Write the area inside closed shapes

Plain text, nothing hidden. Copy it into a file named cxarea.lsp, or download it.

;;; ============================================================================
;;; CXAREA - Write the area inside closed shapes
;;; Version 1.0.0
;;; CADXChange LISP tools - https://cadxchange.net/resources/lisp/cxarea
;;; Tested in: AutoCAD (full version). Other programs that run AutoLISP may work but are not tested.
;;; Copyright (c) CADXChange. Free for personal and commercial use; do not resell or
;;; republish it as a collection. Terms: https://cadxchange.net/legal/lisp-terms
;;; ============================================================================

;; Write the area of every closed polyline, circle and full ellipse in NAMES into the drawing, as a text centered
;; inside the shape. The area is multiplied by FACTOR (a unit conversion), shown with PREC decimals between
;; PREFIX and SUFFIX, and the text gets height HEIGHT and layer LAYER. Other objects are skipped.
;; Returns (count total-area) with the total in drawing units.
(defun cx:area-run (names factor prec prefix suffix height layer / n total ed area)
  (setq n 0 total 0.0)
  (foreach e names
    (setq ed   (entget e)
          area (cx:ent-area ed))
    (if area
      (progn
        (cx:label (cx:ent-label-point ed) (strcat prefix (cx:num (* area factor) prec) suffix) height 0.0 layer)
        (setq total (+ total area) n (1+ n)))))
  (list n total))

(defun c:CXAREA ( / *error* cx:sv ss factor prec prefix suffix r)
  (setq *error* cx:err)
  (if (setq ss (cx:pick "\nSelect closed polylines, circles or ellipses: " '((0 . "LWPOLYLINE,CIRCLE,ELLIPSE"))))
    (progn
      (setq factor (cx:ask-real "Multiply the area by (unit conversion, 0.000001 turns mm2 into m2)" 1.0)
            prec   (cx:ask-int "Decimals" 2)
            prefix (cx:ask-str "Text in front (- for none)" "")
            suffix (cx:ask-str "Text after the number (- for none)" ""))
      (cx:start '(("CMDECHO" . 0)))
      (setq r (cx:area-run (cx:ss->list ss) factor prec prefix suffix (getvar "TEXTSIZE") (getvar "CLAYER")))
      (princ (strcat "\n" (itoa (car r)) " area(s) written. Total: " (cx:num (* (cadr r) factor) prec)))
      (cx:end)))
  (princ))


;;; ---- Shared helpers (used by the command above; identical in every CADXChange tool) ----

(defun cx:dxf (code ed)
  (cdr (assoc code ed)))

;; True for a closed polyline, a circle and a full ellipse.
(defun cx:ent-closed (ed / type)
  (setq type (cx:dxf 0 ed))
  (cond
    ((= type "LWPOLYLINE") (= 1 (logand 1 (cx:dxf 70 ed))))
    ((= type "CIRCLE") T)
    ((= type "ELLIPSE") (< (abs (- (- (cx:dxf 42 ed) (cx:dxf 41 ed)) (* 2.0 pi))) 1e-6))))

;; The vertices of an LWPOLYLINE entity list as ((x y bulge start-width end-width) ...).
(defun cx:lw-verts (ed / out cur)
  (foreach g ed
    (cond
      ((= (car g) 10)
       (if cur (setq out (cons cur out)))
       (setq cur (list (cadr g) (caddr g) 0.0 0.0 0.0)))
      ((and cur (= (car g) 40)) (setq cur (list (nth 0 cur) (nth 1 cur) (nth 2 cur) (cdr g) (nth 4 cur))))
      ((and cur (= (car g) 41)) (setq cur (list (nth 0 cur) (nth 1 cur) (nth 2 cur) (nth 3 cur) (cdr g))))
      ((and cur (= (car g) 42)) (setq cur (list (nth 0 cur) (nth 1 cur) (cdr g) (nth 3 cur) (nth 4 cur))))))
  (if cur (setq out (cons cur out)))
  (reverse out))

