I'm working on the Wii Motionplus and I've extracted the raw values using WiimoteLib Library. However, when I normalize it, I get random values that don't tally with what is actually happening.
This is how I'm normalizing:
Calibrate the Motionplus (i.e. Find the raw value that corresponds to zero; I do this by holding it stationary for a point of time)
For every subsequent raw value read, I subtract the zero value from it to get the "relative" raw value.
Then, I scale this value using http://wiibrew.org/wiki/Wiimote/Extension_Controllers (checking for yaw_fast, pitch_fast etc.), where the numerical values are computed using the measure (raw value of 8192 corresponds to 595 deg/s)
I sum up all these values over time (discrete integration) to get the angle of the wiimote wrt initial orientation.
However, when I calculate this and plot it out on a graph, a step change in one of the axes is NOT being reflected in the graph. I tried using a digital compass with it to compare, but while the compass reflects the values correctly, the wii values are completely different (even the pattern is not the same)
Can anyone tell me where I'm going wrong with the normalization?
Thanks!
The numbers that are being sent out are rotations about the x y and z axis respective to itself. In order to relate this to x,y,z coordinates you will need to use a rotation matrix, and since the rotation readings are not a fixed axis but depend on what orientation you are at you need to use a Euler Matrix to relate this to a fixed x,y,z coordinate
In other words you are receiving roll, yaw and pitch velocities and you need to use a Euler Matrix to relate this to cartessian coordinates. Once you know your initial roll, pitch and yaw you can simply add your next reading of roll, pitch and yaw to that initial times the time interval that that reading applies to.
ROLL is Rotation about the y-axis
PITCH is Rotation about the x-axis
YAW is Rotation about the z-axis
Related
I have an problem I need some help with. I have 2 sensors (a weather sensor and a camera) mounted under a large balloon (basically). The weather sensor records pitch, roll, yaw, altitude, heading (0-360), lon and lat. I also have x,y,z values that represent the offset distance that the weather sensor is from the camera. The camera does not have it's own INS so the values from the weather sensor are sent to the camera. However, since those values are coming from the weather sensor that is not in the same position as the camera, the values are not accurate. I need to perform calculations on the values before sending them to the camera and that is where I need help.
For the record:
Both devices are facing the front of the craft
The X is the Front to Back axis
The Y is the Top to Bottom axis
The Z is the Left to Right axis
coordinate planes diagram
I know the formula to get coordinates for a target point given a starting point, bearing, and distance. I can get the distance by using the Pythagorean Theorem (using the measured X and Z values). Those are 10.58055" and 17.53322" respectively. We already have the starting point (it comes from the weather sensor).
First, am I on the right track here?
Second, how do I appropriately calculate bearing? I can use trig to get the angle that the weather sensor is offset from the camera, which I think is required. I also think I need to account for the orientation of the sensor to the camera (i.e. if the weather sensor is in front of the camera, it needs to "turn around" to get to the camera). This would mean that if the X value is negative and the Z value is positive, I would subtract my angle (let's call it theta) from 180. However, that would only work if I was heading north so I believe you then need to add in the heading (that came from the weather sensor).
I think I am close on this. I need some smarter people letting me know if I am approaching this correctly and then possibly little things like the appropriate way to handle the bearing measurement going above 360 (which I believe is to just subtract 360).
I am trying to represent the orientation of a rigid body, say a pencil in 3 dimensional space with respect to fixed XYZ axes, originating at a fixed origin O. I am trying to visualize arriving at the quaternion representing the orientation of the pencil, by thinking in terms of the axis vector of the pencil's current orientation(i.e axis), and the roll on its own central lengthwise axis, (Following equation for quaternion from axis-angle representation is from Wikipedia).
Now as per my understanding if the roll of the pencil is zero, then the vector part of the quaternion vanishes, since sin(theta/2) shall become zero, and the resulting quaternion no longer has information of horizontal and vertical tilt with respect to the fixed axes. How I can describe the orientation of the pencil using quaternions in cases where the roll of the pencil is zero.
It is clearer if we imagine that the quaternion specifies the rotation from the default orientation of the pencil to its present orientation. One way of specifying this would be to assume that default orientation of the pencil is along the extrinsic X axis, with the default roll being zero when the label face is on the top. Now one possible way to describe the present orientation of the pencil is by the following three rotations:
Rotation about the Z, axis by the yaw angle
Rotation about the new Y axis, by the pitch angle
Rotation about the new X axis, by the roll
The combination of these three rotations, obtained by their quaternion product , will give us the quaternion of the pencil's present orientation, even if the roll, pitch or yaw is zero.
