


Approximating Data with a Multi-Segment Cubic Bezier Curve with Distance and Curvature Constraints
Problem Statement:
The goal is to approximate given geographical data points with a multi-segment cubic Bezier curve under two constraints:
- The maximum distance between the curve and the data points cannot exceed a specified tolerance.
- The curvature of the curve must not exceed a certain sharpness.
Solution:
A two-step solution is proposed:
-
Create a B-Spline Approximation:
- Use the FITPACK library (accessed through the scipy Python binding) to generate a B-spline that least-squares fits the data points.
- B-splines allow for specifying smoothness and provide a way to meet the curvature constraint.
-
Convert B-Spline to Bezier Curve:
- Use a function like the one provided in the solution text to convert the B-spline into a multi-segment Bezier curve.
- The converted Bezier curve inherits the smoothness and curvature properties of the B-spline.
Code Example:
Here is a Python snippet demonstrating the approach:
<code class="python">import matplotlib.pyplot as plt import numpy as np from scipy import interpolate # Assume the data points are stored in lists x and y. # Create B-spline approximation tck, u = interpolate.splprep([x, y], s=3) # Adjust s parameter for smoothness # Generate new parameter values for plotting unew = np.arange(0, 1.01, 0.01) # Evaluate B-spline at new parameter values out = interpolate.splev(unew, tck) # Convert B-spline to Bezier curve bezier_points = b_spline_to_bezier_series(tck) # Plot the data points, B-spline, and Bezier curve plt.figure() plt.plot(x, y, out[0], out[1], *bezier_points) # Replace * with individual Bezier curves plt.show()</code>
Note:
The solution prioritizes smoothness over accuracy. For tighter approximations, it may be necessary to trade off some smoothness to ensure the distance constraint is met.
The above is the detailed content of How to Approximate Data with a Multi-Segment Cubic Bezier Curve Constrained by Distance and Curvature?. For more information, please follow other related articles on the PHP Chinese website!

The reasons why Python scripts cannot run on Unix systems include: 1) Insufficient permissions, using chmod xyour_script.py to grant execution permissions; 2) Shebang line is incorrect or missing, you should use #!/usr/bin/envpython; 3) The environment variables are not set properly, and you can print os.environ debugging; 4) Using the wrong Python version, you can specify the version on the Shebang line or the command line; 5) Dependency problems, using virtual environment to isolate dependencies; 6) Syntax errors, using python-mpy_compileyour_script.py to detect.

Using Python arrays is more suitable for processing large amounts of numerical data than lists. 1) Arrays save more memory, 2) Arrays are faster to operate by numerical values, 3) Arrays force type consistency, 4) Arrays are compatible with C arrays, but are not as flexible and convenient as lists.

Listsare Better ForeflexibilityandMixdatatatypes, Whilearraysares Superior Sumerical Computation Sand Larged Datasets.1) Unselable List Xibility, MixedDatatypes, andfrequent elementchanges.2) Usarray's sensory -sensical operations, Largedatasets, AndwhenMemoryEfficiency

NumPymanagesmemoryforlargearraysefficientlyusingviews,copies,andmemory-mappedfiles.1)Viewsallowslicingwithoutcopying,directlymodifyingtheoriginalarray.2)Copiescanbecreatedwiththecopy()methodforpreservingdata.3)Memory-mappedfileshandlemassivedatasetsb

ListsinPythondonotrequireimportingamodule,whilearraysfromthearraymoduledoneedanimport.1)Listsarebuilt-in,versatile,andcanholdmixeddatatypes.2)Arraysaremorememory-efficientfornumericdatabutlessflexible,requiringallelementstobeofthesametype.

Pythonlistscanstoreanydatatype,arraymodulearraysstoreonetype,andNumPyarraysarefornumericalcomputations.1)Listsareversatilebutlessmemory-efficient.2)Arraymodulearraysarememory-efficientforhomogeneousdata.3)NumPyarraysareoptimizedforperformanceinscient

WhenyouattempttostoreavalueofthewrongdatatypeinaPythonarray,you'llencounteraTypeError.Thisisduetothearraymodule'sstricttypeenforcement,whichrequiresallelementstobeofthesametypeasspecifiedbythetypecode.Forperformancereasons,arraysaremoreefficientthanl

Pythonlistsarepartofthestandardlibrary,whilearraysarenot.Listsarebuilt-in,versatile,andusedforstoringcollections,whereasarraysareprovidedbythearraymoduleandlesscommonlyusedduetolimitedfunctionality.


Hot AI Tools

Undresser.AI Undress
AI-powered app for creating realistic nude photos

AI Clothes Remover
Online AI tool for removing clothes from photos.

Undress AI Tool
Undress images for free

Clothoff.io
AI clothes remover

Video Face Swap
Swap faces in any video effortlessly with our completely free AI face swap tool!

Hot Article

Hot Tools

SublimeText3 Chinese version
Chinese version, very easy to use

Safe Exam Browser
Safe Exam Browser is a secure browser environment for taking online exams securely. This software turns any computer into a secure workstation. It controls access to any utility and prevents students from using unauthorized resources.

EditPlus Chinese cracked version
Small size, syntax highlighting, does not support code prompt function

SublimeText3 Linux new version
SublimeText3 Linux latest version

SecLists
SecLists is the ultimate security tester's companion. It is a collection of various types of lists that are frequently used during security assessments, all in one place. SecLists helps make security testing more efficient and productive by conveniently providing all the lists a security tester might need. List types include usernames, passwords, URLs, fuzzing payloads, sensitive data patterns, web shells, and more. The tester can simply pull this repository onto a new test machine and he will have access to every type of list he needs.
