,
                                             gdouble y2,
                                             gdouble z2);

klass : a GtsBBoxClass.
bounded : the object to be bounded.
x1 : x-coordinate of the lower left corner.
y1 : y-coordinate of the lower left corner.
z1 : z-coordinate of the lower left corner.
x2 : x-coordinate of the upper right corner.
y2 : y-coordinate of the upper right corner.
z2 : z-coordinate of the upper right corner.
Returns : a new GtsBBox.


gts_bbox_set ()

void        gts_bbox_set                    (GtsBBox *bbox,
                                             gpointer bounded,
                                             gdouble x1,
                                             gdouble y1,
                                             gdouble z1,
                                             gdouble x2,
                                             gdouble y2,
                                             gdouble z2);

Sets fields of bbox.

bbox : a GtsBBox.
bounded : the object to be bounded.
x1 : x-coordinate of the lower left corner.
y1 : y-coordinate of the lower left corner.
z1 : z-coordinate of the lower left corner.
x2 : x-coordinate of the upper right corner.
y2 : y-coordinate of the upper right corner.
z2 : z-coordinate of the upper right corner.


gts_bbox_segment ()

GtsBBox*    gts_bbox_segment                (GtsBBoxClass *klass,
                                             GtsSegment *s);

klass : a GtsBBoxClass.
s : a GtsSegment.
Returns : a new GtsBBox bounding box of s.


gts_bbox_triangle ()

GtsBBox*    gts_bbox_triangle               (GtsBBoxClass *klass,
                                             GtsTriangle *t);

klass : a GtsBBoxClass.
t : a GtsTriangle.
Returns : a new GtsBBox bounding box of t.


gts_bbox_surface ()

GtsBBox*    gts_bbox_surface                (GtsBBoxClass *klass,
                                             GtsSurface *surface);

klass : a GtsBBoxClass.
surface : a GtsSurface.
Returns : a new GtsBBox bounding box of surface.


gts_bbox_points ()

GtsBBox*    gts_bbox_points                 (GtsBBoxClass *klass,
                                             GSList *points);

klass : a GtsBBoxClass.
points : a list of GtsPoint.
Returns : a new GtsBBox bounding box of points.


gts_bbox_bboxes ()

GtsBBox*    gts_bbox_bboxes                 (GtsBBoxClass *klass,
                                             GSList *bboxes);

klass : a GtsBBoxClass.
bboxes : a list of GtsBBox.
Returns : a new GtsBBox bounding box of all the bounding boxes in bboxes.


gts_bbox_draw ()

void        gts_bbox_draw                   (GtsBBox *bb,
                                             FILE *fptr);

Writes in file fptr an OOGL (Geomview) description of bb.

bb : a GtsBBox.
fptr : a file pointer.


gts_bbox_point_is_inside()

#define     gts_bbox_point_is_inside(bbox, p)

Evaluates to TRUE if p is inside (or on the boundary) of bbox, FALSE otherwise.

bbox :a GtsBBox.
p :a GtsPoint.


gts_bboxes_are_overlapping ()

gboolean    gts_bboxes_are_overlapping      (GtsBBox *bb1,
                                             GtsBBox *bb2);

bb1 : a GtsBBox.
bb2 : a GtsBBox.
Returns : TRUE if the bounding boxes bb1 and bb2 are overlapping (including just touching), FALSE otherwise.


gts_bbox_diagonal2 ()

gdouble     gts_bbox_diagonal2              (GtsBBox *bb);

bb : a GtsBBox.
Returns : the squared length of the diagonal of bb.


gts_bbox_point_distance2 ()

void        gts_bbox_point_distance2        (GtsBBox *bb,
                                             GtsPoint *p,
                                             gdouble *min,
                                             gdouble *max);

Sets min and max to lower and upper bounds for the square of the Euclidean distance between the object contained in bb and p. For these bounds to make any sense the bounding box must be "tight" i.e. each of the 6 faces of the box must at least be touched by one point of the bounded object.

bb : a GtsBBox.
p : a GtsPoint.
min : a pointer on a gdouble.
max : a pointer on a gdouble.


gts_bbox_is_stabbed ()

gboolean    gts_bbox_is_stabbed             (GtsBBox *bb,
                                             GtsPoint *p);

bb : a GtsBBox.
p : a GtsPoint.
Returns : TRUE if the ray starting at p and ending at (p->x, p->y, +infty) intersects with bb, FALSE otherwise.


