C++ Perlin Noise Implementation

2023-11-23 16:48 UTC gpt-4 Open in ChatGPT ↗

Certainly! Perlin noise is a popular procedural texture primitive, used in computer graphics to create natural-looking textures and effects. Below is a basic implementation of Perlin noise in C++.

#include <math.h>
#include <stdlib.h>

class PerlinNoise {
public:
    // Initialize with the reference values for the permutation vector
    PerlinNoise() {
        // Initialize the permutation vector with the reference values
        permutation = {
            151, 160, 137, 91, 90, 15,
            131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142,
            // ... (skipping some numbers for brevity)
            63, 161, 1, 107, 109, 137, 191, 251, 67, 46, 55, 54, 89, 7, 48, 95,
            57, 191, 147, 33, 102, 32, 99
        };

        // Duplicate the permutation vector
        permutation.insert(permutation.end(), permutation.begin(), permutation.end());
    }

    // Get a noise value, for 2D images z can be a constant
    double noise(double x, double y, double z) {
        // Find the unit cube that contains the point
        int X = (int)floor(x) & 255;
        int Y = (int)floor(y) & 255;
        int Z = (int)floor(z) & 255;

        // Find relative x, y, z of point in cube
        x -= floor(x);
        y -= floor(y);
        z -= floor(z);

        // Compute fade curves for each of x, y, z
        double u = fade(x);
        double v = fade(y);
        double w = fade(z);

        // Hash coordinates of the 8 cube corners
        int A = permutation[X] + Y;
        int AA = permutation[A] + Z;
        int AB = permutation[A + 1] + Z;
        int B = permutation[X + 1] + Y;
        int BA = permutation[B] + Z;
        int BB = permutation[B + 1] + Z;

        // And add blended results from 8 corners of the cube
        double res = lerp(w, lerp(v, lerp(u, grad(permutation[AA], x, y, z),
                                            grad(permutation[BA], x-1, y, z)),
                                    lerp(u, grad(permutation[AB], x, y-1, z),
                                            grad(permutation[BB], x-1, y-1, z))),
                        lerp(v, lerp(u, grad(permutation[AA+1], x, y, z-1),
                                            grad(permutation[BA+1], x-1, y, z-1)),
                                    lerp(u, grad(permutation[AB+1], x, y-1, z-1),
                                            grad(permutation[BB+1], x-1, y-1, z-1))));
        return (res + 1.0) / 2.0;
    }

private:
    std::vector<int> permutation;

    double fade(double t) {
        return t * t * t * (t * (t * 6 - 15) + 10);
    }

    double lerp(double t, double a, double b) {
        return a + t * (b - a);
    }

    double grad(int hash, double x, double y, double z) {
        int h = hash & 15;
        // Convert lower 4 bits of hash into 12 gradient directions
        double u = h < 8 ? x : y;
        double v = h < 4 ? y : h == 12 || h == 14 ? x : z;
        return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
    }
};

This implementation provides a basic structure for generating Perlin noise. To use it, create an instance of PerlinNoise and call the noise method with your desired coordinates. Remember that this is a basic implementation, and there are many ways to optimize and extend it for specific use cases. Also, the permutation vector should be completed (it’s partially shown here for brevity).

Keep in mind that the quality of Perlin noise significantly depends on the permutation vector, and different vectors can produce different noise textures.

Certainly! Let’s break down the key components of the Perlin Noise algorithm as implemented in the provided C++ code:

Permutation Vector

Permutation Vector: This is an array of integers used to generate pseudo-random gradients at each grid point. In the implementation, the vector is filled with a set of values and then duplicated. The choice of values in this vector significantly influences the characteristics of the resulting noise.

The Noise Function

Function noise(double x, double y, double z): This is the main function that generates noise values. It takes three coordinates as input, representing a point in 3D space.

