Turtle graphics is a popular way for introducing programming to kids. It was part of the original Logo programming language developed by Wally Feurzig and Seymour Papert in Imagine a robotic turtle starting at 0, 0 in the x-y plane.
After an import turtlegive it the command turtle. Give it the command turtle. By combining together these and similar commands, intricate shapes and pictures can easily be drawn. The turtle module is an extended reimplementation of the same-named module from the Python standard distribution up to version Python 2. This means in the first place to enable the learning programmer to use all the commands, classes and methods interactively when using the module from within IDLE run with the -n switch.
The turtle module provides turtle graphics primitives, in both object-oriented and procedure-oriented ways. Because it uses tkinter for the underlying graphics, it needs a version of Python installed with Tk support. The TurtleScreen class defines graphics windows as a playground for the drawing turtles. Its constructor needs a tkinter. Canvas or a ScrolledCanvas as argument.
It should be used when turtle is used as part of some application. The function Screen returns a singleton object of a TurtleScreen subclass. This function should be used when turtle is used as a standalone tool for doing graphics. As a singleton object, inheriting from its class is not possible. The procedural interface provides functions which are derived from the methods of the classes Screen and Turtle.
They have the same names as the corresponding methods. A screen object is automatically created whenever a function derived from a Screen method is called.
An unnamed turtle object is automatically created whenever any of the functions derived from a Turtle method is called. In the following documentation the argument list for functions is given. Methods, of course, have the additional first argument self which is omitted here.
Most of the examples in this section refer to a Turtle instance called turtle. Move the turtle forward by the specified distancein the direction the turtle is headed. Move the turtle backward by distanceopposite to the direction the turtle is headed. Turn turtle right by angle units.Yesterday, I re-read a passage by Tony Smith about why one should be interested in Clifford algebras.
I thought, I should segue from the complex numbers in the plane to Clifford algebras to quaternions in 3-space to Clifford algebras again in a series of posts here. You start playing with the equation. WIth a little fiddling, you find this is equivalent to. Then, you take the square root of both sides to find that.
We started with a polynomial equation in one variable in which the highest exponent was two and we found two answers. Pounding your chest and sounding your barbaric yawp, you move on to.
This should be easy, right? With the same fiddling, we find and then. What do we do now? If we start with zero, we end with zero. If we multiply a positive number by itself, we get a positive number. If we multiply a negative number by itself, we get a positive number. So, how do we get around this? We pull an ace out of our sleeve. We just run with the idea that there is such a number and see where it takes us.
We say, There is a number such that.
numpy.rot90() in Python
Everything else is going to stay the same. Where does this take us? It turns out, it takes us very, very far. For starters, our equationa polynomial equation in one variable where the highest exponent is two, now has two answers:.
What about? It is a polynomial equation in one variable where the highest exponent is two. With the same manipulation as before, we find that. Now, we need to remember that if and are positive numbers, then.
If we said thatthen. What happens if we multiply? When we multiply real number, andwe can do it in any order. We could do or or or three other orders. Our equation is a polynomial equation in one variable where the highest exponent is two and it has two solutions. As it turns out, by adding in and real number multiples of to our real numbers, we have the complex numbers. These complex numbers are an algebraic completion of the real numbers.
If you make a polynomial equation in one variable where all of the coefficients are complex numbers and the highest exponent isthen there will be solutions to the equation in the complex numbers.
Above, we decided to say that is and go from there. We also used the idea that to find square roots of all negative numbers. And, we already played around a little bit with multiplying some numbers together.Go to: Synopsis.
Return value. Python examples. This is not depicted in the synopsis. The default behaviour, when no objects or flags are passed, is to do a absolute rotate on each currently selected object in the world space.
Return value None. When true, transform constraints are applied along the vertex normal first and only use the closest point when no intersection is found along the normal. Modifer for -relative flag that specifies rotation values should be added to current XYZ rotation values. When true, euler rotation value will be understood in XYZ rotation order not per transform node basis.
When true, transforming an object will apply an opposite transform to its child transform to keep them at the same world-space position. Default is false. When true, transforming an object will apply an opposite transform to its geometry points to keep them at the same world-space position. When true, UV values on rotated components are projected across the rotation in 3d space. For small edits, this will freeze the world space texture mapping on the object.
When false, the UV values will not change for a selected vertices. When set the component transformation is flipped so it is relative to the negative side of the symmetry plane. The default no flag is to transform components relative to the positive side of the symmetry plane. When true, the command will modify the node's translate attribute instead of its rotateTranslate attribute, when rotating around a pivot other than the object's own rotate pivot.
Apply a transform constraint to moving components. Flag can appear in Create mode of command. Flag can appear in Edit mode of command.
