trigonometry

I'm creating a simple 2D game in javascript/canvas. I need to figure out the angle of a certain object relative to my position. So: say I'm at (10,10) and the object is at (10,5) - that would result in 90 degrees (as positive Y is down, negative Y is up) (10,10) vs (10,15) would be 270 degrees. How would I go about this? Suppose you're at (a, b) and the object is at (c, d). Then the relative position of the object to you is (x, y) = (c - a, d - b). Then you could use the Math.atan2() function to get the angle in radians. var theta = Math.atan2(-y, x); note that the result is in the range [-π,

I am basically making a Java program that will have to run a lot of calculations pretty quickly(each frame, aiming for at least 30 f/s). These will mostly be trigonometric and power functions. The question I'm asking is: Which is faster: using the already-supplied-by-Java Math functions? Or writing my own functions to run? The built-in Math functions will be extremely difficult to beat, given that most of them have special JVM magic that makes them use hardware intrinsics. You could conceivably beat some of them by trading away accuracy with a lot of work, but you're very unlikely to beat the

Given circle centre: vectorA and another Vector on the circle's perimeter:vectorB, how can you determine the shorter route for vectorB to translate to another point on the circle's perimeter that is variable:vectorC? Will the shorter route be clockwise or counter clockwise rotation? If it helps think of a clock. If the times is a random point on the clock's perimeter eg. 6, and the minute hand position is known, eg. 4. Does the hand need to rotate around the clock's centre point clockwise or counter clockwise to reach the random point (6)? See also: Vec1 = Circle centre, Vec2 = mousepos, find

Below is the code I am currently using. With 0 rotation, the image is correctly scaled to fill the canvas. (similar to background-size: cover , except using JavaScript on a Canvas) I'm trying to add a rotate feature, with the following features. Keep image centered while rotating. I tried using width / 2 in translate , and then the opposite in drawImage , but as you can see the image did not stay centered. I'm not sure if this is a conflict with my earlier x and y centering code, or if trigonometry is required here? Automatically scale the image further to cover the canvas. These are arbitrary