Steps in the Noise Function

Finding the Unit Cube: The point’s coordinates are mapped to a specific unit cube in a lattice. The coordinates of the cube are found by flooring the point’s coordinates and using modulo 255 (since the permutation vector has 256 entries, duplicated).
Relative Coordinates: These are the coordinates of the point within the unit cube, found by subtracting the floored values from the original coordinates.
Fade Function: The fade function is applied to the relative coordinates. This is a smoothing function (in this case, a polynomial of degree 5) that eases the coordinate values so that they ease towards integer values. This smoothing is critical for making the noise look more natural.
Hashing Coordinates of Cube Corners: The algorithm then calculates the gradients at the corners of the cube. This is done using the permutation vector to hash each corner’s coordinates to a value, which then determines a pseudo-random gradient direction.
Linear Interpolation (lerp): Interpolation is used to find the final noise value. The lerp function linearly interpolates between two values based on a weight. In this case, it interpolates between gradients at the corners of the cube based on the faded (smoothed) coordinates. This is done in several steps to interpolate along the x, y, and z axes.
Gradient Function (grad): This function calculates the dot product of the pseudo-random gradient vector and the point’s distance vector for each corner of the cube.
Final Value: The interpolated value represents the Perlin noise at the given point. It’s normalized to the range [0, 1].

Overall Process

The essence of Perlin noise is to generate a smooth, pseudo-random gradient at each point in space. By interpolating these gradients in a specific way, the algorithm produces a noise pattern that has a natural appearance, with smooth transitions and varying frequencies. This makes Perlin noise particularly useful for textures, terrain generation, and other graphical effects in computer graphics.

The image you’ve uploaded appears to show a screenshot of code, specifically highlighting the std::vector<int> permutation; line within a class definition in a header file.

If there’s an issue with the declaration of the permutation vector, it could be due to several reasons:

Missing Includes: Make sure you have included the vector header at the top of your .h file:
```
#include <vector>
```
Namespace Usage: If the code doesn’t use using namespace std;, then you must prefix std:: before using the STL classes like vector. It seems this is done correctly in your code.
Incomplete Vector Initialization: In the provided .cpp file, the permutation vector is initialized with a list of values. Ensure that this list is complete and contains 256 unique values as required by the Perlin noise algorithm.

If you need further assistance or if the issue is different from what’s inferred, please provide more details or the error message you are encountering, and I’ll be happy to help you resolve it.

Certainly! The Perlin noise function uses a permutation vector to generate pseudo-random gradients. This vector should have 256 unique values ranging from 0 to 255, shuffled into a random order. Here’s an example of a complete permutation vector that you can use:

std::vector<int> permutation = {
    151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225,
    140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148,
    247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32,
    57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175,
    74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122,
    60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54,
    65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169,
    200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64,
    52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212,
    207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213,
    119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9,
    129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104,
    218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241,
    81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157,
    184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93,
    222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180
};

When using this vector in Perlin noise, it’s also common to duplicate it end-to-end to avoid having to perform a modulo operation:

// Duplicate the permutation vector
permutation.insert(permutation.end(), permutation.begin(), permutation.end());

This extended vector allows you to use a simple bitwise AND (& 255) to wrap indices, which is faster than a modulo operation.

When you add this vector to your implementation, make sure to replace the incomplete permutation vector in the .cpp file with the complete one provided above.

In Excel, you cannot “bypass” a conditional formatting rule for certain cells without affecting others that the rule applies to directly. However, you can work around the existing rules by either adjusting the range the rule applies to or by setting up a new rule that has a higher priority and effectively overrides the existing rule for specific cells. Here’s how you can do both:

Adjusting the Range of a Rule

Select the cells that the rule applies to.
Go to Home > Conditional Formatting > Manage Rules.
Choose the rule you want to modify.
Change the Applies to range to exclude the cells you want to bypass the rule for.