;; The arc a bulge makes between P1 and P2 as (center-x center-y radius start-angle sweep), or nil for a straight segment.
;; The sweep is signed: positive turns counter-clockwise.
(defun cx:bulge-arc (p1 p2 b / theta dx dy len nx ny d ccx ccy)
  (if (< (abs b) 1e-9)
    nil
    (progn
      (setq theta (* 4.0 (atan b))
            dx    (- (car p2) (car p1))
            dy    (- (cadr p2) (cadr p1))
            len   (sqrt (+ (* dx dx) (* dy dy))))
      (if (< len 1e-12)
        nil
        (progn
          (setq nx  (/ (- dy) len)
                ny  (/ dx len)
                d   (/ (/ len 2.0) (/ (sin (/ theta 2.0)) (cos (/ theta 2.0))))
                ccx (+ (/ (+ (car p1) (car p2)) 2.0) (* nx d))
                ccy (+ (/ (+ (cadr p1) (cadr p2)) 2.0) (* ny d)))
          (list ccx ccy (/ len (* 2.0 (sin (/ (abs theta) 2.0))))
                (atan (- (cadr p1) ccy) (- (car p1) ccx)) theta))))))

;; The area of a closed polyline with its arc segments.
(defun cx:lw-area (verts / sum i n a v1 v2)
  (setq sum 0.0 i 0 n (length verts))
  (repeat n
    (setq v1  (nth i verts)
          v2  (nth (rem (1+ i) n) verts)
          sum (+ sum (/ (- (* (car v1) (cadr v2)) (* (car v2) (cadr v1))) 2.0))
          a   (cx:bulge-arc v1 v2 (nth 2 v1)))
    (if a
      (setq sum (+ sum (* 0.5 (nth 2 a) (nth 2 a) (- (nth 4 a) (sin (nth 4 a)))))))
    (setq i (1+ i)))
  (abs sum))

;; The area of a closed polyline, a circle or a full ellipse; nil for other objects.
(defun cx:ent-area (ed / type a)
  (setq type (cx:dxf 0 ed))
  (cond
    ((not (cx:ent-closed ed)) nil)
    ((= type "LWPOLYLINE") (cx:lw-area (cx:lw-verts ed)))
    ((= type "CIRCLE") (* pi (cx:dxf 40 ed) (cx:dxf 40 ed)))
    ((= type "ELLIPSE")
     (setq a (distance '(0.0 0.0 0.0) (cx:dxf 11 ed)))
     (* pi a a (cx:dxf 40 ed)))))

;; A text centered on PT, with height H, rotation ROT (radians) and layer LAYER, in the current text style.
(defun cx:label (pt str h rot layer)
  (entmakex (list '(0 . "TEXT") (cons 8 layer) (list 10 (car pt) (cadr pt) 0.0) (cons 40 h) (cons 1 str)
                  (cons 50 rot) (cons 7 (getvar "TEXTSTYLE")) '(72 . 1)
                  (list 11 (car pt) (cadr pt) 0.0) '(100 . "AcDbText") '(73 . 2))))

;; The number of segments of a polyline with N vertices.
(defun cx:seg-count (n closed)
  (if closed n (1- n)))

;; A polyline as a list of (x y) points; arcs are cut into short straight pieces.
(defun cx:lw-points (verts closed / out i n a v1 v2 k steps ang)
  (setq i 0 n (length verts))
  (repeat (cx:seg-count n closed)
    (setq v1  (nth i verts)
          v2  (nth (rem (1+ i) n) verts)
          a   (cx:bulge-arc v1 v2 (nth 2 v1))
          out (cons (list (car v1) (cadr v1)) out))
    (if a
      (progn
        (setq steps (max 4 (fix (/ (abs (nth 4 a)) 0.15))) k 1)
        (while (< k steps)
          (setq ang (+ (nth 3 a) (* (nth 4 a) (/ (float k) steps)))
                out (cons (list (+ (car a) (* (nth 2 a) (cos ang))) (+ (cadr a) (* (nth 2 a) (sin ang)))) out)
                k   (1+ k)))))
    (setq i (1+ i)))
  (if (not closed)
    (setq out (cons (list (car (last verts)) (cadr (last verts))) out)))
  (reverse out))

