trigonometry

I have two functions that are intended to contain angles between (-180,180] and (-π,π]. The intent is that given any angle from -inf to +inf it will retain the equivalent angle in the intervals specified. For example the angle for 1550° is 110°. public double WrapBetween180(double angle) { return angle - 360d * Math.Round(angle / 360d, MidpointRounding.AwayFromZero); } public double WrapBetweenPI(double angle) { const double twopi = 2d * Math.PI; return angle - twopi * Math.Round(angle / twopi, MidpointRounding.AwayFromZero); } which yields the following results WrapBetween180(-180) = -180

As a Matlab user transitioning to R, I have ran across the problem of applying trigonometric functions to degrees. In Matlab there are trig functions for both radians and degrees (e.g. cos and cosd, respectively). R seems to only include functions for radians, thus requiring me to create my own (see below) cosd<-function(degrees) { radians<-cos(degrees*pi/180) return(radians) } Unfortunately this function does not work properly all of the time. Some results are shown below. > cosd(90) [1] 6.123234e-17 > cosd(180) [1] -1 > cosd(270) [1] -1.836970e-16 > cosd(360) [1] 1 I'd like to understand

I've spent a couple days at this and I give up. I'm trying to get an object to animate along a sine wave infinitely. It should not end after the first period. Main Problem: The cycle ends at approx 1 1/3 Pi rather than just Pi. This extra movement ruins the animation. I'm stuck here: http://jsfiddle.net/WPnQG/12/ . After each period, it skips about 40 pixels and then continues along its path. This is the problem I can't get past -- the value it ends at and proceeds to restart at are not equal, so the object appears to skip around. Could anyone help a man out? Thanks I am using the jQuery Path

Using Java on a Windows 7 PC (not sure if that matters) and calling Math.cos() on values that should return 0 (like pi/2) instead returns small values, but small values that, unless I'm misunderstanding, are much greater than 1 ulp off from zero. Math.cos(Math.PI/2) = 6.123233995736766E-17 Math.ulp(Math.cos(Math.PI/2)) = 1.232595164407831E-32 Is this in fact within 1 ulp and I'm simply confused? And would this be an acceptable wrapper method to resolve this minor inaccuracy? public static double cos(double a){ double temp = Math.abs(a % Math.PI); if(temp == Math.PI/2) return 0; return Math.cos

I'm trying to find a way to calculate the intersection between two arcs. I need to use this to determine how much of an Arc is visually on the right half of a circle, and how much on the left. I though about creating an arc of the right half, and intersect that with the actual arc. But it takes me wayyy to much time to solve this, so I thought about asking here - someone must have done it before. Edit: I'm sorry the previous illustration was provided when my head was too heavy after crunching angles. I'll try to explain again: In this link you can see that I cut the arc in the middle to two

I'm trying to find a point that is equal distance away from the middle of a perpendicular line. I want to use this point to create a Bézier curve using the start and end points, and this other point I'm trying to find. I've calculated the perpendicular line, and I can plot points on that line, but the problem is that depending on the angle of the line, the points get further away or closer to the original line, and I want to be able to calculate it so it's always X units away. Take a look at this JSFiddle which shows the original line, with some points plotted along the perpendicular line:

I wish to get the acceleration vector of an Android phone. The problem is, the accelerometer coordinates are relative to the phone's rotation. What I want is the "absolute" acceleration, i.e., it should return the same values whichever way the phone is facing. (I want to detect if a user that is skiing is sliding down a slope without using GPS. I also need to be able to differentiate sliding and going up the chairlift.) I can probably get those values by combining the accelerometer with the gyroscope, but I have no idea how I could offset the accelerometer's values with the gyroscope's. Is