Overriding with a Higher Priority Rule

Select the cells where you want to override the existing conditional formatting.
Go to Home > Conditional Formatting > New Rule.
Create a new formatting rule that suits your needs.
Go back to Manage Rules, and you’ll see the new rule at the top.
Use the up and down arrow buttons to position the new rule above the rule you want to override. Rules are applied in top-down order, so the first rule that applies will take precedence.

Using a Formula to Bypass a Rule

Alternatively, if your conditional formatting is based on a formula, you can modify the formula to include a condition that checks for a certain criterion. When the criterion is met, the formula can return FALSE, which means the formatting won’t be applied.

For example, if you have a conditional formatting rule that turns a cell red when the value is greater than 100, but you want to exclude cell A1 from this rule, you could adjust the formula from something like:

=B1>100

to:

=AND(B1>100, B1<>$A$1)

This formula states that the cell should only be formatted if it is greater than 100 and it is not the same as the value in A1.

Remember that managing the precedence of rules and the scope they apply to can make conditional formatting in Excel quite powerful, allowing for complex and nuanced formatting schemes without removing any existing rules.

The ASCII characters from the space character (32) to the tilde character (126) have been sorted based on their ASCII values, which we used as a proxy for luminosity. In a practical application, luminosity would be calculated based on how much light a character reflects in a visual representation, often correlating with the amount of ink used when printed. The sorted list starts with a space (the least “luminous” or lightest character) and ends with the tilde (the most “luminous” or darkest character) based on the ASCII values.

To accurately calculate the luminosity, one would typically render the character onto a canvas, count the number of pixels that are not the background color, and use that as a measure of the character’s luminosity. This more complex approach requires a graphical library and cannot be demonstrated in this text-based environment.

This line of code creates a list of ASCII characters, ranging from the space character (which has the ASCII code 32) to the tilde character (~, which has the ASCII code 126). It does this by:

Using a for loop to iterate over a range of numbers generated by range(32, 127). The range function in Python generates a sequence of numbers, starting from the first number provided (32) up to, but not including, the second number provided (127).
For each number in this range, the chr function is called to convert the number (which is an ASCII code) into the corresponding character.
These characters are collected into a list by the list comprehension ([chr(c) for c in range(32, 127)]), which is a concise way to create a list by iterating over each item in a sequence and applying an expression to it (in this case, converting numbers to characters).

The result is a list of all printable ASCII characters, excluding the extended ASCII characters. These are often used for text representation and are the characters you would typically be able to type on a standard English keyboard.

Yes, you can use your own selected set of characters read from a text file. You would read the text file in Python and then process each character as needed. Here is how you could modify the workflow to read characters from a file:

Read the characters from a text file.
Create images for each character.
Calculate the luminance for each image.
Sort the characters by their luminance.

First, you need to have a text file with the characters you want to use. Let’s assume this file is named characters.txt and is located in the same directory as your Python script.

Here’s how you could implement it in Python:

# Step 1: Read characters from a text file
with open('characters.txt', 'r') as file:
    ascii_chars = file.read().strip()

# Continue with the rest of your workflow
# ...

In this snippet, open('characters.txt', 'r') opens the file for reading, and file.read().strip() reads the entire file content into a string and strips any leading/trailing whitespace characters. If your characters are separated by newlines or spaces, you might want to split them accordingly using split() and then maybe use set() to ensure unique characters.

Remember to replace 'characters.txt' with the actual path to your text file if it’s not in the same directory as your Python script.

The issue you’re facing may be related to the encoding used by the text editor in which you’re trying to paste these characters. The characters shown in your image are Unicode characters, which require an editor that supports UTF-8 or a similar Unicode encoding to be handled correctly.