;; An object as a list of (x y) points; circles and ellipses are cut into 120 pieces, arcs into short pieces.
;; Returns nil for an object it does not know.
(defun cx:ent-points (ed / type ctr r a1 a2 k pts ratio ang maj steps)
  (setq type (cx:dxf 0 ed))
  (cond
    ((= type "LWPOLYLINE") (cx:lw-points (cx:lw-verts ed) (= 1 (logand 1 (cx:dxf 70 ed)))))
    ((= type "LINE")
     (list (list (car (cx:dxf 10 ed)) (cadr (cx:dxf 10 ed))) (list (car (cx:dxf 11 ed)) (cadr (cx:dxf 11 ed)))))
    ((= type "CIRCLE")
     (setq ctr (cx:dxf 10 ed) r (cx:dxf 40 ed) k 0)
     (repeat 120
       (setq ang (* 2.0 pi (/ k 120.0))
             pts (cons (list (+ (car ctr) (* r (cos ang))) (+ (cadr ctr) (* r (sin ang)))) pts)
             k   (1+ k)))
     (reverse pts))
    ((= type "ARC")
     (setq ctr (cx:dxf 10 ed) r (cx:dxf 40 ed) a1 (cx:dxf 50 ed) a2 (cx:dxf 51 ed))
     (if (<= a2 a1) (setq a2 (+ a2 (* 2.0 pi))))
     (setq steps (max 8 (fix (/ (- a2 a1) 0.05))) k 0)
     (repeat (1+ steps)
       (setq ang (+ a1 (* (- a2 a1) (/ (float k) steps)))
             pts (cons (list (+ (car ctr) (* r (cos ang))) (+ (cadr ctr) (* r (sin ang)))) pts)
             k   (1+ k)))
     (reverse pts))
    ((= type "ELLIPSE")
     (setq ctr (cx:dxf 10 ed) maj (cx:dxf 11 ed) ratio (cx:dxf 40 ed) a1 (cx:dxf 41 ed) a2 (cx:dxf 42 ed))
     (if (<= a2 a1) (setq a2 (+ a2 (* 2.0 pi))))
     (setq k 0)
     (repeat 121
       (setq ang (+ a1 (* (- a2 a1) (/ k 120.0)))
             pts (cons (list (+ (car ctr) (* (car maj) (cos ang)) (* (- (cadr maj)) ratio (sin ang)))
                             (+ (cadr ctr) (* (cadr maj) (cos ang)) (* (car maj) ratio (sin ang))))
                       pts)
             k   (1+ k)))
     (reverse pts))))

;; The centroid of the polygon PTS ((x y) ...) and its area: (centroid area).
(defun cx:poly-centroid (pts / a sx sy i n p q f)
  (setq a 0.0 sx 0.0 sy 0.0 i 0 n (length pts))
  (repeat n
    (setq p  (nth i pts)
          q  (nth (rem (1+ i) n) pts)
          f  (- (* (car p) (cadr q)) (* (car q) (cadr p)))
          a  (+ a f)
          sx (+ sx (* (+ (car p) (car q)) f))
          sy (+ sy (* (+ (cadr p) (cadr q)) f)))
    (setq i (1+ i)))
  (if (< (abs a) 1e-12)
    (list (list (car (car pts)) (cadr (car pts))) 0.0)
    (list (list (/ sx (* 3.0 a)) (/ sy (* 3.0 a))) (abs (/ a 2.0)))))

;; True when the point PT lies inside the polygon PTS (ray casting).
(defun cx:pt-in-poly (pt pts / inside i n p q)
  (setq inside nil i 0 n (length pts))
  (repeat n
    (setq p (nth i pts) q (nth (rem (1+ i) n) pts))
    (if (and (/= (> (cadr p) (cadr pt)) (> (cadr q) (cadr pt)))
             (< (car pt) (+ (car p) (/ (* (- (cadr pt) (cadr p)) (- (car q) (car p))) (- (cadr q) (cadr p))))))
      (setq inside (not inside)))
    (setq i (1+ i)))
  inside)

;; Merge sort of LST with PRED (a function of two items that is true when the first goes first).
(defun cx:sort (lst pred / half a b out)
  (cond
    ((or (null lst) (null (cdr lst))) lst)
    (T
     (setq half (/ (length lst) 2) a nil b lst)
     (repeat half (setq a (cons (car b) a) b (cdr b)))
     (setq a (cx:sort (reverse a) pred) b (cx:sort b pred) out nil)
     (while (and a b)
       (if (apply pred (list (car b) (car a)))
         (setq out (cons (car b) out) b (cdr b))
         (setq out (cons (car a) out) a (cdr a))))
     (append (reverse out) a b))))

