topic Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp in Visual LISP, AutoLISP and General Customization Forum

NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Mon, 13 Dec 2021 10:52:51 GMT

How to evaluate the NURBS Equations, De Boor's algorithm by Autolisp?

I checked this forum to see if the topic has been addressed before, but I did not find anything relevant.

However, here is the code.

; *** ; * Nurbs@u Evaluates the coordinates of a point on a Nurbs curve (Spline) ; * Simulates the function 'vlax-curve-getPointAtParam ; * #Author - _Bilal ; * p [int] the degree of the curve. ; * @u [Real] the parameter value of the knot vector at a specified point ; * ulst [List] the knot vectors as sequence of parameter values ; * plst [List] the list of control points of the Nurbs curve ;====================================================== (defun Nurbs@u ( p @u ulst plst / addlist nips i clst ) ;====================================================== ;This function Adds the atoms(sublist) in the list (lst) ;the atoms are a sublist of reals numbers like a point. (defun addlist ( lst / v ) (setq v (car lst)) (while (setq lst (cdr lst)) (setq v (mapcar '+ v (car lst)))) );end ;Loop over plst (setq i 0 clst nil) (repeat (length plst) (if (setq nips (Nips@u i p @u ulst)) (setq clst (cons nips clst))) (setq i (1+ i)) ) (addlist (mapcar '(lambda (c p) (mapcar '(lambda (x) (* c x)) p)) (reverse clst) plst)) ;--------------- );Endof//Nurbs@u ;--------------- ; *** ; * Nips@u The B-spline basis functions used in the construction of NURBS curves ; * i [int] Corresponds to the ith control point ; * p [int] Corresponds with the degree of the basis function. ; * @u [Real] The parameter value of the knot vector at a specified point ; * ulst [List] The knot vectors as sequence of parameter values ;============================================================================== (defun Nips@u ( i p @u ulst / f@u g@u Bin@u i@u binlst n b1 b2 bin bin+ niplst ) ;============================================================================== (defun f@u ( i p @u ulst / dn ) (if (= (setq dn (- (nth (+ i p) ulst) (nth i ulst))) 0.0) 0.0 (/ (- @u (nth i ulst)) dn)) );end (defun g@u ( i p @u ulst / dn ) (if (= 0.0 (setq dn (- (nth (+ i p 1) ulst) (nth (+ i 1) ulst)))) 0.0 (/ (- (nth (+ i p 1) ulst) @u) dn)) );end (defun i@u ( p @u ulst / i imx ) ;Initial values (setq i 0 imx (- (length ulst) p 2)) ;Is @u within the knots domain definition? (if (<= (car ulst) @u (nth (1+ imx) ulst)) (if (= @u (nth (1+ imx) ulst)) imx (while (<= (nth (1+ i) ulst) @u) (setq i (1+ i)))) ) );end (defun Bin@u ( i p @u ulst / i* iu binlst ) (if (setq iu (i@u p @u ulst)) (progn (setq i* i binlst nil) (While (<= i* (+ i p)) (setq binlst (if (= i* iu) (cons (list i* 0 1.0) binlst) (cons (list i* 0 0.0) binlst) ) ) (setq i* (1+ i*)) ) ;Retval (reverse binlst) ) ) );end ;Loop (if (setq binlst (Bin@u i p @u ulst)) (repeat p (setq n 0 niplst nil) (setq binlst (reverse (repeat (1- (length binlst)) (setq b1 (nth n binlst) b2 (nth (setq n (1+ n)) binlst)) (setq i (car b1) p (1+ (cadr b1)) bin (caddr b1) bin+ (caddr b2)) (setq bin (list i p (+ (* (f@u i p @u ulst) bin) (* (g@u i p @u ulst) bin+)))) (setq niplst (cons bin niplst)) ) ) ) ) ) ;Retval (caddar binlst) ;------------- );Endof//Nips@u ;------------- ;++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ;+++++++++++++++++ DEMONSTRATION ++++++++++++++++++++++ ; * grSpline GRDRAW an spline ; * st [int] Spline status Clamped, Closed... ; * p [int] Spline degree 1-2-3--5-6 .... 10 ; * ulst [list] List of Knots vectors u0 u1 .... um ; * plst [list] List of control points in WCS ; * ns [Real] Number of segments for each knot vectors ; * (precision for curve presentation) ; * ; * +++++++++++ FOR EXAMPLE ++++++++++++++++ ; * +++++ Let say we have the following data ;| (setq p 3 st 0 ns 10) Clamped opened curve of degree 3 (setq plst '( (74.8 96.5 0.0) (105.6 51.6 0.0) (163.7 130.5 0.0) (209.8 130.6 0.0) (252.3 85.2 0.0) (310.1 223.9 0.0) (111.3 237.4 0.0) ) ) m=n+p+1=7+3+1=11 m:length of ulst n:number of control points p:degree (setq ulst '(0.0 0.0 0.0 0.0 1.0 2.0 3.0 4.0 4.0 4.0 4.0)) Now, Grdraw the Spline curve according to the above data (grSpline st p ulst plst ns) |; ;========================================================== (defun grSpline ( st p ulst plst ns / imx @umx n du @u pt ) ;========================================================== ;Initial values (setq imx (- (length ulst) p 2)) (setq @umx (nth (1+ imx) ulst) n (length plst) du (/ (apply 'min (vl-remove 0.0 ulst)) ns)) ;Nurbs status (cond ;Uniform Non-Rational Nurbs (Clamped) ((= st 0) (setq @u (nth 0 ulst))) ;Uniform Non-Rational Nurbs (AutoCAD Closed) ((= st 1) (setq @u (nth 0 ulst))) ;Uniform Non-Rational Nurbs (Opened) ((= 2 st)) ;Not applicable at moment ;Uniform Non-Rational Nurbs (Closed) ((= 3 st) (setq @u (nth (1- p) ulst))) ) ;Loop over Knots vectors (setq pt (Nurbs@u p @u ulst plst)) (while (< (setq @u (+ @u du)) (+ @umx du)) (if (> @u @umx) (setq @u @umx)) (cond ((vl-position st '(0 1)) (grdraw pt (setq pt (Nurbs@u p @u ulst plst)) 1)) ((= 2 st)) ((= 3 st) (if (< (nth (1- p) ulst) @u (nth (+ n (* -2 p) 1) ulst)) (grdraw pt (setq pt (Nurbs@u p @u ulst plst)) 1) ) ) ) ) ;---------------- );Endof//grSpline ;----------------