Flag can appear in Query mode of command. Flag can have multiple arguments, passed either as a tuple or a list.I've gotten the code to draw my Plane. I read that this is because when it turns the sprite, it adds padding to resize the image while it is turning.
I think that each time it turns, it adds more padding, making it add exponentially for each keypress. I can't figure out how to stop this from happening. Any help for a beginner greatly appreciated! The Colours import is just a file where I keep my pre-defined colours for easier colour filling, and Plane.
You have to use an auxiliar image variable, so you rotate the image and saves it in the aux var, and the original image is not modified. Maybe you will see some strange rotation behavior and it depends on how you managed the center of the image or rect.
I forgot to say in my previous post that you have to obtain the rect from each rotated image and set self. Well, try it, maybe I'm doing something unnecessary. QUIT: pygame. Maybe it's similar to the strange effects I encountered here: exploring module pygame draw a white ellipse on a black screen and move it note: rect behaves strange, stretches the ellipse!!! It doesn't change if you have delta only for x1, but rect position turns weird. Getting Started: Have something to contribute to this discussion?
The dark mode beta is finally here. Change your preferences any time. 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.
Rotating a sprite using pygame
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. The package is on github mgen and can be installed via pip:. Note that the matrices are just regular numpy arrays, so no new data-structures are introduced when using this package. Using pyquaternion is extremely simple; to install it while still in pythonrun in your console:.
I used the following simple function:. Use scipy's Rotation. The argument is the rotation vector a unit vector multiplied by the rotation angle in rads. There are several more ways to use Rotation based on what data you have about the rotation:. Off-topic note: One line code is not necessarily better code as implied by some users.
Learn more. Rotation of 3D vector? Ask Question. Asked 8 years, 8 months ago. Active 9 months ago. Viewed 98k times.If you find this content useful, please consider supporting the work by buying the book!
Matplotlib was initially designed with only two-dimensional plotting in mind. Around the time of the 1. With this three-dimensional axes enabled, we can now plot a variety of three-dimensional plot types. The most basic three-dimensional plot is a line or collection of scatter plot created from sets of x, y, z triples. In analogy with the more common two-dimensional plots discussed earlier, these can be created using the ax. The call signature for these is nearly identical to that of their two-dimensional counterparts, so you can refer to Simple Line Plots and Simple Scatter Plots for more information on controlling the output.
Here we'll plot a trigonometric spiral, along with some points drawn randomly near the line:. Notice that by default, the scatter points have their transparency adjusted to give a sense of depth on the page.
While the three-dimensional effect is sometimes difficult to see within a static image, an interactive view can lead to some nice intuition about the layout of the points. Analogous to the contour plots we explored in Density and Contour Plotsmplot3d contains tools to create three-dimensional relief plots using the same inputs.
Like two-dimensional ax. Here we'll show a three-dimensional contour diagram of a three-dimensional sinusoidal function:. In the following example, we'll use an elevation of 60 degrees that is, 60 degrees above the x-y plane and an azimuth of 35 degrees that is, rotated 35 degrees counter-clockwise about the z-axis :. Again, note that this type of rotation can be accomplished interactively by clicking and dragging when using one of Matplotlib's interactive backends. Two other types of three-dimensional plots that work on gridded data are wireframes and surface plots.
These take a grid of values and project it onto the specified three-dimensional surface, and can make the resulting three-dimensional forms quite easy to visualize. Here's an example of using a wireframe:. A surface plot is like a wireframe plot, but each face of the wireframe is a filled polygon. Adding a colormap to the filled polygons can aid perception of the topology of the surface being visualized:.
Note that though the grid of values for a surface plot needs to be two-dimensional, it need not be rectilinear. Here is an example of creating a partial polar grid, which when used with the surface3D plot can give us a slice into the function we're visualizing:.
For some applications, the evenly sampled grids required by the above routines is overly restrictive and inconvenient. In these situations, the triangulation-based plots can be very useful. What if rather than an even draw from a Cartesian or a polar grid, we instead have a set of random draws?
This leaves a lot to be desired. The function that will help us in this case is ax. The result is certainly not as clean as when it is plotted with a grid, but the flexibility of such a triangulation allows for some really interesting three-dimensional plots. Topologically, it's quite interesting because despite appearances it has only a single side!Sign in to answer this question.
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You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. How can I rotate a set of points in a plane by a certain angle about an arbitrary point? MathWorks Support Team on 27 Jun Vote 1. Answered: Stanley Howard on 29 Jun I have a set of data points, and I would like to rotate them counterclockwise in the plane by a certain angle about a specific point in the same plane.
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