Question about recursive function
Hello all. First time poster, but long-time OpenSCAD user (2+ yrs).
I have the following code.
//Obtain vector of points on circumference of circle of radius = 50, start
angle=10, end angle=45, step of 2 degrees
circum_pts1 = circum_pts([[]], 10, 50, 2, 45);
echo(circum_pts1);
function circum_pts(pts, angle, rad, angle_step = 1, end_angle=360) =
let(x =rad * cos(angle))
let(y =rad * sin(angle))
angle < (end_angle+1) ?
concat(pts, [[x,y]], circum_pts(pts, angle+angle_step, rad, angle_step,
end_angle))
:
pts;
//-- End function ------------
This outputs the following value for result
ECHO: [[], [49.2404, 8.68241], [], [48.9074, 10.3956], [], [48.5148,
12.0961], [], [48.0631, 13.7819], [], [47.5528, 15.4508], [], [46.9846,
17.101], [], [46.3592, 18.7303], [], [45.6773, 20.3368], [], [44.9397,
21.9186], [], [44.1474, 23.4736], [], [43.3013, 25], [], [42.4024, 26.496],
[], [41.4519, 27.9596], [], [40.4508, 29.3893], [], [39.4005, 30.7831], [],
[38.3022, 32.1394], [], [37.1572, 33.4565], [], [35.967, 34.7329], []]
Notice that every other value is a null value. I can program around this,
but would like to figure out how to avoid.
Any ideas?
Thanks
Kevin Toppenberg
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Let's see, working on this some more....
The following code gets rid of the every-other bad value. So this is
almost there. It just has a final null value that I wish I could get rid
of.
Thanks
Kevin
//Obtain vector of points on circumference of circle of radius = 50, start
angle=0, end angle=90, step of 10 degrees
circum_pts1 = circum_pts(0, 50, 10, 90);
echo(circum_pts1);
function circum_pts(angle, rad, angle_step = 1, end_angle=360) =
let(x =rad * cos(angle))
let(y =rad * sin(angle))
angle <= (end_angle) ?
concat([[x,y]], circum_pts(angle+angle_step, rad, angle_step,
end_angle))
:
[[]];
//-- End function ------------
ECHO: [[50, 0], [49.2404, 8.68241], [46.9846, 17.101], [43.3013, 25],
[38.3022, 32.1394], [32.1394, 38.3022], [25, 43.3013], [17.101, 46.9846],
[8.68241, 49.2404], [0, 50], []]
On Sun, Nov 11, 2018 at 5:11 PM kdtop kdtop3@gmail.com wrote:
Hello all. First time poster, but long-time OpenSCAD user (2+ yrs).
I have the following code.
//Obtain vector of points on circumference of circle of radius = 50, start
angle=10, end angle=45, step of 2 degrees
circum_pts1 = circum_pts([[]], 10, 50, 2, 45);
echo(circum_pts1);
function circum_pts(pts, angle, rad, angle_step = 1, end_angle=360) =
let(x =rad * cos(angle))
let(y =rad * sin(angle))
angle < (end_angle+1) ?
concat(pts, [[x,y]], circum_pts(pts, angle+angle_step, rad, angle_step,
end_angle))
:
pts;
//-- End function ------------
This outputs the following value for result
ECHO: [[], [49.2404, 8.68241], [], [48.9074, 10.3956], [], [48.5148,
12.0961], [], [48.0631, 13.7819], [], [47.5528, 15.4508], [], [46.9846,
17.101], [], [46.3592, 18.7303], [], [45.6773, 20.3368], [], [44.9397,
21.9186], [], [44.1474, 23.4736], [], [43.3013, 25], [], [42.4024, 26.496],
[], [41.4519, 27.9596], [], [40.4508, 29.3893], [], [39.4005, 30.7831], [],
[38.3022, 32.1394], [], [37.1572, 33.4565], [], [35.967, 34.7329], []]
Notice that every other value is a null value. I can program around this,
but would like to figure out how to avoid.
Any ideas?
Thanks
Kevin Toppenberg
--
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OpenSCAD mailing list
Discuss@lists.openscad.org
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On 11/11/2018 2:10 PM, kdtop wrote:
Hello all. First time poster, but long-time OpenSCAD user (2+ yrs).
I have the following code.
//Obtain vector of points on circumference of circle of radius = 50, start
angle=10, end angle=45, step of 2 degrees
circum_pts1 = circum_pts([[]], 10, 50, 2, 45);
echo(circum_pts1);
function circum_pts(pts, angle, rad, angle_step = 1, end_angle=360) =
let(x =rad * cos(angle))
let(y =rad * sin(angle))
angle < (end_angle+1) ?
concat(pts, [[x,y]], circum_pts(pts, angle+angle_step, rad, angle_step,
end_angle))
:
pts;
//-- End function ------------
This outputs the following value for result
ECHO: [[], [49.2404, 8.68241], [], [48.9074, 10.3956], [], [48.5148,
12.0961], [], [48.0631, 13.7819], [], [47.5528, 15.4508], [], [46.9846,
17.101], [], [46.3592, 18.7303], [], [45.6773, 20.3368], [], [44.9397,
21.9186], [], [44.1474, 23.4736], [], [43.3013, 25], [], [42.4024, 26.496],
[], [41.4519, 27.9596], [], [40.4508, 29.3893], [], [39.4005, 30.7831], [],
[38.3022, 32.1394], [], [37.1572, 33.4565], [], [35.967, 34.7329], []]
Notice that every other value is a null value. I can program around this,
but would like to figure out how to avoid.
