Как сделать градиент в питоне

Как сделать градиент в питоне

The gradient of a function simply means the rate of change of a function. We will use numdifftools to find Gradient of a function.

Examples:

Approach:

• For Single variable function: For single variable function we can define directly using “lambda” as stated below:-
• For Multi-Variable Function: We will define a function using “def” and pass an array “x” and it will return multivariate function as described below:-

Similarly, We can define function of more than 2-variables also in same manner as stated above.

How to make circular color gradient in Python? [SOLVED]

Different methods to create circular color gradient in Python

A color gradient is a way to smoothly transition between two or more colors. A circular gradient is a type of color gradient that transitions in a circular pattern, typically starting with one color at the center and gradually transitioning to other colors as you move outward.

There are several ways to create a circular color gradient in Python, some of the most common methods include:

1. Using the matplotlib.colors.LinearSegmentedColormap class: This is a method that I explained in my previous answer, it uses a list of colors to create a colormap and numpy to calculate the distance from the center of the grid to each point in the grid. This distance is then used as the input for the colormap.
2. Using the matplotlib.colors.ListedColormap class: This method uses a discrete set of colors to create the gradient, it could be useful when you have a fixed number of colors.
3. Using a polar coordinate system and a color map: This method uses a polar coordinate system to create the circular gradient, and a color map to map the values of the coordinates to colors.
4. Using the PIL library: You can use the ImageDraw.pieslice() method of the PIL library to create a circular gradient by filling a pie-shaped area with a gradient.

Pre-requisite — Install matplotlib module

We are going to be using matplotlib module in most of our examples but it is not part of Python’s built-in default library and hence must be installed separately. I am using Python3.9 in my environment so I will use pip3 to install this module:

Example-1: Using matplotlib.colors.LinearSegmentedColormap class

Here is an example of how to create a circular color gradient using the matplotlib.colors.LinearSegmentedColormap class:

In this example, the colors list defines a sequence of RGB tuples that represent the colors in the gradient. The LinearSegmentedColormap.from_list() method is used to create a colormap from this list of colors.

The numpy function meshgrid is used to create a grid of coordinates, and the numpy function sqrt is used to calculate the distance from the center of the grid to each point in the grid. This distance is then used as the input for the colormap.

Finally, the plt.pcolormesh method is used to plot the color map, and the plt.axis method is used to make sure that the aspect ratio of the plot is equal.

This code will create a circular color gradient with the defined colors, if you want to change the colors, you can change the colors tuple. And you can adjust the size of the plot by changing the figsize parameter in plt.figure() .

Example-2: Using matplotlib.colors.ListedColormap class

Here is an example of how to create a circular color gradient using the matplotlib.colors.ListedColormap class:

Here we define colors list, which contains a sequence of RGB tuples that represent the colors in the gradient. The LinearSegmentedColormap.from_list() method is used to create a colormap from this list of colors.

Then, numpy functions linspace and meshgrid are used to create a polar grid of coordinates. The coordinates are given by the polar angle theta and the distance from the origin r .

Then, using these polar coordinates, the distance between each point in the grid and the center of the grid is calculated using the numpy.sqrt((R — 0.5)**2 + (Theta — np.pi)**2) expression. This distance is used as the input for the colormap.

Finally, the plt.pcolormesh method is used to plot the color map, and the plt.axis method is used to make sure that the aspect ratio of the plot is equal.

This will create a circular color gradient in a polar coordinate system. You can adjust the number of points in the grid by changing the parameters of the linspace function, and you can change the colors by modifying the colors list.

Example-3: Using ImageDraw.pieslice() method

Here is an example of how to create a circular color gradient using the ImageDraw.pieslice() method of the PIL library:

In this example, an image of size 200×200 is created using the Image.new() method. Then, a draw object is created using the ImageDraw.Draw() method.

Then, I define the color stops, a list of tuples where each tuple represents a color and a position in the gradient (from 0 to 1), this is similar to the css linear gradient.

Then, the ImageDraw.pieslice() method is used to draw a pie-shaped area with a gradient, it takes four parameters that define the bounding box of the pie slice, and two angles that define the start and end of the slice in degrees. The fill parameter is used to specify the color of the slice. The method is called multiple times to draw the different slices, each slice representing a color stop.

Finally, im.show() is used to display the image.

This will create a circular color gradient with the defined color stops. You can adjust the size of the image by changing the parameters of the Image.new() method and you can adjust the position and colors of the color stops by modifying the color_stops list.

Summary

Matplotlib is a multiplatform data visualization library built on NumPy arrays, and designed to work with the broader SciPy stack. We used the matplotlib.colors.LinearSegmentedColormap class to create a colormap from a list of colors and numpy to create a grid of coordinates, and the numpy function sqrt is used to calculate the distance from the center of the grid to each point in the grid.

The matplotlib.colors.CircularSegmentedColormap class is similar to the LinearSegmentedColormap , but it uses polar coordinates instead of cartesian coordinates to create the color gradient.

