(setq pi 3.141592653589793) (setq i (complex 0 1)) (setq twopi (mult 2 pi)) (defun cbox (c al fl pl ab fb pb ar fr pr at ft pt) (list (ClosedPoly c (Liss 0 al fl pl 0 ab fb pb) (Liss 0 ar fr pr 0 ab fb pb) (Liss 0 ar fr pr 0 at ft pt) (Liss 0 al fl pl 0 at ft pt) ) ) ) (defun box (al fl pl ab fb pb ar fr pr at ft pt) (list (ClosedPoly invert (Liss 0 al fl pl 0 ab fb pb) (Liss 0 ar fr pr 0 ab fb pb) (Liss 0 ar fr pr 0 at ft pt) (Liss 0 al fl pl 0 at ft pt) ) ) ) (defun ChooseFreq (fMax) (mult (quot (plus 15 (mult (Choose 0 20) (Choose 1 fMax))) 20) (minus (mult (Choose 0 1) 2) 1) ) ) (defun randcbox (c fMax) (cbox c 1 (ChooseFreq fMax) (Choose 0 360) 1 (ChooseFreq fMax) (Choose 0 360) 1 (ChooseFreq fMax) (Choose 0 360) 1 (ChooseFreq fMax) (Choose 0 360) ) ) (defun randbox (fMax) (box 1 (ChooseFreq fMax) (Choose 0 360) 1 (ChooseFreq fMax) (Choose 0 360) 1 (ChooseFreq fMax) (Choose 0 360) 1 (ChooseFreq fMax) (Choose 0 360) ) ) (defun PowerSeries (closed color nTerms radiusFactor freqFactor deltaPhase) (letrec ( (tail (lambda (n radius freq phase) (if (lt n 1) nil (cons (Liss 0 radius freq (plus phase 90) 0 radius freq phase) (tail (minus n 1) (mult radius radiusFactor) (mult freq freqFactor) (rem (plus phase deltaPhase) 360) ) ) ) ) ) ) (list (ListPoly closed color (Series (cons (Constant 0 0) (tail nTerms 1 1 0))) ) ) ) ) (defun mapints (f first last) (if (lt last first) nil (cons (f first) (mapints f (plus first 1) last)))) (defun MapBothInts (f first last) (if (lt last first) nil (cons (f (minus 0 first)) (f first) (MapBothInts f (plus first 1) last)))) (defun PtolSeries (closed color nTerms syn typicalRadius) (letrec ((Term (lambda (n) (letrec ((An (syn n)) (r (abs An)) (t (mult 180 (div (arg An) pi)))) (Liss 0 r n (plus t 90) 0 r n t))))) (list (ListPoly closed color (Series (cons (Term 0) (MapBothInts Term 1 nTerms)) typicalRadius))))) (defun PtolAnalWork (n pts) (if (lt (length pts) 2) 0 (let ( (t1 (car (car pts))) (z1 (car (cdr (car pts)))) (t2 (car (car (cdr pts)))) (z2 (car (cdr (car (cdr pts)))))) (plus (if (equal t1 t2) 0 (if (equal n 0) (div (mult (plus z1 z2) (minus t2 t1)) 2) (plus (mult (div (minus (mult z1 t2) (mult z2 t1)) (minus t2 t1)) (div (minus (exp (mult -1 i n t2)) (exp (mult -1 i n t1))) (mult -1 i n))) (mult (div (minus z2 z1) (minus t2 t1)) (plus (div (minus (mult t2 (exp (mult -1 i n t2))) (mult