Napiers formula
- To: mathgroup at smc.vnet.net
- Subject: [mg17629] Napiers formula
- From: Kjell Stenman <kjells at ydab.se>
- Date: Fri, 21 May 1999 03:37:27 -0400
- Organization: ITV
- Sender: owner-wri-mathgroup at wolfram.com
My problem is to decide which point that is the true point. I want to calculate a intersection point on the average earth (radius = 6371000 meter) The formula I use is Napier´s equations (10a & 10b). A = point1 B = point2 I = Intersection point beta = bearing A to B - bearing A to I gamma = bearing B to I - bearing B to A It says: k1 = cos((beta + gamma)/2); /* 10a */ k2 = tan(a/2) * cos((beta - gamma) / 2); k3 = atan(k2/k1) * 2; // b + c = k3 k4 = sin((beta + gamma) / 2); /* 10b */ k5 = tan(a/2) * sin((beta - gamma)/2); k6 = atan(k5/k4) * 2; // b - c = k6 -> c = b - k6 bb = fabs((k6 + k3)/2); // b + b - k6 = k3 ->2b = k3 + k6 cc = fabs(bb - k6); lengthn_b = bb * 6371000; lengthn_c = cc * 6371000; if I move point A lengthn_b (meter) in direction A to I, I believe I got the intersection point (p1) if I move point B lengthn_c (meter) in direction B to I, I believe I got the intersection point (p2) but p1 != p2 Where is the error? :