References

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Color gradients with Python

Investigating a few «Pythonic» ways to calculate gradients across given input colors (12.03.13)

Color is one of the most powerful tools for conveying information about data. Differences in color can inspire or imply emotions (positive or negative), give a sense of magnitude (dark and dense, or light and sparse), or even hint at political persuasion (redness» and «blueness» of states on a map).

One way to convey continuous variation through colors is by using a gradient. Most graphics applications provide an easy and intuitive way to apply a gradient to a project or dataset. The ubiquitous Microsoft Excel is an easy example, with its suprisingly useful conditional formatting. Interested in how these spectra are actually constructed, I decided to try out a few ways of manually calculating color gradients using Python, given some desired input colors. Here’s what I came up with!

Colors as points in 3D space

In order to «calculate» color gradients, we must first think of them as mathematical objects. Fortunately, as with everything on a computer, colors are represented numerically. This normally done as a sequence of three numbers indicating the varying amounts of Red, Green, and Blue, either in decimal tuple (70,130,180) or hex triplet (#4682B4) form (both examples given represent steel blue, the main color used on this site). This means we can think of a color abstractly as a vector (@@@\vec@@@) in three dimensional space.

Practically, within Python, I sometimes want to pass these colors / vectors as hex triplet strings and other times as RGB tuples (implemented as lists to allow mutable components). Here are two basic functions I ended up using for converting accross formats:

With colors as vectors, gradients can then be thought of as functions of colors, with each component of @@@\vec@@@ evolving for different input values.

Linear Gradients and Linear Interpolation

The simplest type of gradient we can have between two colors is a linear gradient. As the name suggests, this gradient is a function representing a line between the two input colors. The following is an example of a gradient that varies from black to gray to white, taking in a value of @@@t \in [0,1]@@@ which specifies how far along the gradient the desired output color should be:

@@@ \displaystyle gradient(t) = \vec_1 + (t)\left(\vec_2-\vec_1\right) @@@

@@@ \displaystyle BlackToWhite(t) = [0,0,0] + (t)[255,255,255] @@@

In Python, I implemented this as a function which, given two hex imputs, returns a dictionary containing a desired number of hex colors evenly spaced between them as well as the corresponding RGB decimal components as individual series.

Outputting the RGB components as points in 3D space, and coloring the points with their corresponding hex notation gives us something like this (gradient ranges from #4682B4 to #FFB347 ):

Multiple Linear Gradients ⇒ Polylinear Interpolation

While one linear gradient is fun, multiple linear gradients are more fun. Taking linear_gradient() and wrapping it in a function which takes in a series of colors, we get the following gradient function (I’ve also included a function for generating random hex colors, so I don’t have to spend time choosing examples):

This means we can pick a few colors we want to our data to «evolve through», and get back a series of corresponding interpolated colors. Below is an example of linear gradients running through 5 different random colors, with 50 total interpolated colors.

While this serves the purpose of providing a gradient through multiple colors, it does so in a sort of jagged, inelegant way. What would be better is a smooth evolution accross the colors, with each input color providing various amounts of influence as we move through the gradient. For this, we can turn to Bezier Curves.

Nonlinear Gradients: Bezier Interpolation

While I will leave the denser mathematical description of Bezier Curves to Wikipedia and this guys awesome notes (PDF), they can easily be used to provide smooth gradients through various control colors (corresponding to Bezier control points). To implement Bezier gradients in Python, I took advantage of the following polynomial notation for n-degree Bezier curves (@@@(t)@@@) through @@@n+1@@@ control colors (@@@\vec_i@@@):

@@@ \displaystyle t\in [0,1] \quad\quad i\in , 0 \leq x \leq n> @@@

The Python implementation of this took the following form, with a helper function for the Bernstein coefficient. I also chose to memoize the factorial function, it can be expected that the inputs will be consistantly similar due to its range consisting of integers in @@@[0,255]@@@ and its recursive implementation.

The result of this more technical gradient calculation is a smoother range, influenced by its given control colors. The following example takes in 3 control colors, but the above function can handle Bezier Curves of arbitrary degree.

Matplotlib Plotting Stuff

Finally, here is the code I used to plot the points generated by the various gradient functions. All that is required is the matplotlib package.

Как сделать градиент в питоне

In this chapter, we will learn to:

• Find Image gradients, edges etc
• We will see following functions : cv.Sobel(), cv.Scharr(), cv.Laplacian() etc

Theory

OpenCV provides three types of gradient filters or High-pass filters, Sobel, Scharr and Laplacian. We will see each one of them.

1. Sobel and Scharr Derivatives

Sobel operators is a joint Gaussian smoothing plus differentiation operation, so it is more resistant to noise. You can specify the direction of derivatives to be taken, vertical or horizontal (by the arguments, yorder and xorder respectively). You can also specify the size of kernel by the argument ksize. If ksize = -1, a 3×3 Scharr filter is used which gives better results than 3×3 Sobel filter. Please see the docs for kernels used.

2. Laplacian Derivatives

It calculates the Laplacian of the image given by the relation, \(\Delta src = \frac<\partial ^2> <\partial x^2>+ \frac<\partial ^2><\partial y^2>\) where each derivative is found using Sobel derivatives. If ksize = 1, then following kernel is used for filtering:

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