I did some research about this topic on this forum and in general. The subject was discussed here before but with no-code solutions for 3D.

I like to address that topic again with the hope to find an easy solution that can help me and the following to come. Following that i manage to rotate the XY positions accordingly, but still not for Z. XY rotations are correct, still missing Z rotation.

As noted - Any pointers will be greatly appreciated Thanks! Hello, I may not have the exact solution, but you may find a simple workaround using these few lines of code:. As soon as you need something general-purpose, though, representing rotation state in terms of xyz has lots of known problems. Instead, use quaternions. They are complicated and it is a pain — but they actually work.

The PeasyCam library has a great reference implementation. Thankyou for the good answer, jeremy! I intend to study the suggested peasycam example. For now, i have aimed my predatory cone using bennyhackers code. I had to use acos instead of asin. I have so much to learn, as i would like to work with vr.

Now having said that there are a number of caveats with using quaternions and using them with Processing. Creating your own quaternion class is a possibility provided you are seriously good at maths and matrices, the alternative is to find a library implementation.

This class is a wrapper for quaternions but concentrates on providing methods for rotating vectors which is what you want. Sounds too good to be true?In linear algebraa rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix.

The examples in this article apply to active rotations of vectors counterclockwise in a right-handed coordinate system y counterclockwise from x by pre-multiplication R on the left. If any one of these is changed such as rotating axes instead of vectors, a passive transformationthen the inverse of the example matrix should be used, which coincides with its transpose.

Since matrix multiplication has no effect on the zero vector the coordinates of the originrotation matrices describe rotations about the origin. Rotation matrices provide an algebraic description of such rotations, and are used extensively for computations in geometryphysicsand computer graphics.

These combine proper rotations with reflections which invert orientation. In other cases, where reflections are not being considered, the label proper may be dropped. The latter convention is followed in this article. Rotation matrices are square matriceswith real entries. This rotates column vectors by means of the following matrix multiplication.

Thus the clockwise rotation matrix is found as. The two-dimensional case is the only non-trivial i. Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphicswhich often have the origin in the top left corner and the y -axis down the screen or page.

See below for other alternative conventions which may change the sense of the rotation produced by a rotation matrix. Then according to Euler's formulaany. A basic rotation also called elemental rotation is a rotation about one of the axes of a coordinate system.

The same matrices can also represent a clockwise rotation of the axes. R zfor instance, would rotate toward the y -axis a vector aligned with the x -axisas can easily be checked by operating with R z on the vector 1,0,0 :. This is similar to the rotation produced by the above-mentioned two-dimensional rotation matrix.

See below for alternative conventions which may apparently or actually invert the sense of the rotation produced by these matrices. Other rotation matrices can be obtained from these three using matrix multiplication. For example, the product. Similarly, the product. These matrices produce the desired effect only if they are used to premultiply column vectorsand since in general matrix multiplication is not commutative only if they are applied in the specified order see Ambiguities for more details.The set of special orthogonal matrices is a closed set.

What does that mean, and why do we care? A question like this is usually discussed only in an upper-division set theory class, which is a class for seniors majoring in math on the theoretical side. Not math for engineering or science, but math for its own sake. By the time you get to a set theory class, you have passed all the difficult classes. Geometry, trigonometry, calculus and differential equations are behind you. As Terry Pratchett might say, you have gone through mathematics and come out the other side.

In an upper division set theory class, you will consider a math fact such as "a set contains its elements".

**Angles of Vectors in 3D**

This fact will be given a fancy name, like "The Baire Category Theorem", and you will be asked to prove it. Since you are in the habit of following along or you wouldn't have made it all the way through mathematics and out the other sideyou know exactly what to do. You pull out a sharp pencil, and using the precise notation you were given earlier, you work out the proof in 4 or 5 lines.