Every call to circum_pts receives a "pts" array and returns that array,
with a point and a recursive call to circum_pts appended. Nothing ever
makes pts be anything other than what is initially passed in.
The initial call to circum_pts passes an array consisting of one empty
array. To that it appends the first [x,y] pair and the results from a
recursive call, so the result of that concat is [ [ ], [ x1, y1 ],
<recurse> ]. The first recursive call receives the same
array-of-empty-array, and so its concat is similarly [ [ ], [ x2, y2 ],
<recurse> ], and so when that gets returned, the result of the initial
concat is [ [ ], [ x1, y1 ], [ ], [ x2, y2 ], <recurse> ]. And so on.
The first step is to eliminate that "pts" parameter. It doesn't do
anything except contribute these empty arrays.
//Obtain vector of points on circumference of circle of radius = 50, start angle=10, end angle=45, step of 2 degrees
circum_pts1 = circum_pts(10, 50, 2, 45);
echo(circum_pts1);
function circum_pts(angle, rad, angle_step = 1, end_angle=360) =
let(x =rad * cos(angle))
let(y =rad * sin(angle))
angle < (end_angle+1) ?
concat([[x,y]], circum_pts(angle+angle_step, rad, angle_step, end_angle))
:
[];
//-- End function ------------
Note that the empty array at the end of the loop contributes no elements
to the concatenation, and that addresses the problem you saw in your
second message.
But really you're better off avoiding recursion entirely and using a
list comprehension:
function circum_pts2(angle, rad, angle_step, end_angle) = [
for (i = [angle:angle_step:end_angle]) [
rad * cos(i),
rad * sin(i)
]
];
I wouldn't code such a function as recursive function. It is much faster and
straight forward to code it as simple loop:
circum_pts1 = circum_pts(0, 50, 2, 90);
echo(circum_pts1);
polygon(circum_pts1); // visual control
function circum_pts(angle, rad, angle_step = 1, end_angle=360) =
[for(i=[angle:angle_step:end_angle]) rad*[cos(i), sin(i)]];
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I like your solution of having this all in 1 line. I didn't realize that
one could use the following pattern:
<for loop producing scalar> * [vector dependent on loop variable]
thanks!
Kevin
On Mon, Nov 12, 2018 at 7:03 AM Parkinbot rudolf@digitaldocument.de wrote:
I wouldn't code such a function as recursive function. It is much faster
and
straight forward to code it as simple loop:
circum_pts1 = circum_pts(0, 50, 2, 90);
echo(circum_pts1);
polygon(circum_pts1); // visual control
function circum_pts(angle, rad, angle_step = 1, end_angle=360) =
[for(i=[angle:angle_step:end_angle]) rad*[cos(i), sin(i)]];
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kdtop wrote
I like your solution of having this all in 1 line. I didn't realize that
one could use the following pattern:
<for loop producing scalar>
- [vector dependent on loop variable]
Good to know some basic tips, too:
- a*[b,c] = [ab,ac];
- a*[b,c,d] = [ab,ac,ad];
- [a,b]*[c,d] = ac + bd;
- [a,b,c]*[d,e,f] = ad + be + cf;
- [a,b,c]*[c,d] = undef;
- [a,b]*[d,e,f] = undef;
And, for points P,Q,R:
a. (P+Q)/2 = the mid point between P,Q;
(P+Q+R)/3 = the centroid point (the gravity) of PQR;
b. n*[P,Q] = a line parallel to line PQ;
n*[P,Q,R] = a plane parallel to plane PQR;
c. iP+jQ is:
--- on line PQ if i+j=1; // 1.2P -0.2Q
--- within PQ line segment if i+j=1 AND i,j>0 ; // 0.2P + 0.8Q
d. iP+jQ+kR is:
--- on plane PQR if i+j+k = 1; // 0.2P + 1.1Q - 0.3R
--- within PQR triangle if i+j+k=1 AND i,j,k>0 ; // 0.2P + 0.5Q + 0.3R
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer ); $ Tips ; $ Snippets
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kdtop wrote
I like your solution of having this all in 1 line. I didn't realize that
one could use the following pattern:
<for loop producing scalar>
- [vector dependent on loop variable]
Good to know some basic tips, too:
- a*[b,c] = [ab,ac];
- a*[b,c,d] = [ab,ac,ad];
- [a,b]*[c,d] = ac + bd;
- [a,b,c]*[d,e,f] = ad + be + cf;
- [a,b,c]*[c,d] = undef;
- [a,b]*[d,e,f] = undef;
And, for points P,Q,R:
a. (P+Q)/2 = the mid point between P,Q;
(P+Q+R)/3 = the centroid point (the gravity) of PQR;
b. n*[P,Q] = a line parallel to line PQ;
n*[P,Q,R] = a plane parallel to plane PQR;
c. iP+jQ is:
--- on line PQ if i+j=1; // 1.2P -0.2Q
--- within PQ line segment if i+j=1 AND i,j>0 ; // 0.2P + 0.8Q
d. iP+jQ+kR is:
--- on plane PQR if i+j+k = 1; // 0.2P + 1.1Q - 0.3R
--- within PQR triangle if i+j+k=1 AND i,j,k>0 ; // 0.2P + 0.5Q +
0.3R
$ Runsun Pan, PhD $ libs: scadx , doctest , faces ( git ), offline doc (
git ), runscad.py ( 2 , git ), editor of choice: CudaText ( OpenSCAD lexer
); $ Tips ; $ Snippets
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