deletions | additions       diff --git a/First_each_joint_was_surrounded__.tex b/First_each_joint_was_surrounded__.tex  index ed24f2c..71a592e 100644  --- a/First_each_joint_was_surrounded__.tex  +++ b/First_each_joint_was_surrounded__.tex 
...
First, each joint was surrounded by a 3-dimensional bounding volume. Each joint was sorted to determine which objects were overlapping. If two joints collide their orthogonal projections onto the xy, yz and xz-planes, and x-y and z-axes must overlap. Second, the researchers determined the size of each rectangular bounding box in their particular location. These were determined using the minimum, and maximum x,y, and z-coordinates of each joints. As the object moves, the minimum, and maximum coordinates were recomputed. This algorithm recomputes the coordinates of each joint in a bounding box at an expected constant rate. This approach was optimized further by determining which coordinates per joint are the researchers more interested wherein, the researchers used only the coordinates of the joint that matters in a certain gesture. So instead of recomputing all the 3d coordinates per joint, the arithmetic operation for computing the joint locations was lessened by two-thirds. Once the object transformation was done, the researchers used a pruning algorithm, namely, One-dimensional sweep and prune algorithm wherein the focus was the overlapping intervals between the pair of bounding box joints, because a pair of bounding boxes can overlap if and only if their intervals overlap in all three dimensions. The researchers constructed a list for each coordinate. Each list has the values of the endpoints of the intervals corresponding to their certain coordinate. The pairwise exact collision detection follows afterwards used if and only if the results for the one-dimensional sweep and prune has densely clustered intervals. So, this part was really unnecessary.  Then, once a collision to a certain coordinate was determined, the gesture was recorded as a hit, otherwise, miss.