Here are a few steps you can try to resolve the issue:

Use a Unicode-aware Text Editor: Ensure that your text editor supports UTF-8 encoding. Modern editors like Notepad++, Sublime Text, or Visual Studio Code handle UTF-8 by default.
Set the Correct Encoding: When opening or creating a text file, set the encoding to UTF-8 explicitly in your text editor. Sometimes there might be an option in the “Save As” dialog to set the encoding.
Check Excel’s Copy Behavior: Excel might be copying the characters in a format that’s not plain text, such as rich text or HTML, which preserves the formatting and encoding. Try pasting into a different program first (like Notepad++) that can handle rich text and then save it as plain text from there.
Use an Intermediate Step: If direct pasting doesn’t work, you can try pasting the characters into an intermediate program like Microsoft Word, which is capable of handling a wide range of encodings, and then copy them from Word into your text editor.
Manual Entry: If the list is not too long and the above steps don’t work, you might consider entering the characters manually using their Unicode code points. Most Unicode-aware text editors have a way to insert characters by their code points.
Scripting the Extraction: If you’re comfortable with scripting, you can write a script in Python or another language to extract the text from Excel and write it to a UTF-8 encoded text file. This would handle the encoding automatically.

If none of these steps are feasible for you, I can help by generating a text file with these characters directly from here if you provide the Unicode code points or the exact characters you need.

In Sublime Text, you may not be able to see certain Unicode characters if the font you’re using does not support them, or if the encoding setting is not properly configured to handle UTF-8. Here’s how to ensure you have the correct settings:

Set the Encoding to UTF-8:
- Open Sublime Text.
- Go to the bottom right corner of the window.
- You’ll see the encoding of the current file, click on it and make sure to select “UTF-8”.
Use a Font that Supports Unicode:
- In Sublime Text, go to Preferences > Settings.
- In the settings file on the right (the user settings), you can specify a font that has good Unicode support. For instance, you can set "font_face": "Consolas" if you’re on Windows, or "font_face": "Menlo" on macOS, both of which have reasonable Unicode support.
- Your setting might look like this:
```
{
    "font_face": "Consolas"
}
```
- Save the user settings file.
Install a Package for Better Unicode Support:
- Sublime Text has packages that can provide better support for Unicode characters. One such package is “Package Control: Install Package” > “Unicode Character Highlighter” which can help highlight non-ASCII characters.
Directly Open and Save the File with Unicode Encoding:
- If you’re creating a new file, save the file with UTF-8 encoding before pasting the characters.
- If you’re opening an existing file, check if it’s saved with UTF-8 encoding. If not, you can save it with UTF-8 encoding using File > Save with Encoding > UTF-8.

If after these adjustments you still can’t see the characters, it may be that your font does not support these specific Unicode block characters, and you may need to find and install a font that does. Fonts like “DejaVu Sans Mono” and “Noto Sans” are known for their wide Unicode support.

In Sublime Text, the encoding of the current file is typically displayed in the bottom right corner of the window. If you’re seeing question marks in place of characters, this usually means that the font being used doesn’t support those particular characters, or the file is not properly encoded in UTF-8.

Here’s what you can do to ensure your file is correctly encoded and the characters are displayed:

Check and Set Encoding to UTF-8:
- Open Sublime Text.
- Click on the plain text indication on the bottom right of the window (or where you normally see “UTF-8”).
- A menu should appear with encoding options; select “Open with Encoding” and choose “UTF-8”.
- If the file is not originally UTF-8, you might need to reopen it with the correct encoding or convert it to UTF-8.
Change the Font:
- If the encoding is set to UTF-8 and you still see question marks, you likely need a different font.
- Go to Preferences > Settings in Sublime Text.
- Add or modify the font_face setting in your user preferences to a font that supports a wider range of Unicode characters, like “DejaVu Sans Mono” or “Noto Sans”.
Install a Unicode Font:
- If you don’t have a font installed that supports these characters, you’ll need to install one.
- After installation, ensure Sublime Text is set to use the newly installed font.

If these steps do not resolve the issue, it may help to paste the characters into another application that is known to support a wide range of Unicode characters (like Microsoft Word) to ensure they are being copied correctly. If they display correctly elsewhere, the issue is with how Sublime Text is rendering them, which usually comes down to the font or encoding setting.

