Output of file : LAUZZANA.LST contained in archive : DDJ-9008.ZIP
_IMPLEMENTING BICUBIC SPLINES_
by G. Raymond Lauzzana and Denise E.M. Penrose

[LISTING ONE]

/* include all of the files that you might need. */

#include
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/* --------------------------------------------------------------------- */
/* The low-level help functions for graphics. */

/* Mean-squared distance between to coordinate pairs. */

int distance(i0, j0, i1, j1)
int i0, j0, i1, j1;
{ int res;
double x1, x2, y1, y2;

x1 = i0; x2 = i1; y1 = j0; y2 = j1;
res = sqrt((x1-x2)*(x1-x2) + (y1-y2)*(y1-y2));
return(res);
}

/* --------------------------------------------------------------------- */
/* The low-level SPLINE function. This function calculates and draws a
curved line along the path of a bi-cubic spline the equation for a coordinate
of the points on the spline is:
j = j1*t + j2*(1 - t) + W*(j2-j3)*t*(1 - t)*(1 - t) + W*(j1-j0)*t*t*(1 - t);
where: j : the coordinate being calculated.
t : the cubic variable.
W : a weighting factor.
(j1, j2) : the end-coordinates of the spline.
(j0, j3) : The control coordinates.
*/

_Spline (i0, j0, i1, j1, i2, j2, i3, j3)
int i0, j0, i1, j1, i2, j2, i3, j3;
{ float dt, t0, t1, t2, t3, t5, inc, dist, W;
int i, j, i5, j5, count;

inc = 2.5; /* Two pixel wide sampling rate */
W = 0.9; /* Set the weighting factor. */
MoveTo(j1, i1); /* Move to P1 */
dist = distance(i1, j1, i2, j2); /* The distance between the two points*/
if (inc < dist)
{ j5 = j1-j0;
i5 = i1-i0;
j3 = j2-j3;
i3 = i2-i3;
dt = inc/dist; /* Transform the sampling rate to a function of T */
count = 1.0/dt; /* Number of samples to be taken in a unit interval */
while (count-- > 0)
{ t1 = dt*count; /* calculate I and J as a function of T */
t2 = 1.0 - t1; /* (1 - t) */
t5 = W*t1*t1*t2; /* W*t*t*(1 - t) */
t3 = W*t1*t2*t2; /* W*t*(1 - t)*(1 - t) */
j = j1*t1 + j2*t2 + t3*j3 + j5*t5;
i = i1*t1 + i2*t2 + t3*i3 + i5*t5;
LineTo(j, i);
} }
else LineTo(i2, j2);
}

[LISTING TWO]

;; ----------------------------------------------------------------------
;; You need to change this to the directory where you have stored FF.fasl

;; ----------------------------------------------------------------------
;; You need to change this to the directory where C libraries is stored
(def-logical-pathname "CLIB;" "Lauzzana:Ray:Projects:Artifex:CLIB")

;; ----------------------------------------------------------------------
;; The high-level SPLINE function
(defun SPLINE (&rest p)
"
SPLINE (&rest point-list)

Sets up the front window as a graphics port to draw in, and calls
DO-SPLINE to do the actual work of drawing a spline.

"
(with-port (ask (front-window) wptr) (do-spline p)))

(defun DO-SPLINE (p)
"
D0-SPLINE (point-list)

A smooth curve coonecting the points.

"
(let ((p1 (car p))
(cond ((or (null (pointp p1)) (null (pointp p4))) nil)
((and (pointp p1) (pointp p2) (pointp p3) (pointp p4))
(_Spline (I-coord p1)
(J-coord p1)
(I-coord p2)
(J-coord p2)
(I-coord p3)
(J-coord p3)
(I-coord p4)
(J-coord p4))
(if (pointp p5)
(append (list 'SPLINE p1) (cdr (DO-SPLINE (cdr p))))
(cons 'SPLINE p))))))

;; ----------------------------------------------------------------------
;; The high-level help functions for graphics
;; @@, representation for a point.
(defun @@ (a &optional b)
"
@@ () or (I-coordinate J-coordinate) or (integer)
A single user point or a point.

A screen location, in physical coordinates. (@@ 0 0) is the upper-left
corner. If single integer is recieved it is interpretted as a packed point,
and it is unpacked into a coordinate pair.

"
(cond ((and (numberp a) (numberp b)) (list '@@ (round a) (round b)))
((numberp a) (let ((i (floor (/ a 65536))))
(list '@@ i (- a (* 65536 i)))))))

;; The type test for a POINT.
(defun POINTP (p)
"
POINTP (item)

If the item is a point represented in in coordinates, ie. (@@ I J)
then TRUE, else NIL.