;; A point inside the polygon PTS: the centroid when it is inside, otherwise the middle of the widest
;; stretch of the horizontal line through the centroid.
(defun cx:interior-point (pts / c y xs i n p q best from to w)
  (setq c (car (cx:poly-centroid pts)))
  (if (cx:pt-in-poly c pts)
    c
    (progn
      (setq y (cadr c) n (length pts) i 0)
      (repeat n
        (setq p (nth i pts) q (nth (rem (1+ i) n) pts))
        (if (/= (> (cadr p) y) (> (cadr q) y))
          (setq xs (cons (+ (car p) (/ (* (- y (cadr p)) (- (car q) (car p))) (- (cadr q) (cadr p)))) xs)))
        (setq i (1+ i)))
      (setq xs (cx:sort xs '<) best 0.0 i 0)
      (while (< (1+ i) (length xs))
        (setq from (nth i xs) to (nth (1+ i) xs) w (- to from))
        (if (> w best) (setq best w c (list (/ (+ from to) 2.0) y)))
        (setq i (+ i 2)))
      c)))

;; A point inside a closed object where its label can go.
(defun cx:ent-label-point (ed)
  (if (= (cx:dxf 0 ed) "CIRCLE")
    (list (car (cx:dxf 10 ed)) (cadr (cx:dxf 10 ed)))
    (cx:interior-point (cx:ent-points ed))))

;; Real X as text with at most PREC decimals and no trailing zeros ("2.50" -> "2.5", "3.00" -> "3").
(defun cx:num (x prec / s)
  (setq s (rtos x 2 prec))
  (if (wcmatch s "*.*")
    (progn
      (while (= (substr s (strlen s)) "0") (setq s (substr s 1 (1- (strlen s)))))
      (if (= (substr s (strlen s)) ".") (setq s (substr s 1 (1- (strlen s)))))))
  (if (or (= s "-0") (= s "")) "0" s))

;; Close the undo step and put the system variables back.
(defun cx:end ()
  (foreach v cx:sv (setvar (car v) (cdr v)))
  (command "_.UNDO" "_End")
  (setq cx:sv nil)
  (princ))

;; Error handler: restores everything, stays quiet on Esc.
(defun cx:err (msg)
  (if (> (getvar "CMDACTIVE") 0) (command))
  (cx:end)
  (if (and msg (not (wcmatch (strcase msg) "*BREAK*,*CANCEL*,*EXIT*")))
    (princ (strcat "\nError: " msg)))
  (princ))

;; Use the objects already selected, or ask the user to select; FILTER is an ssget filter list or nil.
(defun cx:pick (msg filter / ss)
  (setq ss (if filter (ssget "_I" filter) (ssget "_I")))
  (if (null ss)
    (progn
      (princ msg)
      (setq ss (if filter (ssget filter) (ssget)))))
  ss)

(defun cx:ask-real (msg def / v)
  (setq v (getreal (strcat "\n" msg " <" (cx:num def 6) ">: ")))
  (if v v def))

;; Ask for an integer with a default; returns the default on Enter.
(defun cx:ask-int (msg def / v)
  (setq v (getint (strcat "\n" msg " <" (itoa def) ">: ")))
  (if v v def))

;; Ask for a string (spaces allowed) with a default; "-" means an empty string.
(defun cx:ask-str (msg def / v)
  (setq v (getstring T (strcat "\n" msg " <" def ">: ")))
  (cond ((= v "") def) ((= v "-") "") (T v)))

;; Save the system variables in VARS ((name . value) ...), set them, and open one undo step.
;; The caller declares cx:sv as a local so the saved values live exactly as long as the command.
(defun cx:start (vars)
  (setq cx:sv (mapcar (function (lambda (v) (cons (car v) (getvar (car v))))) vars))
  (command "_.UNDO" "_Begin")
  (foreach v vars (setvar (car v) (cdr v)))
  (princ))

;; Selection set to a list of entity names.
(defun cx:ss->list (ss / i out)
  (setq i 0)
  (if ss
    (repeat (sslength ss)
      (setq out (cons (ssname ss i) out)
            i   (1+ i))))
  (reverse out))

(princ "\nCXAREA loaded. Type CXAREA to start.")
(princ)

More commands: Measuring and polylines

• CXLENWrite the length along lines, arcs and polylines
• CXSUMTotal length and area by layer
• CXCENTROIDFind and mark the centre of closed shapes
• CXDISTMeasure a path point by point
• CXPLCLOSEClose polylines whose ends almost meet
• CXPLREVReverse the direction of lines and polylines
• CXPLCLEANRemove duplicate and straight-line vertices
• CXPLWIDTHSet one width for many polylines
• CXJOINJoin lines and arcs into polylines, gaps allowed