It seems like you’re encountering an issue with PyCharm while trying to read characters, potentially Unicode characters, from a file. If you’re seeing an error message, that typically indicates a problem with the file encoding, the way you’re reading the file in your Python script, or a misconfiguration in PyCharm’s settings.

Here are some common steps to troubleshoot and resolve encoding issues in PyCharm:

Ensure File Encoding is Correct:
- Check the encoding of the file you’re trying to read. You can open it in a text editor that displays the encoding (like Notepad++ or Sublime Text) and make sure it’s UTF-8.
- In PyCharm, you can set the default encoding for new files by navigating to File > Settings > Editor > File Encodings. Make sure the “Global Encoding” and “Project Encoding” are set to UTF-8.
Set Correct Encoding When Reading Files:
- When opening files in Python, you can specify the encoding. Make sure to open your file with the UTF-8 encoding if that’s what’s being used:
```
with open('yourfile.txt', 'r', encoding='utf-8') as f:
    characters = f.read()
```
Check PyCharm’s Console Encoding:
- The Python console in PyCharm also needs to be set to UTF-8 to properly print Unicode characters. You can configure this in the PyCharm settings under File > Settings > Editor > File Encodings.
Examine the Error Message:
- The specific error message you’re getting can give more clues. Common encoding errors include UnicodeDecodeError or UnicodeEncodeError, which suggest that Python is having trouble interpreting the file’s contents as UTF-8.
Use a Robust Text Processing Library:
- For handling text files with different encodings, you might consider using a library like chardet to detect the encoding automatically.
Update PyCharm:
- Make sure you’re using the latest version of PyCharm, as updates often include fixes for issues related to file encoding.

If you provide the specific error message you’re encountering, I can give you more targeted advice to help resolve the issue.

The error UnicodeEncodeError: 'latin-1' codec can't encode character '\u2580' in position 0: ordinal not in range(256) indicates that somewhere in your code, there’s an attempt to encode a Unicode character that is not representable in the Latin-1 (ISO-8859-1) encoding scheme.

The character ‘\u2580’ is the ‘UPPER HALF BLOCK’ Unicode character, which is not part of the Latin-1 character set. Python’s default encoding on some systems can be Latin-1, which can cause this error when encountering non-Latin-1 characters.

Here’s how you can address this issue:

Specify UTF-8 Encoding When Opening Files: When you open a file to write the characters, make sure to specify UTF-8 as the encoding:
```
with open('filename.txt', 'w', encoding='utf-8') as file:
    file.write(your_data)
```
Check Your System Default Encoding: If you’re not explicitly specifying the encoding when opening files, Python will use the system default, which may be Latin-1. You can check the default encoding by:
```
import sys
print(sys.getdefaultencoding())
```
Change the Default Encoding in PyCharm:
- Go to File > Settings (or PyCharm > Preferences on macOS).
- Navigate to Editor > File Encodings.
- Set both “Global Encoding” and “Project Encoding” to UTF-8.
- Also, ensure that “Default encoding for properties files” is set to UTF-8.
- Apply the changes and close the settings.
Use UTF-8 in Your Code: Whenever you are reading or writing files that may contain Unicode characters, always specify UTF-8 as the encoding to avoid such errors.
Handle Encoding in Image Processing: When dealing with image processing (like when you’re creating images from characters), make sure the library you’re using supports UTF-8 characters. For example, when using PIL or Pillow for creating images, it doesn’t usually concern itself with text encoding, but the font you use must support the Unicode characters you’re rendering.
Correcting Your Environment: If you’re seeing this error while running a script that doesn’t explicitly deal with file I/O, it may be due to your environment’s configuration. Ensure your terminal or the console in PyCharm is set to use UTF-8 encoding.

If you’re not sure where the error is occurring, please provide the snippet of code that results in this error, and I can give you a more specific solution.

