1
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0answers
24 views

How to find Latitudes and Longitudes of projections of the vertices of a rectangular plane below earth's surface?

I want to find out the latitudes and longitudes of projections of the vertices of a rectangular plane inside the earth's surface. I know dimensions of rectangle, angles of orientation and latitude and ...
1
vote
2answers
69 views

Computing distance from line to point in geodetic environment

Supposing to be in a cartesian plan and that I have the following point: $$A(x_{1},y_{1}), B(x_{2},y_{2}), C(x_{3},y_{3}), D(x_{4},y_{4})$$ $$P(x_{0},y_{0})$$ Now immagine two lines, the fist one ...
2
votes
2answers
739 views

Different ways for calculating distance between two geodetic points give me different results

I'm trying to calculate the distance between two geodetic points in two different ways. The points are: A:(41.466138, 15.547839) B:(41.467216, 15.547025) The ...
1
vote
1answer
52 views

Which icosahedral triangles projected onto sphere's surface contain points in P?

I am working on a Python script to: Compute the vertex coordinates of a geodesic sphere/icosahedron, Project the triangles onto a sphere, then Find which spherical triangle contains an arbitrary ...
1
vote
2answers
668 views

Determine depth of a partially filled hemisphere

Recently came across a question in a Year 9 math book of which there was no "working out" supplied and offers now description on how they obtained the answer. The question goes like this: A bowl ...
0
votes
1answer
36 views

approximation of law sines from spherical case to planar case

we know for plane triangle cosine rule is $\cos C=\frac{a^+b^2-c^2}{2ab}$ and on spherical triangle is $ \cos C=\frac{\cos c - \cos a \cos b} {\sin a\sin b}$ suppose $a,b,c<\epsilon$ which are ...
0
votes
1answer
67 views

The law of cosines for a sphere

$\cos(c) = \cos(a)\cos(b) + \sin(a)\sin(b)\cos(C)$ Prove that if $a$, $b$, and $c$ is approximately $0$, then $c^2 = a^2 + b^2 - 2ab~\cos(C)$. I wasn't sure how to prove this. One thought I had was ...
1
vote
1answer
193 views

Distance measurement between latitude/longiture pairs.

I need to calculate the distance between two lat/lng coordinate pairs. In addition, If given an initial lat/lng coordinate, angle of travel, and distance, I need to calculate the resulting lat/lng ...
8
votes
1answer
231 views

Circle on sphere

Foreword This question was inspired by initial mistakes in this question. I wanted to explore the strange circle with $A>\pi r^2$ and got lost into geometrical jungle. A spherical cap is usually ...
2
votes
1answer
2k views

Angle between GPS coordinates

I realize GPS Coordinates are spherical coordinates. However I know the earth is more of an ellipsoid. I need to compute with a fairly high degree of accuracy the pitch and yaw between two objects ...
2
votes
1answer
169 views

Sine rule and equal angles

Is it true that if a triangle on a unit sphere has 2 sides with equal length then their opposit angles must be equal? I think it is true. I think we can use the spherical sine law. Call the sides with ...
0
votes
1answer
321 views

I have equations for getting x,y,z given latitude, longitude, and altitude. How do I reverse them?

I am using equations that look like the following to get x, y, and z given latitude, longitude, and altitude. ...
0
votes
1answer
662 views

Using the spherical law of cosines

Compute angular length c of the great-circle route between these two cities: Daytona Beach (location A): $29^\circ12'\ N, 81^\circ1' \ W$. Sidi Ifni (location B): $29^\circ23' \ N. 10^\circ10' \ ...
3
votes
2answers
3k views

Napier's Rules applied to spherical distance calculations

I was in the middle of writing the same old geographic distance calculation using the Haversine formula when it occurred to me: shouldn't there be simpler way to do this? Haversine is of course ...
6
votes
1answer
864 views

How to calculate a heading on the earths surface?

Given an initial position and a subsequent position, each given by latitude and longitude in the WGS-84 system. How do you determine the heading in degrees clockwise from true north of movement?