The above code is based on the form shown in the figure

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

diagodose2009 — Sun, 12 Dec 2021 12:28:45 GMT

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Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

hak_vz — Sun, 12 Dec 2021 13:15:28 GMT

@_Bilal

Here you have my code related to Catmull-Rom spline. Simple principle can be applied to Nurbs curves.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

stevor — Sun, 12 Dec 2021 13:17:31 GMT

Did not run it, but a syntax check :

about line 80, in (defun grSpline

it probably should be:

du (/ (apply 'min (vl-remove 0. ulst)) ns) ; revised

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

hak_vz — Sun, 12 Dec 2021 13:21:26 GMT

@diagodose2009 Why not supply direct solution written in autolisp/visual lisp. This forum is about autolisp/visual lisp and not about conversion from c++ or anything else. Your software is great but this is not the point of this forum. What we looking fore is a simple code that can me human readable and can be used to beginner programmers to learn some codding techniques. Maybe I', wrong but I just see it that way.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

leeminardi — Sun, 12 Dec 2021 14:56:54 GMT

As noted by @stevor , there's a problem in the line

(setq @umx (nth (1+ imx) ulst) n (length plst) (apply 'min (vl-remove 0.0 ulst)) du (/ ns))

; error: bad variable name in SETQ: (APPLY (QUOTE MIN) (VL-REMOVE 0.0 ULST))

For my better understanding of NURBS math I created a custom VBA/Excel B-spline function hoping to tackle the more complex NURBS math later. If the weight values for all the CVs of a NURBS spline equal 1 then the NURBS curve reduces to a B-spline. The attached macro-enable Excel file includes the example data from your listing and a plot of the resulting curve. The program uses the recursive deBoor algorithm to compute the coefficients for the B-spline function. It successively duplicates the splines created in AutoCAD with the default weight of 1 for all CVs.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Sun, 12 Dec 2021 16:54:59 GMT

Thank you for your comment, I fixed now.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Sun, 12 Dec 2021 17:12:24 GMT

The macro in your excel excel file is great, it do the same recursive calculation as in my code Nips@u and Nurbs@u posted here, but when I changed the curve degree from 3 to 5 in your excel file the recursive calculation doesnt works!!

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Sun, 12 Dec 2021 17:15:47 GMT

I saw your code two days ago, it's great.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

leeminardi — Sun, 12 Dec 2021 17:53:40 GMT

I think this version of the Excel/VBA B-spline function should handle degree changes correctly.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Sun, 12 Dec 2021 18:04:38 GMT

The same problem exists in both versions!

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

leeminardi — Sun, 12 Dec 2021 19:47:46 GMT

Can you post a copy of the file with the data you are using and note the degree you want to use?

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Sun, 12 Dec 2021 21:27:08 GMT

I utilized the same data in the file, just I changed the degree from 3 to 5, the result as show in the figure (before/after)

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

leeminardi — Sun, 12 Dec 2021 22:00:18 GMT

Here's what I see.

Are you sure you have macros enabled? The cells are showing that they don't recognize the custom function.

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

_Bilal — Mon, 13 Dec 2021 08:48:37 GMT

All right, it was my mistake, the macro was disabled, I enabled the macro and it is working now

Re: NURBS Equations evaluation, De Boor's algorithm with Autolisp

diagodose2009 — Sat, 15 Jan 2022 17:23:51 GMT

Perhaps you build Applet.zip before the programs.Lisp.ascii was written.