"
(and (listp p)
(or (= 3 (length p)) (= 2 (length p))) (equal (car p) '@@)))

;; I-COORDINATE
(defun I-COORD (p)
"
I-COORD (point)

Returns the vertical screen coordinate of a point.

"

;; J-COORDINATE
(defun J-COORD (p)
"
J-COORD (point)

Returns the horizontal screen coordinate of a point.

"
;; ----------------------------------------------------------------------
;; The binding to the low-level SPLINE function
;; There are two methods to bind a C function to Allegro.
;; The first method uses DEFFCFUN. Though this is a simpler function,
;; The binding will be lost if you build a stand-alone application.
;; Using DEFFCFUN the code would be:
;; (deffcfun (Mac_Spline "_Spline")
;; (integer integer integer integer integer integer integer integer) :novalue)
;; The second and preferred method uses MULTIPLE-VALUE-BIND and FF-CALL
;; to bind a physical entry-point to a symbol. This is a hardware dependent
;; solution, in that you need to represent the binding in terms of the
;; physical size and ordering of the machines stack. In the case of the
;; Mac II, parameters are stored in reverse order on the stack. Therefore,
;; the foreign function call must reverse the order of the parameters.
;; MULTIPLE-VALUE-BIND is used to perform the mapping of parametes.
;; FF-LOOKUP-ENTRY find the physical address of the entry-point for function.
;; FF-CALL executes the coda stored at a physical address.

(defun _Spline (a b c d e f g h)
"
_Spline (i0 j0 i1 j1 i2 j2 i3 j3)

Draws a spline between p1 and p2 to the control points p0 and p3.
"
(multiple-value-bind (entry a5) (ff-lookup-entry "_Spline")
(ff-call entry
:a5 a5 :long h :long g :long f :long e :long d :long c :long b :long a
:novalue)))

;; ----------------------------------------------------------------------
;; FF-LOAD is used to load binary files and their associated libraries.
;; In this case the object module for the function _Spline is stored in
;; the file . FF-LOAD searches this file for the symbolic name
;; _Spline and load the binary code associated with it.
;; In addition, it searches the libraries for unsatisfied symbolic references

;; which which may have occurred within the code and loads them as well.
;; You need to change this to the directory where you have stored your C spline

:entry-names
(list "_Spline" )
:libraries
(list "CLIB;StdCLib.o" "CLIB;CRuntime.o" "CLIB;CInterface.o"
"CLIB;math.o" "CLIB;CSANElib.o"))

[Example 1: Cubic equations]

j = j1t + j2(1 - t) + W(j2 - j3)(1 - t)2t + W(j1 - j0)(1 - t)t2
i = i1t + i2(1 - t) + W(i2 - i3)(1 - t)2t + W(i1 - i0)(1 - t)t2

[Example 2: Calculating coordinates]

while (t < 1)
{ j = j1*t + j2*(1 - t) + W*(j2-j3)*t*(1 - t)*(1 - t) + W*(j1-j0)*t*t*(1 - t);
i = i1*t + i2*(1 - t) + W*(i2-i3)*t*(1 - t)*(1 - t) + W*(i1-i0)*t*t*(1 - t);
t = t + dt;
LineTo(i,j);
}

[Example 3: Partitioning the equation shown in Example 2.]

while (t1 < 1)
{ t1 = t1 + dt;
t2 = 1.0 - t1;
t5 = W*t1*t1*t2;
t3 = W*t1*t2*t2;
j = j1*t1 + j2*t2 + t3*j3 + j5*t5;
i = i1*t1 + i2*t2 + t3*i3 + i5*t5;
LineTo(j, i);
}

(a)

(require 'FF)

(b)

(c)

(def-logical-pathname "CLIB;" ":MPW:CLibrary")

(d)

:entry-names
(list "_Spline" )
:libraries
(list "CLIB;StdCLib.o" "CLIB;CRuntime.o" "CLIB;CInterface.o"
"CLIB;math.o" "CLIB;CSANElib.o"))

[Example 5: Binding C to Lisp]

(a)

(deffcfun (Mac_Spline "_Spline")
(integer integer integer integer integer integer integer integer) :novalue)

(b)

(defun Mac_Spline (a b c d e f g h)
(multiple-value-bind (entry a5) (ff-lookup-entry "_Spline")
(ff-call entry
:a5 a5 :long h :long g :long f :long e :long d :long c :long b :long a :novalue)))

(c)

(Mac_Spline 3 4 120 140 300 260 490 600)



### 3 Responses to “Category : Files from MagazinesArchive   : DDJ-9008.ZIPFilename : LAUZZANA.LST”

1. Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

2. This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

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