I have 5 {x,y} points randomly placed on a grid
Each of the points do not know the {x,y} coordinates of the other points
Each of the points do know the distance of each of the other points from their {x,y} position
Each of the points exchanges this distance information with every other point
So every point knows every distance of every other point
Using this distance information every point can calculate (by finding the angles) triangles for every other point using itself as a reference point
Example, point 1 can calculate the following triangles:
1-2-3,
1-2-4,
1-2-5,
1-3-4,
1-3-5,
1-4-5,
and using the distance data recieved from the other points it can also calculate
2-3-4,
2-3-5,
2-4-5,
3-4-5
I would like to build a map of the location of every other point relative to a single point
How should I go about doing this? I am asuming it would be some kind of triangulation algorithm but these mainly seem to compute the location of a point from three other points, not the other way around where the other points {x,y} coordinates are discovered based on only the distance information.
I have tried plotting the two possible triangles for every 3 triangle points and then rotating them on a fixed known point to try and align them, but I think this avenue will end up with too many possibilities and errors
Ultimately I would like every point to end up with {x,y} coordinates of every other point relative to itself
You know the distance from one point to every other, dij. Thus, point 2 lies in a circumference of center point 1 and radius = d12. Point 3 lies in a circumference of center point 1 and R=d13 and it also lies in another circumference of center point 2 and R=d23.
See this picture:
I've set point 2 in X-axis for simplicity.
As you see, point 3 is on the intersection of two cicrcumferences centered at P1 and P2. There is a second intersection, P3a. Let's choose the one that is upwards and continue.
For P4 we can use three circumferences, centered at P1, P2 and P3. Again we get two solutions.
The same process can be done with the rest of points. For Pn you have n-1 circumferences.
I'm sure you can find the maths for circle-circle intersection.
Some remarks must be observed:
1) The construction is simpler if you first sort the points by distance to P1.
2) Not all distances generate a solution. For example, increase d13 an there's no intersection between the two circumferences for P3. Or increase d14 and now the three circumferences don't intersect in just the two expected points 4 and 4a.
3) This fact can be overworked by considering the average of intersections and the distance from each solution to this average. You can set a tolerance in these distances and tell if the average is a solution or else some dij is wrong. Since two solutions are possible, you must consider two averages.
4) The two possible triangulations are symmetric, over X-axis in the case I've drawn.
The real solution is obtained by a rotation around P1. To calculate the angle of rotation you need the {x,y} coordinates of another point.
I have a chart that has several existing curves on it that I have tried to interpolate new curves in between. I have used linear interpolation in the form of y = ((x - x1)(y2 - y1) / (x2 - x1)) + y1, however the new curves look out of place.
You can see in the picture that every second line (from the bottom) is the interpolated line. While the very second line data points are exactly centered between the first and third data points in the y axis, the third line data points are not centered between the second and fourth y data points, making the graph look skew.
So I am thinking linear interpolation may not be what I am after here. Can someone recommend another method that would create curves between the existing ones, but replicates the same form?
Sudden changes in gradient are hard to interpolate. When you're at the point where you want an interpolated line to suddenly change gradient, there is no information from the points in close proximity that give information as to where the sudden change in gradient should occur.
To replicate the pattern, you actually need to copy the gradient of the line below then smoothly transition to the gradient of the line above. Visually we can see that it should occur half way between the change in gradients for the lines above and below on either side, but detecting the locations of those changes is not trivial.
The points where the sudden change in gradient are occurring are separated by a large change in the x-axis by only a small change in the y-axis. When calculating y-values for x-values in between the the changes in gradient you get the aberrations. I suggest trying to interpolate x-values based on y-values instead. For each curve, for each small arbitrary step in the y-axis, find/calculate the closest x-values from the curve on either side and take the average to plot your interpolation.
An unconventional approach may be a piece-meal style of interpolation. It may be possible to model the 3 regions of different gradients separately.
Start by identifying the 2 lines that would be drawn through the 2 sets of kinks, creating 3 regions of space. The vertical line would stop at the horizontal line near the bottom right corner of the graph.
For each region (and potentially for each value of x in each region) determine the gradient of the lines. When you're doing your interpolation of a new line, for each starting point (x1, y1), look at which region it falls in. Use the gradient of that region as a significant factor when determining the next point. Keep doing this until you reach a region boundary. When the interpolated point crosses into a different region, then use the gradient of that region as a significant factor to interpolate the next point.
It will be quite pointy if you did this strictly, so graph with some smoothing (or incorporate a smoothing factor using weighted averages of the gradients as you transition between regions, but this could be a whole lot of effort without necessarily closer results!)
I have a set of vertices to draw a circle, but I want to draw a high-res circle by drawing twice the number of vertices, I cant just increase the number of vertices what I need is to calculate the mid points from the supplied vertices, if that makes sense
So from that image how can I calculate the points A, B, C, ... given the points V0, V1, V2, ... and the center point of the circle ?
Please note that I cant just calculate the mid-points by rotating the vertices they need to be calculated using their position
Thanks
The center of the circle can be determined by making a perpendicular line to two neighboring "sides", and intersecting them.
If there are an even number of vertices, just pick two which are opposite to each other, and "avarage them" - calculate the midpoint.
Then, you can just rotate all the vertices to either way by 180°/No.vertices around this center, so you get the ones you are looking for. Of course, you should keep the existing ones too.