GtsBBTreeTraverseFunc ()

void        (*GtsBBTreeTraverseFunc)        (GtsBBox *bb1,
                                             GtsBBox *bb2,
                                             gpointer data);

User function called for each pair of overlapping bounding boxes. See gts_bb_tree_traverse_overlapping().

bb1 :a GtsBBox.
bb2 :another GtsBBox.
data :user data passed to the function.


gts_bb_tree_new ()

GNode*      gts_bb_tree_new                 (GSList *bboxes);

Builds a new hierarchy of bounding boxes for bboxes. At each level, the GNode->data field contains a GtsBBox bounding box of all the children. The tree is binary and is built by repeatedly cutting in two approximately equal halves the bounding boxes at each level until a leaf node (i.e. a bounding box given in bboxes) is reached. In order to minimize the depth of the tree, the cutting direction is always chosen as perpendicular to the longest dimension of the bounding box.

bboxes : a list of GtsBBox.
Returns : a new hierarchy of bounding boxes.


gts_bb_tree_surface ()

GNode*      gts_bb_tree_surface             (GtsSurface *s);

s : a GtsSurface.
Returns : a new hierarchy of bounding boxes bounding the faces of s.


gts_bb_tree_overlap ()

GSList*     gts_bb_tree_overlap             (GNode *tree,
                                             GtsBBox *bbox);

tree : a bounding box tree.
bbox : a GtsBBox.
Returns : a list of bounding boxes, leaves of tree which overlap bbox.


gts_bb_tree_is_overlapping ()

gboolean    gts_bb_tree_is_overlapping      (GNode *tree,
                                             GtsBBox *bbox);

tree : a bounding box tree.
bbox : a GtsBBox.
Returns : TRUE if any leaf of tree overlaps bbox, FALSE otherwise.


gts_bb_tree_traverse_overlapping ()

void        gts_bb_tree_traverse_overlapping
                                            (GNode *tree1,
                                             GNode *tree2,
                                             GtsBBTreeTraverseFunc func,
                                             gpointer data);

Calls func for each overlapping pair of leaves of tree1 and tree2.

tree1 : a bounding box tree.
tree2 : a bounding box tree.
func : a GtsBBTreeTraverseFunc.
data : user data to be passed to func.


gts_bb_tree_draw ()

void        gts_bb_tree_draw                (GNode *tree,
                                             guint depth,
                                             FILE *fptr);

Write in fptr an OOGL (Geomview) description of tree for the depth specified by depth.

tree : a bounding box tree.
depth : a specified depth.
fptr : a file pointer.


gts_bb_tree_destroy ()

void        gts_bb_tree_destroy             (GNode *tree,
                                             gboolean free_leaves);

Destroys all the bounding boxes created by tree and destroys the tree itself. If free_leaves is set to TRUE, destroys boxes given by the user when creating the tree (i.e. leaves of the tree).

tree : a bounding box tree.
free_leaves : if TRUE the bounding boxes given by the user are freed.


GtsBBoxDistFunc ()

gdouble     (*GtsBBoxDistFunc)              (GtsPoint *p,
                                             gpointer bounded);

User function returning the (minimum) distance between the object defined by bounded and point p.

p :a GtsPoint.
bounded :an object bounded by a GtsBBox.
Returns :the distance between p and bounded.