You are filled with a feeling of peace and confidence, as the rightness of the proof is crystal clear. Then you put the pencil away. You have finished your homework before your coffee has grown cold. Meanwhile, your friends across the hall in the Comp Sci department are receiving their homework assignment: Write an operating system. From scratch. Due Tuesday. And those guys wondered why I majored in math. In this class, I am not going to ask you to prove the Baire Category Theorem, or any similar observation of obvious properties from the field of set theory.

We are going to take it on faith that the set of special orthogonal matrices is a closed set. We are not theoretical mathematicians, after all, we are software engineers. We are not concerned with the "why" so much as the "what is it good for".

It turns out, the closed set of special orthogonal matrices is good for some very powerful things.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. The rotation should appear to be counter clockwise for an observer to whom the axis vector is pointing. This is called the right hand rule. It provides a vector class which has a method A.

It also provides a helper function rotate A,theta,B if you don't want to call the method on A. Using the Euler-Rodrigues formula :. It can be a good way if you have few rotations to do but a lot of vectors.

I just wanted to mention that if speed is required, wrapping unutbu's code in scipy's weave. Here is an elegant method using quaternions that are blazingly fast; I can calculate 10 million rotations per second with appropriately vectorised numpy arrays. It relies on the quaternion extension to numpy found here. We start by converting your axis and angle to a quaternion whose imaginary dimensions are given by your axis of rotation, and whose magnitude is given by half the angle of rotation in radians.

The 4 element vectors w, x, y, z are constructed as follows:. The axis angle representation is then constructed by normalizing then multiplying by half the desired angle theta. See here for why half the angle is required. Now create the quaternions v and qlog using the library, and get the unit rotation quaternion q by taking the exponential. For further clarification of how quaternion multiplication etc.

It still does not use Cython, but relies heavily on the efficiency of numpy. You can find it here with pip:. Once installed, in python you may create the orientation object which can rotate vectors, or be part of transform objects.

This is more efficient, by a factor of approximately four, as far as I can time it, than the oneliner using scipy posted by B. However, it requires installation of my math3d package. While special classes for rotations can be convenient, in some cases one needs rotation matrices e. To avoid everyone implementing their own little matrix generating functions, there exists a tiny pure python package which does nothing more than providing convenient rotation matrix generating functions.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. I am making an android project in opengl es that uses accelerometer to calculate change in specific axes and my aim is to rotate my spacecraft-like object's movement vector.

The problem is that i can't understand the math behind rotation matrices. I can gather rotation changes in phone.

How can i rotate my movement vector using rotation matrix? If you want to rotate a vector you should construct what is known as a rotation matrix. When you understand this, creating a matrix to do this becomes simple. A matrix is just a mathematical tool to perform this in a comfortable, generalized manner so that various transformations like rotation, scale and translation moving can be combined and performed in a single step, using one common method. From linear algebra, to rotate a point or vector in 2D, the matrix to be built is.

That works in 2D, while in 3D we need to take in to account the third axis. Rotating a vector around the origin a point in 2D simply means rotating it around the Z-axis a line in 3D; since we're rotating around Z-axis, its coordinate should be kept constant i.

In 3D rotating around the Z-axis would be. Note 1 : axis around which rotation is done has no sine or cosine elements in the matrix. Note 2: This method of performing rotations follows the Euler angle rotation system, which is simple to teach and easy to grasp.

This works perfectly fine for 2D and for simple 3D cases; but when rotation needs to be performed around all three axes at the same time then Euler angles may not be sufficient due to an inherent deficiency in this system which manifests itself as Gimbal lock.

People resort to Quaternion s in such situations, which is more advanced than this but doesn't suffer from Gimbal locks when used correctly. This rotation will be with respect to the world space origin a. Since not all objects are at the world origin, simply rotating using these matrices will not give the desired result of rotating around the object's own frame.

The order in which the transforms are applied matters. Combining multiple transforms together is called concatenation or composition. I urge you to read about linear and affine transformations and their composition to perform multiple transformations in one shot, before playing with transformations in code. Without understanding the basic maths behind it, debugging transformations would be a nightmare.

