I know this is pretty obvious but I'm having some trouble with a simple calculation.
I have an object that has X and Y components for its speed.
I am calculating its total speed simply by square root of squares of the X and Y components:
var totalSpeed:Number = Math.sqrt(b.currentSpeedY * b.currentSpeedY + b.currentSpeedX * b.currentSpeedX);
I also have a variable called divergence, which is guaranteed to be between -1 and 1. According to the divergence, I calculate my new X component of the speed after the collision, by multiplying divergence and total speed:
var sX:Number = -totalSpeed * divergence;
Now, as I have the new X speed, and the total speed, I simply obtain my new Y speed by subtracting the square of my new X value from total speed, and taking its square root:
var sY:Number = -Math.sqrt(totalSpeed - (sX * sX));
Here is my problem: The total speed before and after the calculations don't match. I can confirm this by both printing the total speed (root of sum of squares) before and after the collision, and by simply looking at the speed of the objects visually. After collision, the speed of the object always tends to be slower.
I am obviously missing something very simple somewhere, but unfortunatelly couldn't find it anywhere. Where is the error that prevents total sums from matching?
In the sY calculatin it should be
var sY:Number = -Math.sqrt(totalSpeed * totalSpeed - (sX * sX));
Related
I have a variable of a that is equal to (weight./(1360*pi)).^(1/3), where the weight ranges between 4 and 8kg.
I then have guess of the time taken ,which is 14400 seconds.
The function in question is attached, where infinity is replaced by k=22.
Function in question
This function should be equal to 57/80
r/a can be replaced by 0.464, meaning that the multiplication of the summation can be written as 2/(0.464*pi).
alpha will be equal to 0.7*10^-7
How would i be able to plot the times taken for the masses to cook in hours, for weight in the given range?
I have tried to code this function for a couple of days now but it wont seem to work, due to array size issues and the general function just not working.
Any help would be greatly appreciated :)
First, you need a master equation as a function of weight and t, which you want fsolve to find the zero of. Then for each weight, you can capture it in another function that you then solve for t:
alpha = 0.7e-7;
rbya = 0.464;
k = 1:22;
a = #(weight)(weight./(1360*pi)).^(1/3);
eqn = #(weight,t)2/pi/rbya*sum((-1).^(k-1)./k.*sin(k*pi*rbya).*exp(-1.*k.^2.*pi^2.*alpha.*t./(a(weight).^2)))-57/80;
weights = 4:8;
ts = zeros(size(weights));
for i = 1:numel(weights)
sub_eqn = #(t)eqn(weights(i),t);
ts(i)=fsolve(sub_eqn,14400);
end
plot(weights,ts/(60*60))
xlabel("Weight (kg)")
ylabel("Cooking Time (hrs)")
If you want to solve the entire set of equations at once, then you need to be careful of array sizes (as you have experienced, read more here). k should be a column vector so that sum will sum along each column, and weights should be a row vector so that element-wise operations will repeat the k’s for each weight. You also need your list of initial guesses to be the same size as weights so that fsolve can have a guess for each weight:
alpha = 0.7e-7;
rbya = 0.464;
k = (1:22)';
a = #(weight)(weight./(1360*pi)).^(1/3);
weights = 4:8;
eqn = #(t)2/pi/rbya*sum((-1).^(k-1)./k.*sin(k*pi*rbya).*exp(-1.*k.^2.*pi^2.*alpha.*t./(a(weights).^2)))-57/80;
ts=fsolve(eqn,repmat(14400,size(weights)));
plot(weights,ts/(60*60))
xlabel("Weight (kg)")
ylabel("Cooking Time (hrs)")
Note that you do get slightly different answers with the two methods.
My stage size is 640 x 1136
I want to spawn my objects randomly but only inside of the stage.
I used this
object.x = Math.random() * stage.stageHeight;
How can I make the x position spawn within the stage area?
You would want a "random in range" function like the one here
(included below).
