core.form-ula

All using Autolisp program SPIRAL-002.LSP and (4)POLAR ARRAY .

From right to left surfces created by:

(a)Adding Intermediate ARC between intersections. Then connecting using RULE SURFACE.

(b)Adding Intermediate LINE between intersections. Then connecting using RULE SURFACE.

(a)Connecting spirals using EDGE SURFACE.

SPIRAL-002.LSP : copy/paste:-

(defun c:Spiral ()
(setq OriginalOSMODE (getvar “OSMODE”))
(if (< OriginalOSMODE 16384)
(progn
(setq OSMODEchanged T)
(setvar “OSMODE” (+ 16384 OriginalOSMODE))
))
(setvar “CMDECHO” 0)

(setq
NumberOfPoints 100
HeightStart 0.0
HeightEnd 15.0 ; if HeightEnd = HeightStart, then spiral will be in a plane (the ground plane)
AngleStart 0.0
AngleEnd 720.0 ; if AngleEnd = AngleStart, then spiral will be a straight line
RadiusStart 5.0
RadiusEnd 2.0 ; if RadiusEnd = RadiusStart, then spiral will be a helix
)
; angles are specified in degrees, and are converted to radians in the program (with “dtr” function)

(setq SpiralPointlist nil)
; points defining the spiral are stored in “SpiralPointlist”
; which is a simple list of “coordinate triplets” (list of xyz coordinates)
; the list is then used to create a 3d polyline

(setq i 0) (while (<= i NumberOfPoints)
(setq
HeightCurrent (Slider 0 NumberOfPoints i HeightStart HeightEnd)
AngleCurrent (Slider 0 NumberOfPoints i AngleStart AngleEnd)
RadiusCurrent (Slider 0 NumberOfPoints i RadiusStart RadiusEnd)
)
(setq CurrentPoint (polar (list 0.0 0.0 HeightCurrent) (dtr AngleCurrent) RadiusCurrent))
(setq SpiralPointlist (append SpiralPointlist (list CurrentPoint)))
(setq i (1+ i)) )

(Create3DPoly SpiralPointlist nil)

; if you want to create a SPLINE instead of a POLYLINE, use the following line instead
; (CreateSpline SpiralPointlist nil nil nil)

; increments are “arithmetic”, simply adding a constant value to the previous value
; try using different methods to create different kinds of spirals
; (for example, the radius can get larger and smaller)
; if we keep track of two or more sets of points, they can be “connected” to create spiral surfaces or volumes

(setvar “OSMODE” OriginalOSMODE)
)

;——————————————————————————-
; DEGREES TO RADIANS —————————————- DEGREES TO RADIANS
(defun dtr (InputAngle)
(* pi (/ InputAngle 180.0))
)

;——————————————————————————-
; RADIANS TO DEGREES —————————————- RADIANS TO DEGREES
(defun rtd (InputAngle)
(* 180.0 (/ InputAngle pi))
)
;——————————————————————————-
; CREATE POLYLINE ————————– CREATE POLYLINE FROM LIST OF POINTS
(defun Create3DPoly ( ListOf3DPoints ClosePolyline / pt)
; ListOf3DPoints is a list of 3D points
; ClosePolyline is T or nil

(command “.3DPOLY”)
(foreach pt ListOf3DPoints
(command pt)
)
(if ClosePolyline
(command “CLOSE”)
(command “”)
)
)

;——————————————————————————-
; CREATE SPLINE —————————— CREATE SPLINE FROM LIST OF POINTS
(defun CreateSpline ( ListOfPoints CloseSpline FitPoint1 FitPoint2 / pt)
; ListOfPoints is a list of points
; CloseSpline is T or nil
; FitPoint1 may be a point, or nil; if a point, then determines tangent
; FitPoint2 may be a point, or nil; if a point, then determines tangent
; (if CloseSpline is T, then FitPoint2 is ignored)

(command “.SPLINE”)
(foreach pt ListOfPoints
(command pt)
)
(if CloseSpline
(command “CLOSE”)
(command “”)
)
(if FitPoint1
(command FitPoint1)
(command “”)
)
(if (and (not CloseSpline) FitPoint2)
(command FitPoint2)
(command “”)
)
)

;——————————————————————————-
; SLIDER —————————————————————- SLIDER
(defun Slider (minA maxA curA minB maxB)
;
; given minA maxA curA minB maxB, find curB
;
; minA curA maxA
; | V |
; +————————–+
; | ^ |
; minB curB maxB
;
(setq minA (float minA) maxA (float MaxA) curA (float curA))
(setq minB (float minB) maxB (float MaxB))

; if minApercent=0 and maxApercent=1, find curApercent
(if (= minA maxA) ; we will get a “divide by zero” error
(setq curApercent 0.0) ; we should check the consequences of this — is it correct?
(setq curApercent (/ (- curA minA) (- maxA minA))) ; <– this is the correct formula, if minA /= maxA
)

(setq curB (+ minb (* curApercent (- maxB minB))))
)

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