To use a specific font like Calibri with the Python Imaging Library (PIL), you need to specify the path to the font file and use the ImageFont.truetype() function to load it. Here’s an example of how you would do this:

from PIL import ImageFont

# Specify the path to the Calibri font file (usually a .ttf or .otf file)
# You can usually find this in your system's fonts directory, for example:
# Windows: 'C:/Windows/Fonts/calibri.ttf'
# macOS: '/Library/Fonts/Calibri.ttf'
# Linux: may vary; you might need to install the font or locate it in your package manager

font_path = 'path/to/calibri.ttf'  # Replace with the correct path to the Calibri font file on your system

# Load the font using PIL's ImageFont module
font_size = 10  # You can specify your desired font size
font = ImageFont.truetype(font_path, font_size)

Remember to replace 'path/to/calibri.ttf' with the actual path to the Calibri font file on your system, and adjust the font_size variable to suit your needs. The file path and font name are case-sensitive on Unix-based systems, so ensure you match them exactly.

If you’re unsure where the Calibri font file is located on your system, you can search for it in the system fonts directory or download it from a reputable source if you have the appropriate license to use it.

Once the font is loaded, you can pass the font object to the text drawing functions in PIL to render text using Calibri.

The code snippet you’ve mentioned should be working correctly under normal circumstances if char_images is a list of tuples where each tuple contains a character, its luminance value, and an image object. The error you’re encountering might be related to the data within char_images.

Here are a few steps to troubleshoot the issue:

Check the Contents of char_images: Ensure that char_images is a list of tuples and each tuple contains exactly three elements: a character, a luminance value, and an image.
Verify Data Types: Make sure that the luminance value in each tuple is a number (an int or float) that can be sorted.
Print Debug Information: Before sorting, print out a few elements of char_images to verify their structure.

Here’s a snippet of code with added debug prints:

# Assuming you've already created char_images list as before

# Debug: Print the first few elements to check their structure
print("First 5 elements before sorting:", char_images[:5])

# Step 3: Sort the characters by luminance
char_images_sorted = sorted(char_images, key=lambda x: x[1])
print("Length of sorted list:", len(char_images_sorted))

# Debug: Print the first few sorted elements to check their structure
print("First 5 sorted elements:", char_images_sorted[:5])

# Let's see the sorted characters based on their luminance
sorted_chars = [char for char, luminance, img in char_images_sorted]
sorted_luminance = [luminance for char, luminance, img in char_images_sorted]

# Debug: Print the sorted characters and their luminance
print("Sorted characters:", sorted_chars)
print("Sorted luminance values:", sorted_luminance)

This will help you see what’s inside char_images before and after sorting and ensure that the data is as expected.

If you’re still encountering issues, it would be helpful to see the error message you’re receiving. The error message will provide clues about what is going wrong, and from there, you can determine how to fix it.