However, if you are doing a game you may not be satisfied with the result of randomly spawning objects (e.g. objects piling up on each other, etc.) and want to exert more control. Lots of ways to be clever with that – like defining a set of regions or quadrants, picking one of those randomly and then generating random coordinates within that region, or having an array of defined "good" points and randomly selected from it. Actual randomness is often less interesting than the idea or appearance of randomness.
public function randRange(minNum:Number, maxNum:Number):Number {
return (Math.floor(Math.random() * (maxNum - minNum + 1)) + minNum);
}
TOMATO answer is the same as what you actually do so it's not really helpful. What you need to do is account for the object size. If you have an object that is at maximum 100 pixel wide then:
var size:Number = object.width;
object.x = size + Math.random() * (stage.stageWidth - size * 2);
This make sure the object spawn on the x axis inside the stage x axis. Same operation needs to be repeated for the y axis of course.
I have an acceleration data for X-axis and time vector for it. I determined the peaks more than threshold and now I should find the FFT for every peak.
As result I have this:
Peak Value 1 = 458, index 1988
Peak Value 2 = 456, index 1990
Peak Value 3 = 450, index 12081
....
Peak Value 9 = 432, index 12151
To find these peaks I used the peakfinder script.
The command [peakLoc, peakMag] = peakfinder(x0,...) gives me location and magnitude of peaks.
Also I have the Time (from time data vector) for each peak.
So what I suppose, that I should take every peak, find its width (or some data points around the peak) and make the FFT. Am I right? Could you help me in that?
I'm working in Octave and I'm new here :)
Code:
load ("C:\\..patch..\\peakfinder.m");
d =dlmread("C:\\..patch..\\acc2.csv", ";");
T=d(:,1);
Ax=d(:,2);
[peakInd peakVal]=peakfinder(Ax,10,430,1);
peakTime=T(peakInd);
[sortVal sortInd] = sort(peakVal, 'descend');
originInd = peakInd(sortInd);
for k = 1 : length(sortVal)
fprintf(1, 'Peak #%d = %d, index%d\n', k, sortVal(k), originInd (k));
end
plot(T,Ax,'b-',T(peakInd),Ax(peakInd),'rv');
and here you can download the data http://www.filedropper.com/acc2
FFT
d =dlmread("C:\\..path..\\acc2.csv", ";");
T=d(:,1);
Ax=d(:,2);
% sampling frequency
Fs_a=2000;
% length of FFT
Length_Ax=numel(Ax);
% number of lines of Fourier spectrum
fft_L= Fs_a*2;
% an array of time samples
T_Ax=0:1/Fs_a: Length_Ax;
fft_Ax=abs(fft(Ax,fft_L));
fft_Ax=2*fft_Ax./fft_L;
F=0:Fs_a/fft_L:Fs_a/2-1/fft_L;
subplot(3,1,1);
plot(T,Ax);
title('Ax axis');
xlabel('time (s)');
ylabel('amplitude)'); grid on;
subplot(3,1,2);
plot(F,fft_Ax(1:length(F)));
title('spectrum max Ax axis');
xlabel('frequency (Hz)');
ylabel('amplitude'); grid on;
It looks like you have two clusters of peaks, so I would plot the data over three plots: one of the whole timeseries, one zoomed in on the first cluster, and the last one zoomed in on the second cluster (note I have divided all your time values by 1e6 otherwise the tick labels get ugly):
figure
subplot(3,1,1)
plot(T/1e6,Ax,'b-',peakTime/1e6,peakVal,'rv');
subplot(3,1,2)
plot(T/1e6,Ax,'b-',peakTime(1:4)/1e6,peakVal(1:4),'rv');
axis([0.99*peakTime(1)/1e6 1.01*peakTime(4)/1e6 0.9*peakVal(1) 1.1*peakVal(4)])
subplot(3,1,3)
plot(T/1e6,Ax,'b-',peakTime(5:end)/1e6,peakVal(5:end),'rv');
axis([0.995*peakTime(5)/1e6 1.005*peakTime(end)/1e6 0.9*peakVal(5) 1.1*peakVal(end)])
I have set the axes around the extreme time and acceleration values, using some coefficients to have some "padding" around (the values of these coefficients were obtained through trial and error). This gives me the following plot, hopefully this is the sort of thing you are after. You can add x and y labels if you wish.
