See if you can make sense of the following function. Compare it to the pseudo-code and try to catch the geometric calculations just described. There may be a few AutoLISP functions that are new to you. If you need help with these functions, refer to the AutoLISP Reference. For now, just read the code; do not write anything.

```(defun gp:Calculate-and-Draw-Tiles (BoundaryData / PathLength
```
```		 TileSpace TileRadius SpaceFilled SpaceToFill
```
```		 RowSpacing offsetFromCenter
```
```		 rowStartPoint pathWidth pathAngle
```
```		 ObjectCreationStyle   TileList)
```
```  (setq PathLength	(cdr (assoc 41 BoundaryData))
```
```		TileSpace	 (cdr (assoc 43 BoundaryData))
```
```		TileRadius	(cdr (assoc 42 BoundaryData))
```
```		SpaceToFill   (- PathLength TileRadius)
```
```		RowSpacing	(* (+ TileSpace (* TileRadius 2.0))
```
```						 (sin (Degrees->Radians 60))
```
```					) ;_ end of *
```
```		SpaceFilled   RowSpacing
```
```		offsetFromCenter 0.0
```
```		offsetDistance (/ (+ (* TileRadius 2.0) TileSpace) 2.0)
```
```		rowStartPoint  (cdr (assoc 10 BoundaryData))
```
```		pathWidth	(cdr (assoc 40 BoundaryData))
```
```		pathAngle	(cdr (assoc 50 BoundaryData))
```
```		ObjectCreationStyle (strcase (cdr (assoc 3 BoundaryData)))
```
```  ) ;_ end of setq
```
```  ;; Compensate for the first call to gp:calculate-Draw-tile Row
```
```  ;; in the loop below.
```
```  (setq rowStartPoint
```
```	 (polar rowStartPoint
```
```			(+ pathAngle pi)
```
```			(/ TileRadius 2.0)
```
```	 ) ;_ end of polar
```
```  ) ;_ end of setq
```
```  ;; Draw each row of tiles.
```
```  (while (<= SpaceFilled SpaceToFill)
```
```	;; Get the list of tiles created, adding them to our list.
```
```	(setq tileList   (append tileList
```
```			(gp:calculate-Draw-TileRow
```
```				(setq rowStartPoint
```
```					 (polar rowStartPoint
```
```							pathAngle
```
```							RowSpacing
```
```					 ) ;_ end of polar
```
```				) ;_ end of setq
```
```				TileRadius
```
```				TileSpace
```
```				pathWidth
```
```				pathAngle
```
```				offsetFromCenter
```
```				ObjectCreationStyle
```
```			) ;_ end of gp:calculate-Draw-TileRow
```
```			) ;_ end of append
```
```	 ;; Calculate the distance along the path for the next row.
```
```	 SpaceFilled   (+ SpaceFilled RowSpacing)
```
```	 ;; Alternate between a zero and a positive offset
```
```	 ;; (causes alternate rows to be indented).
```
```	 offsetFromCenter
```
```		 (if (= offsetFromCenter 0.0)
```
```				offsetDistance
```
```				0.0
```
```		 ) ;_ end of if
```
```	) ;_ end of setq
```
```  ) ;_ end of while
```
```  ;; Return the list of tiles created.
```
```  tileList
```
```) ;_ end of defun
```

A couple of sections from the code may need a little extra explanation.

The following code fragment occurs right before the while loop begins:

```;; Compensate for the very first start point!!
```
```(setq rowStartPoint(polar rowStartPoint
```
```(+ pathAngle pi)(/ TileRadius 2.0)))
```

There are three pieces to the puzzle of figuring out the logic behind this algorithm:

• The rowStartPoint variable starts its life within the gp:Calculate-and-Draw-Tiles function by being assigned the point the user selected as the start point of the path.
• The very first argument passed to the gp:calculate-Draw-TileRow function does the following:

(setq rowStartPoint(polar rowStartPoint pathAngle RowSpacing))

Another way of stating this is: At the time the gp:calculate-Draw-TileRow function is called, the rowStartPoint variable is set to one RowSpacing distance beyond the current rowStartPoint.

• The rowStartPoint argument is used within gp:calculate-Draw-TileRow as the starting point for the centers of the circles in the row.

To compensate for the initial forward shifting of the rowStartPoint during the drawing of the first row (that is, the first cycle through the while loop), you will want to shift rowStartPoint slightly in the opposite direction. The aim is to avoid the appearance of a large margin of empty space between the path boundary and the first row. Half the TileRadius is a sufficient amount by which to move the point. This can be achieved by using polar to project rowStartPoint along a vector oriented 180 degrees from the PathAngle. If you think about it, this places the point temporarily outside the path boundary.

The next fragment (modified for readability) may be a little puzzling:

```(setq tileList (append tileList
```
```				(gp:calculate-Draw-TileRow
```
```					(setq rowStartPoint
```
```					(polar rowStartPoint pathAngle RowSpacing)
```
```					) ;_ end of setq
```
```					TileRadius TileSpace pathWidth pathAngle
```
```					offsetFromCenter ObjectCreationStyle
```
```				)))
```

In essence, there is setq wrapped around an append wrapped around the call to gp:calculate-Draw-TileRow.

The gp:calculate-Draw-TileRow function will return the Object IDs for each tile drawn. (The Object ID points to the tile object in the drawing.) You are drawing the tiles row by row, so the function returns the Object IDs of one row at a time. The append function adds the new Object IDs to any existing Object IDs stored in tileList.

```Near the end of the function, you can find the following code fragment:
```
```(setq offsetFromCenter
```
```  (if (= offsetFromCenter 0.0)
```
```	 offsetDistance
```
```	 0.0
```
```  )
```
```)
```

This is the offset toggle, which determines whether the row being drawn should begin with a circle centered on the path or offset from the path. The pseudo-code for this algorithm follows:

```Set the offset amount to the following:
```
```   If the offset is currently zero, set it to the offset distance;
```
```	Otherwise, set it back to zero.
```