The jsMath package is an option that uses LaTeX markup and native fonts. Quoting from their webpage http://www.math.union.edu/~dpvc/jsMath/: The jsMath package provides a method of including mathematics in HTML pages that works across multiple browsers under Windows, Macintosh OS X, Linux and other flavors of unix. It overcomes a number of the shortcomings of the … Read more
I guess it should not be difficult to find the spherical polar coordinates from x,y,z (3d-coordinate system). r is always constant if it’s on surface. (90 – θ) your latitude (negative means it’s on the bottom) as it’s measured from top. φ is your longitude. (but not quite sure about longitude system) Also check this … Read more
Notation As is the convention both in mathematics and programming, the “log” function is taken to be base-e. The “exp” function is the exponential function. Remember that these functions are inverses we take the functions as: exp : ℝ → ℝ+, and log : ℝ+ → ℝ. Solution You’re just solving a simple equation here: … Read more
Your teacher gave you: Public Key: (10142789312725007, 5) which means n = 10142789312725007 e = 5 where n is the modulus and e is the public exponent. In addition, you’re given Private Key: (10142789312725007, 8114231289041741) meaning that d = 8114231289041741 where d is the decryption exponent that should remain secret. You can “break” RSA by … Read more
Let P0, P1, P2 be the control points, and Pc be your fixed point you want the curve to pass through. Then the Bezier curve is defined by P(t) = P0*t^2 + P1*2*t*(1-t) + P2*(1-t)^2 …where t goes from zero to 1. There are an infinite number of answers to your question, since it might … Read more
Binary floating point math is like this. In most programming languages, it is based on the IEEE 754 standard. The crux of the problem is that numbers are represented in this format as a whole number times a power of two; rational numbers (such as 0.1, which is 1/10) whose denominator is not a power … Read more
Contrary to popular belief in the computer graphics industry, there is a straightforward algorithm to solve this problem which is robust, accurate, and simple that comes from the aerospace industry. It runs in time linear in the number of quaternions being averaged plus a (largish) constant factor. Let Q = [a1q1, a2q2, …, anqn], where … Read more
Paraphrased from the wikipedia article on Mercator projection: Given a “mapping sphere” of radius R, the Mercator projection (x,y) of a given latitude and longitude is: x = R * longitude y = R * log( tan( (latitude + pi/2)/2 ) ) and the inverse mapping of a given map location (x,y) is: longitude = … Read more
Use options(scipen=5) or some other high enough number. The scipen option determines how likely R is to switch to scientific notation, the higher the value the less likely it is to switch. Set the option before making your plot, if it still has scientific notation, set it to a higher number.
It seems you are measuring distance (R) in meters, and bearing (theta) counterclockwise from due east. And for your purposes (hundereds of meters), plane geometry should be accurate enough. In that case, dx = R*cos(theta) ; theta measured counterclockwise from due east dy = R*sin(theta) ; dx, dy same units as R If theta is … Read more