EDIT
Here's how I would do the FFT:
Fs = 2000;
L = length(Ax);
NFFT = 2^nextpow2(L); % Next power of 2 from length of Ax
Ax_FFT = fft(Ax,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
% Plot single-sided amplitude spectrum.
figure
semilogx(f,2*abs(Ax_FFT(1:NFFT/2+1))) % using semilogx as huge DC component
title('Single-Sided Amplitude Spectrum of Ax')
xlabel('Frequency (Hz)')
ylabel('|Ax(f)|')
ylim([0 300])
giving the following result:
I'm trying to implement steering behaviors but I have a problem with "including" the passed time in the calculation and then allowing me to control the speed of the game. I have seen various sources of steering behaviors and I've come up with this (Arrive behavior):
var toTarget:Vector2D = new Vector2D( mEntity.targetPosition.x, mEntity.targetPosition.y );
toTarget.subtract( mEntity.position );
var dist:Number = toTarget.length;
toTarget.normalize().scale( mEntity.maxSpeed );
if( dist < slowDownDist ) {
toTarget.scale( dist / slowDownDist );
}
return toTarget.subtract( mEntity.velocity );
And here's the advanceTime method of MovingEntity:
var steeringForce:Vector2D = mSteering.calculate();
steeringForce.x /= mMass;
steeringForce.y /= mMass;
steeringForce.scale( time );
mVelocity.x += steeringForce.x;
mVelocity.y += steeringForce.y;
x += mVelocity.x * time;
y += mVelocity.y * time;
The steering force should be (at some point) directly opposite to the entity's velocity and thus making it stop. The problem I see and do not understand is that in order to simulate acceleration the force needs to be divided by mass and also to consider the passed time it needs to be multiplied by that time - but this scales the steering force down a lot and causes the entity to overshoot the target spot instead of stopping there so then it returns back which effectively causes oscillation. If I do not multiply the force with the time then the moving entity behaves slightly differently depending on the game speed.
By second (?) Newton's law F = m * a where F is force, m is mass and a is acceleration. Force is measured in newtons, mass in kilograms and acceleration in meters per second per second. So, you just need to apply bigger force, and lave the calculation as is.
Suppose there are N points in a 2-D graph.Each point has some weight attached to it.I am required to draw a straight line such a way that the line divides the points into 2 groups such that total weight(sum of weight of points in that group) of part with smaller weight be as many as possible.My task is to find this value.How to go about it ?
Note:No three points lie on the same line.
This is not a homework or part of any contest.
You could just scan over all angles and offsets until you find the optimal solution.
For ease of computation, I would rotate all the points with a simple rotation matrix to align the points with the scanline, so that you only have to look at their x coordinates.
You only have to check half a circle before the scanline doubles up on itself, that's an angle of 0 to PI assuming that you're working with radians, not degrees. Also assuming that the points can be read from the data as some kind of objects with an x, y and weight value.
Pseudocode:
Initialize points from input data
Initialize bestDifference to sum(weights of points)
Initialize bestAngle to 0
Initialize bestOffset to 0
Initialize angleStepSize to an arbitrary small value (e.g. PI/100)
For angle = 0:angleStepSize:PI
Initialize rotatedpoints from points and rotationMatrix(angle)
For offset = (lowest x in rotatedpoints) to (highest x in rotatedpoints)
weightsLeft = sum of the weights of all nodes with x < offset
weightsRight = sum of the weights of all nodes with x > offset
difference = abs(weightsLeft - weightsRight)
If difference < bestDifference
bestAngle = angle
bestOffset = offset
bestDifference = difference
Increment angle by stepsize
Return bestAngle, bestOffset, bestDifference
Here's a crude Paint image to clarify my approach: