Re: Calculate points in an arc
I'm not quite clear on what you're doing, but this looks more complicated
than need be.
Let's say one side is a horizontal line from point A to point B, and the
other side is a vertical line from point C to point D, and that B and C are
the two closest points.
Then, if the arc is a perfect semicircle, the center is (B.x, C.y) and the
radius is B.y - C.y (or C.x - B.x).
If the arc is not a perfect circle, then let X = C.x - B.x and Y = B.y -
C.y. You can produce an arc whose tangents match up perfectly to the
endpoints by constructing a circle with radius = min(X, Y) and then scaling
it. If X > Y then scale by (X/Y, 1), and if Y>X then scale by (1, Y/X).
On Mon, Apr 4, 2022 at 4:30 PM Jan Öhman via Discuss <
discuss@lists.openscad.org> wrote:
---------- Forwarded message ----------
From: "Jan Öhman" jan_ohman@yahoo.com
To: OpenSCAD General Discussion discuss@lists.openscad.org
Cc:
Bcc:
Date: Mon, 4 Apr 2022 21:30:27 +0000 (UTC)
Subject: [OpenSCAD] Calculate points in an arc
I have tried to make different calculations to put the rounded corners
together with a long bend.
I know the points where the long bend begins and where it ends, as well as
how high it should be.
but my calculations do not work
start (left)* x1=10.00, y1=49.25*
middle x2 = 60.50, y2 = 51
end (right) x3 = 101, y3 = 49.25
First, I calculate the radius of an imaginary circle using the formula
below
The center of the virtual circle has the coordinates x0 and y0
[image: Infoga bild]
s = x3 - x1 91,00000000
h = y2 - y1 1,75000000
r = ((s^2) + (4h^2)) / (8h) 592,37500000
h = r - ( rot(4 * r^2 - s^2) / 2) 1,75000000
s = 2 * rot( h * (2*r - h)) 90,99038411
x0 = x2 60,50000000
y0 = y2 – r -541,37500000
Previously, I calculated the angles of the circle sector and used "my"
function to create the [x,y]-values for the arc. (but failed)
Either the arc did not reach the start and stop values or it ended up a
little too high or low.
(I have no idea why)
In this caset, I thought to create a table with the start value first and
the end value last.
Now I know x0, y0 and the r (radius) - from above and use this
formula .:
[image: Infoga bild]
Rewrites the formula so that it becomes a function of y
Step1 .: r² = (x - x0)² + (y – y0)²
Step2 .: (y - b)² = r² - (x – a)²
Step3 .: y = ROT(r² - (x - x0)²)+y0
Finally, I set the start value (x1), middle value(x2)
and the end value(x3)
and calculate the y values.
x = *y0 = * desire difference
10 49,64766471 49,25 -0,397664708819093
60,5 51,49981502 51,5 0,00018497967755593
101 50,25505002 49,25 -1,00505001815964
(it was complicated to make the tables in the email)
I do not know why the calculated result differs from the desired value.
I think it's quite a lot - In the column on the far right - The center
point differed the least
(However, got better result than using angles)
What can be done to get an even better result?
[10, 49.25], [60.5, 51.5], [101, 49.25] (and many values between these)
Attach some code for possible test
$fa = 12;
$fs = 0.5;
fn = 50;
// y = 80-2000;
// points3 = circSect(0, 0, 2000, [0, 180], "left", 1, fn);
// points3 = circSect(0, 80-2000, 2000, [87, 93], "left", 1, 1000);
// points3 = circSect(55.5, 50.55-2000, 2000, [87.151, 92.826], "left", 1,
1000);
// polygon(points3);
p1x = 10; // the start value
p1y = 49.25;
p2x = 60.50; // the middle value
p2y = 51;
p3x = 101; // the end value
p3y = p1y;
// http://matmin.kevius.com/cirkel.php
// r = ((s^2) + (4h^2)) / (8h)
s = p3x - p1x; // 91
h = p2y - p1y; // 1.25
radius = ((s^2) + (4h^2)) / (8h); // 828.725
echo(s, s^2, h, 4h^2, 8h, radius);
echo("");
// http://www.rasmus.is/sv/t/G/su30k3.html
// deg = degrade( sin( a / radius ));
deg1 = asin( (s/2) / radius ); // 3.14733
deg2 = deg1*2; // 6.29466
echo( deg1, deg2 );
echo("");
// frDeg = 90-30;
// toDeg = 90+30;
frDeg = 90-deg1; // 3.8183 (3.872)
toDeg = 90+deg1; // (4)
xPos = 55;
yPos = 51.5-radius; // 50.79
points0 = circSect( xPos, yPos, radius, [frDeg, toDeg], "left", 1, 4000);
// Hörn nere till vänster
polygon(points0);
//points1 = circSect( 10, 11.25, 10, [0, 90], "bottom", 1, fn); // Hörn
nere till vänster
points2 = circSect( 10, 39.25, 10, [0, 90], "left", 1, 100); // Hörn
uppe till vänster
points3 = circSect( 101, 39.25, 10, [0, 90], "top", 1, 100); // Hörn
uppe till höger
//points4 = circSect( 101, 11.25, 10, [0, 90], "right", 1, fn); // Hörn
nere till höger
echo(points2) // [0,39.25] - [10, 49.25]
echo("");
echo(points0) // [9.5, 50.25] - [97.9774, 50.3849]
echo("");
echo(points3)
color("cyan"){
polygon(points0);
// polygon(points1);
polygon(points2);
polygon(points3);
// polygon(points4);
// polygon(concat(points2, points0, points3));
};
// polygon(concat(points1, points2, points3, points4));
// https://openhome.cc/eGossip/OpenSCAD/SectorArc.html
function circSect(x=0, y=0, radius=10, angles=[0,270], startRef="bottom",
rotate=1, fn=24) =
let(
startAngel = (startRef == "left") ? 0
: (startRef == "bottom") ? 90
: (startRef == "right") ? 180
: (startRef == "top") ? 270
: undef,
r = radius,
//r = radius / cos(180 / fn),
step = 360 / fn,
// points = [[x, y],
points = [
for(a = [angles[0]-startAngel : step : angles[1]-startAngel])
[-rotate * r * cos(a)+x, r * sin(a)+y]]
) points;
---------- Forwarded message ----------
From: "Jan Öhman via Discuss" discuss@lists.openscad.org
To: OpenSCAD General Discussion discuss@lists.openscad.org
Cc: "Jan Öhman" jan_ohman@yahoo.com
Bcc:
Date: Mon, 4 Apr 2022 21:30:27 +0000 (UTC)
Subject: [OpenSCAD] Calculate points in an arc
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