t1 (exp (mult -1 i n t1)))) (mult -1 i n)) (div (minus (exp (mult -1 i n t2)) (exp (mult -1 i n t1))) (mult n n))))))) (PtolAnalWork n (cdr pts)))))) (defun PtolAnal (pts) (let ((last (nth (length pts) pts))) (let ((closedpts (cons (list (minus (car last) twopi) (nth 2 last)) pts))) (lambda (n) (div (PtolAnalWork n closedpts) twopi))))) (defun TriangleFilter (i r1 r2) (cond ((le i r1) 1) ((ge i r2) 0) (T (minus 1 (div (minus i r1 0.0) (minus r2 r1)))) ) ) (defun FilteredPowerSeries (closed color nTerms radiusFactor freqFactor deltaPhase flat) (prog (defun tail (i radius freq phase) (if (gt i nTerms) nil (cons (let ((fr (mult radius (TriangleFilter i (mult nTerms flat 1.0) (plus nTerms 1))))) (Liss 0 fr freq (plus phase 90) 0 fr freq phase) ) (tail (plus i 1) (mult radius radiusFactor) (mult freq freqFactor) (rem (plus phase deltaPhase) 360) ) ) ) ) (list (ListPoly closed color (Series (cons (Constant 0 0) (tail 1 1 1 0))) ) ) ) ) (defun FilteredSeries (closed color parms oneWidth zeroWidth) (prog (defun Fixit ((freq xAmpl xPhase yAmpl yPhase)) (let ((scale (TriangleFilter (abs freq) oneWidth zeroWidth))) (Liss 0 (mult scale xAmpl) freq xPhase 0 (mult scale yAmpl) freq yPhase) ) ) (ListPoly closed color (Series (cons (Constant 0 0) (mapcar Fixit parms))) ) ) ) (defun Generate (nTerms MakeIt) (do ((i (plus nTerms 1) (minus i 1)) (ans nil (let (((ax px ay py) (MakeIt i))) (if (and (equal ax 0) (equal ay 0)) ans (cons (list i ax px ay py) ans) ) ))) ((gt i 0) ans) ans ) ) (defun circpts (r n) (mapints (lambda (j) (let ((tau (mult j (div twopi n)))) (list tau (mult r (exp (mult i tau)))))) 1 n)) (defun lines (r n nTerms) (PtolSeries false white nTerms (PtolAnal (circpts r n)) r)) PPolyHack.preload Last Edited by: Spreitzer, June 18, 1985 5:33:24 pm PDT Êu˜J™J™7J˜J˜J˜J˜J˜˜J˜'˜˜ J˜J˜J˜J˜—J˜—J˜—J˜J˜˜ J˜%˜˜J˜J˜J˜J˜—J˜—J˜—J˜J˜˜˜J˜8J˜—J˜—J˜J˜˜˜J˜"J˜"J˜"J˜"—J˜—J˜J˜˜˜J˜"J˜"J˜"J˜"—J˜—J˜J˜˜J˜8˜˜˜˜J˜˜J˜J˜˜J˜8˜J˜J˜J˜J˜!—J˜—J˜—J˜—J˜—J˜—J˜˜˜J˜2—J˜—J˜—J˜—J˜J˜˜˜J˜J˜˜J˜ J˜"———J˜˜!˜J˜J˜˜J˜J˜ J˜&———J˜˜J˜'˜˜˜J˜ J˜ J˜"J˜$——˜˜J˜F————J˜˜J˜˜J˜J˜˜˜J˜J˜J˜J˜!—˜˜J˜ J˜˜J˜J˜)˜˜˜˜J˜J˜ —J˜—˜˜J˜J˜—J˜——˜˜J˜ J˜—˜˜˜J˜ J˜!—J˜—˜˜J˜J˜—J˜——————J˜————J˜˜J˜˜J˜˜J˜EJ˜6———J˜˜J˜ ˜J˜ J˜ J˜2—J˜—J˜J˜˜J˜=˜˜!˜J˜ J˜˜˜J˜NJ˜0—J˜˜J˜ J˜J˜J˜!—J˜—J˜—J˜—J˜˜˜J˜-—J˜—J˜—J˜—J˜J˜˜J˜'˜˜J˜"˜J˜8J˜H—J˜—J˜˜J˜3—J˜—J˜—J˜J˜˜J˜˜J˜ ˜J˜˜J˜˜J˜J˜J˜—J˜—J˜—J˜J˜—J˜—J˜J˜˜J˜˜˜˜J˜J˜(——J˜J˜——J˜˜J˜;—J˜J˜—…—üÁ