(41) Intersection points between circles
12-01-2020, 02:04 PM (This post was last modified: 12-01-2020 04:29 PM by rawi.)
Post: #12
 rawi Member Posts: 174 Joined: Nov 2019
RE: Intersection points between circles
Hi Albert,

I tried it and you are totally right. Thanks for pointing that out to me.

Here is the improved method description:

Let (x1, y1) be the coordinates of midpoint of circle 1 and (x2, y2) be the coordinates of midpoint of circle 2 and r1 resp. r2 be the radii.
Let z be the distance between the midpoints: z=((x1-x2)²+(y1-y2)²)^0.5
The angle alpha between the line between the midpoints and the parallel to the x-axis through (x1, y1) using the sinus-function is:

alpha = arcsin((y2-y1)/z)
Beta can be computed by using the Law of Cosine:

beta = arccos((z²+r1²-r2²)/(2*z*r1))
We must take into account, whether x2<x1 or x2>=x1.
We set sg = 1 if x2>=x1 and sg1 = -1 if x2<x1
Then the coordinates of the two intersection points are:

sx1 = x1 + r1*(cos(alpha+beta))*sg
sy1 = y1 + r1*(sin(alpha+beta))
sx2 = x1 + r1*(cos(alpha-beta))*sg
sy2 = y1 + r1*(sin(alpha-beta))

And here is the improved code, which is shorter and easier than the previous one:

Code:
01 LBL „CIP“ 02 CF 01 03 “CIRCLE1?” 04 PROMPT        Input of midpoint and radius of circle 1 05 STO 03 06 RDN 07 STO 02 08 RDN 09 STO 01 10 “CIRCLE2?” 11 PROMPT        Input of midpoint and radius of circle 2 12 STO 06 13 RDN 14 STO 05 15 RCL 02 16 - 17 X² 18 X<>Y 19 STO 04 20 RCL 01  21 X>Y? 22 SF 01 23 - 24 X² 25 + 26 SQRT 27 STO 07        Distance between midpoints 28 RCL 05 29 RCL 02 30 - 31 X<>Y 32 / 33 ASIN 34 STO 08        Angle between line between midpoints and x-axis 35 RCL 07 36 X² 37 RCL 03 38 X² 39 + 40 RCL 06 41 X² 42 - 43 2 44 / 45 RCL 07 46 / 47 RCL 03 48 / 49 ACOS 55 STO 09 51 + 52 COS 53 LASTX 54 SIN 55 RCL 03 56 * 57 RCL 02 58 + 59 STO 12 60 X<>Y 61 RCL 03 62 * 63 FS? 01 64 CHS 65 RCL 01  66 + 67 STO 11 68 STOP        X-register: x-coordinate, Y register: y-coordinate of first intersection point 69 RCL 08 70 RCL 09 71 - 72 COS 73 LASTX 74 SIN 75 RCL 03 76 * 77 RCL 02 78 + 79 STO 14 80 X<>Y 81 RCL 03 82 * 83 FS? 01 84 CHS 85 RCL 01 86 + 87 STO 13 88 GTO 02 89 LBL 01 90 “NO SOLUTION” 91 AON 92 STOP 93 AOFF 94 LBL 02 95 CF 01 96 END
 « Next Oldest | Next Newest »

 Messages In This Thread (41) Intersection points between circles - rawi - 11-25-2020, 03:07 PM RE: Intersection points between circles - Albert Chan - 11-25-2020, 06:16 PM RE: Intersection points between circles - rawi - 11-25-2020, 06:48 PM RE: Intersection points between circles - Albert Chan - 11-26-2020, 12:22 AM RE: Intersection points between circles - Albert Chan - 11-30-2020, 02:19 PM RE: Intersection points between circles - rawi - 11-30-2020, 05:19 PM RE: Intersection points between circles - Albert Chan - 11-30-2020, 09:03 PM RE: Intersection points between circles - Albert Chan - 12-01-2020, 12:17 AM RE: Intersection points between circles - SlideRule - 11-30-2020, 08:51 PM RE: Intersection points between circles - rawi - 12-01-2020, 09:25 AM RE: Intersection points between circles - Albert Chan - 12-01-2020, 11:59 AM RE: Intersection points between circles - rawi - 12-01-2020 02:04 PM RE: Intersection points between circles - Albert Chan - 12-10-2020, 01:34 PM

User(s) browsing this thread: 1 Guest(s)