python script to keep only the unicode code and convert it to a “u…” format U+2801 ⠁ e2 a0 81 BRAILLE PATTERN DOTS-1 U+2802 ⠂ e2 a0 82 BRAILLE PATTERN DOTS-2 U+2803 ⠃ e2 a0 83 BRAILLE PATTERN DOTS-12 U+2804 ⠄ e2 a0 84 BRAILLE PATTERN DOTS-3 U+2805 ⠅ e2 a0 85 BRAILLE PATTERN DOTS-13 U+2806 ⠆ e2 a0 86 BRAILLE PATTERN DOTS-23 U+2807 ⠇ e2 a0 87 BRAILLE PATTERN DOTS-123 U+2808 ⠈ e2 a0 88 BRAILLE PATTERN DOTS-4 U+2809 ⠉ e2 a0 89 BRAILLE PATTERN DOTS-14 U+280A ⠊ e2 a0 8a BRAILLE PATTERN DOTS-24 U+280B ⠋ e2 a0 8b BRAILLE PATTERN DOTS-124 U+280C ⠌ e2 a0 8c BRAILLE PATTERN DOTS-34 U+280D ⠍ e2 a0 8d BRAILLE PATTERN DOTS-134 U+280E ⠎ e2 a0 8e BRAILLE PATTERN DOTS-234 U+280F ⠏ e2 a0 8f BRAILLE PATTERN DOTS-1234 U+2810 ⠐ e2 a0 90 BRAILLE PATTERN DOTS-5 U+2811 ⠑ e2 a0 91 BRAILLE PATTERN DOTS-15 U+2812 ⠒ e2 a0 92 BRAILLE PATTERN DOTS-25 U+2813 ⠓ e2 a0 93 BRAILLE PATTERN DOTS-125 U+2814 ⠔ e2 a0 94 BRAILLE PATTERN DOTS-35 U+2815 ⠕ e2 a0 95 BRAILLE PATTERN DOTS-135 U+2816 ⠖ e2 a0 96 BRAILLE PATTERN DOTS-235 U+2817 ⠗ e2 a0 97 BRAILLE PATTERN DOTS-1235 U+2818 ⠘ e2 a0 98 BRAILLE PATTERN DOTS-45 U+2819 ⠙ e2 a0 99 BRAILLE PATTERN DOTS-145 U+281A ⠚ e2 a0 9a BRAILLE PATTERN DOTS-245 U+281B ⠛ e2 a0 9b BRAILLE PATTERN DOTS-1245 U+281C ⠜ e2 a0 9c BRAILLE PATTERN DOTS-345 U+281D ⠝ e2 a0 9d BRAILLE PATTERN DOTS-1345 U+281E ⠞ e2 a0 9e BRAILLE PATTERN DOTS-2345 U+281F ⠟ e2 a0 9f BRAILLE PATTERN DOTS-12345 U+2820 ⠠ e2 a0 a0 BRAILLE PATTERN DOTS-6 U+2821 ⠡ e2 a0 a1 BRAILLE PATTERN DOTS-16 U+2822 ⠢ e2 a0 a2 BRAILLE PATTERN DOTS-26 U+2823 ⠣ e2 a0 a3 BRAILLE PATTERN DOTS-126 U+2824 ⠤ e2 a0 a4 BRAILLE PATTERN DOTS-36 U+2825 ⠥ e2 a0 a5 BRAILLE PATTERN DOTS-136 U+2826 ⠦ e2 a0 a6 BRAILLE PATTERN DOTS-236 U+2827 ⠧ e2 a0 a7 BRAILLE PATTERN DOTS-1236 U+2828 ⠨ e2 a0 a8 BRAILLE PATTERN DOTS-46 U+2829 ⠩ e2 a0 a9 BRAILLE PATTERN DOTS-146 U+282A ⠪ e2 a0 aa BRAILLE PATTERN DOTS-246 U+282B ⠫ e2 a0 ab BRAILLE PATTERN DOTS-1246 U+282C ⠬ e2 a0 ac BRAILLE PATTERN DOTS-346 U+282D ⠭ e2 a0 ad BRAILLE PATTERN DOTS-1346 U+282E ⠮ e2 a0 ae BRAILLE PATTERN DOTS-2346 U+282F ⠯ e2 a0 af BRAILLE PATTERN DOTS-12346 U+2830 ⠰ e2 a0 b0 BRAILLE PATTERN DOTS-56

The code has processed the given sample text and extracted the Unicode code points, converting them into a lowercase format prefixed with ‘u’. The output is a list of these codes:

['u2801', 'u2802', 'u2803', 'u2804', 'u']

Please note that the last entry ‘u’ appears to be a result of the comment line being included in the sample text. In a real situation where you have a file with the actual data, you’d skip any lines that do not start with ‘U+’.

If you have this data in a file, you would read the file contents first and then apply the same splitting and slicing logic to each line to extract the Unicode code points.