I found this lecture video to be a very good resource. Another resource is this tutorial on transformations that aims to be intuitive and illustrates the ideas with animation caveat: authored by me! A product of the aforementioned matrices should be enough if you only need rotations around cardinal axes X, Y or Z like in the question posted. The Rodrigues' formula a. If you're using Quaternion s, just build a quaternion with the required vector and angle. Quaternions are a superior alternative for storing and manipulating 3D rotations; it's compact and fast e.I have been into my Golf betting for a number of years and have been involved with both Golf Betting expert and SJP Golf Tips.

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## Rotation matrix

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This backs up the history of high odds returns from Golf Betting Expert and it is one service I intend to keep. Have missed a couple of weeks and quoted prices are not always available, nevertheless have made over 90 points profit. Will stick with it and probably raise stakes in the near future. Really impressed with Craig's knowledge of the PGA, European, and Challenge tour having tipped winners in them all, the most impressive was SSP Chawrasia at the Indian Open at 100-1 (I managed to get on at 110-1 for the biggest win I've ever had.See the Section on Random Decision Forests below.

The range of successive instances to build the model. See the Section on Sampling below. So, if it is 3, then a both children of a new split must have 3 instances supporting them.

Since instances may have non-integer weights, non-integer values are valid. Example: 16 tags optional Array of Strings A list of strings that help classify and index your model.

By default, rows from the input dataset are deterministically shuffled before being processed, to avoid inaccurate models caused by ordered fields in the input rows. Since the shuffling is deterministic, i. However, you can modify this default behaviour by including the ordering argument in the model creation request, where "ordering" here is a shortcut for "ordering for the traversal of input rows".

The row range is specified with the range argument defined in the Section on Arguments above. To specify a sample, which is taken over the row range or over the whole dataset if a range is not provided, you can add the following arguments to the creation request: Finally, note that the "ordering" of the dataset described in the previous subsection is used on the result of the sampling.

The default is false. When randomized, the model considers only a subset of the possible fields when choosing a split. The size of the subset will be the square root of the total number of input fields.

### The Mathematics of the 3D Rotation Matrix

So if there are 100 input fields, each split will only consider 10 fields randomly chosen from the 100. Every split will choose a new subset of fields. Although randomize could be used for other purposes, it's intended for growing random decision forests.

To grow tree models for a random forest, set randomize to true and select a sample from the dataset. Traditionally this is a 1. Once a model has been successfully created it will have the following properties.

This will be 201 upon successful creation of the model and 200 afterwards.

### Rotation in 2D

Make sure that you check the code that comes with the status attribute to make sure that the model creation has been completed without errors. This is the date and time in which the model was created with microsecond precision. It has an entry per each field type (categorical, datetime, numeric, and text), an entry for preferred fields, and an entry for the total number of fields. It includes a very intuitive description of the tree-like structure that makes the model up and the field's dictionary describing the fields and their summaries.

In a future version, you will be able to share models with other co-workers or, if desired, make them publicly available. This is the date and time in which the model was updated with microsecond precision. A Model Object has the following properties: Creating a model is a process that can take just a few seconds or a few days depending on the size of the dataset used as input and on the workload of BigML's systems.

The model goes through a number of states until its fully completed. Through the status field in the model you can determine when the model has been fully processed and ready to be used to create predictions.

Support is a number from 0 to 1 that specifies the minimum fraction of the total number of instances that a given branch must cover to be retained in the resulting tree. If you repeat the support parameter in the query string, the last one is used.

Non-parseable support values are ignored. Value is a concrete value or interval of values (for regression trees) that a leaf must predict to be kept in the returning tree. Intervals can be closed or open in either end. Confidence is a concrete value or interval of values that a leaf must have to be kept in the returning tree. The specification of intervals follows the same conventions as those of value. Since confidences are a continuous value, the most common case will be asking for a range, but the service will accept also individual values.

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