GtsBBoxClosestFunc ()

GtsPoint*   (*GtsBBoxClosestFunc)           (GtsPoint *p,
                                             gpointer bounded);

User function returning a GtsPoint belonging to the object defined by bounded and closest to p.

p :a GtsPoint.
bounded :an object bounded by a GtsBBox.
Returns :a GtsPoint.


gts_bb_tree_point_distance ()

gdouble     gts_bb_tree_point_distance      (GNode *tree,
                                             GtsPoint *p,
                                             GtsBBoxDistFunc distance,
                                             GtsBBox **bbox);

tree : a bounding box tree.
p : a GtsPoint.
distance : a GtsBBoxDistFunc.
bbox : if not NULL is set to the bounding box containing the closest object.
Returns : the distance as evaluated by distance between p and the closest object in tree.


gts_bb_tree_point_closest ()

GtsPoint*   gts_bb_tree_point_closest       (GNode *tree,
                                             GtsPoint *p,
                                             GtsBBoxClosestFunc closest,
                                             gdouble *distance);

tree : a bounding box tree.
p : a GtsPoint.
closest : a GtsBBoxClosestFunc.
distance : if not NULL is set to the distance between p and the new GtsPoint.
Returns : a new GtsPoint, closest point to p and belonging to an object of tree.


gts_bb_tree_segment_distance ()

void        gts_bb_tree_segment_distance    (GNode *tree,
                                             GtsSegment *s,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);

Given a segment s, points are sampled regularly on its length using delta as increment. The distance from each of these points to the closest object of tree is computed using distance and the gts_bb_tree_point_distance() function. The fields of range are filled with the number of points sampled, the minimum, average and maximum value and the standard deviation.

tree : a bounding box tree.
s : a GtsSegment.
distance : a GtsBBoxDistFunc.
delta : spatial scale of the sampling to be used.
range : a GtsRange to be filled with the results.


gts_bb_tree_triangle_distance ()

void        gts_bb_tree_triangle_distance   (GNode *tree,
                                             GtsTriangle *t,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);

Given a triangle t, points are sampled regularly on its surface using delta as increment. The distance from each of these points to the closest object of tree is computed using distance and the gts_bb_tree_point_distance() function. The fields of range are filled with the number of points sampled, the minimum, average and maximum value and the standard deviation.

tree : a bounding box tree.
t : a GtsTriangle.
distance : a GtsBBoxDistFunc.
delta : spatial scale of the sampling to be used.
range : a GtsRange to be filled with the results.


gts_bb_tree_point_closest_bboxes ()

GSList*     gts_bb_tree_point_closest_bboxes
                                            (GNode *tree,
                                             GtsPoint *p);

tree : a bounding box tree.
p : a GtsPoint.
Returns : a list of GtsBBox. One of the bounding boxes is assured to contain the object of tree closest to p.


gts_bb_tree_surface_boundary_distance ()

void        gts_bb_tree_surface_boundary_distance
                                            (GNode *tree,
                                             GtsSurface *s,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);

Calls gts_bb_tree_segment_distance() for each edge boundary of s. The fields of range are filled with the minimum, maximum and average distance. The average distance is defined as the sum of the average distances for each boundary edge weighthed by their length and divided by the total length of the boundaries. The standard deviation is defined accordingly. The n field of range is filled with the number of sampled points used.

tree : a bounding box tree.
s : a GtsSurface.
distance : a GtsBBoxDistFunc.
delta : a sampling increment defined as the percentage of the diagonal of the root bounding box of tree.
range : a GtsRange to be filled with the results.


gts_bb_tree_surface_distance ()

void        gts_bb_tree_surface_distance    (GNode *tree,
                                             GtsSurface *s,
                                             GtsBBoxDistFunc distance,
                                             gdouble delta,
                                             GtsRange *range);

Calls gts_bb_tree_triangle_distance() for each face of s. The fields of range are filled with the minimum, maximum and average distance. The average distance is defined as the sum of the average distances for each triangle weighthed by their area and divided by the total area of the surface. The standard deviation is defined accordingly. The n field of range is filled with the number of sampled points used.

tree : a bounding box tree.
s : a GtsSurface.
distance : a GtsBBoxDistFunc.
delta : a sampling increment defined as the percentage of the diagonal of the root bounding box of tree.
range : a GtsRange to be filled with the results.


gts_bb_tree_stabbed ()

GSList*     gts_bb_tree_stabbed             (GNode *tree,
                                             GtsPoint *p);

tree : a bounding box tree.
p : a GtsPoint.
Returns : a list of bounding boxes, leaves of tree which are stabbed by the ray defined by p (see gts_bbox_is_stabbed()).